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  <url><loc>https://www.quantrexacademy.com/q/1951/an-artificial-pacemaker-is-implanted-subcutaneously-and-connected-to-the-heart-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/1954/assertion-smaller-the-organism-higher-is-the-rate-of-metabolism-per-gram-weight</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/1959/assertion-the-regulation-of-rbc-production-is-accompanied-by-the-kidneys-reason</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/1963/assertion-blood-coagulate-in-uninjured-blood-vessels-reason-uninjured-blood-vess</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/1966/cattle-fed-with-spoilt-hay-of-sweet-clover-which-contains-dicumarol</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/1967/the-volume-of-anatomical-dead-space-air-is-normally</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/11266/if-and-are-two-distinct-negative-roots-of-x-5-5-x-3-5-x-2-1-0-then-the-equation</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11267/if-the-number-of-real-roots-of-x-9-x-5-x-4-1-0-is-n-the-number-of-complex-roots</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11268/if-is-a-common-root-of-x-2-5-x-0-and-x-2-8-x-2-0-0-and-are-the-other-roots-of-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11269/the-equation-x-4-x-3-6-x-2-4-x-8-0-has-two-equal-roots-if-are-the-other-two-root</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11270/the-condition-that-the-roots-of-x-3-b-x-2-c-x-d-0-are-in-arithmetic-progression</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/11272/roots-of-the-equation-a-b-c-x-2-b-c-a-x-c-a-b-0-are</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11273/if-3-i-is-a-root-of-x-2-a-x-b-0-then-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11274/the-algebraic-equation-of-degree-4-whose-roots-are-the-translates-of-the-roots-o</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11275/let-r-denote-the-largest-integer-not-exceeding-r-and-the-roots-of-the-equation-3</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11276/for-any-real-value-of-x-if-11-x-2-12-x-6-x-2-4-x-2-a-b-then-the-value-x-for-whic</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11277/if-the-roots-of-1-y-y-y-1-y-5-2-are-and-and-the-equation-x-4-25-x-2-0-has-real-r</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11278/if-and-are-two-double-roots-of-x-2-3-a-3-x-9-a-0-for-different-values-of-then-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11279/if-2-x-2-3-x-2-0-and-3-x-2-a-x-2-0-have-one-common-root-then-the-sum-of-all-poss</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11280/if-the-sum-of-two-roots-of-x-3-p-x-2-q-x-5-0-is-equal-to-its-third-root-then-p-p</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11281/if-p-x-x-5-a-x-4-b-x-3-c-x-2-d-x-e-is-a-polynomial-such-that-p-0-1-p-1-2-p-2-5-p</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11282/if-x-2-5-a-x-6-0-and-x-2-3-a-x-2-0-have-a-common-root-then-that-common-root-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11283/if-are-roots-of-the-equation-x-3-a-x-2-b-x-c-0-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11284/if-the-roots-of-the-equation-x-3-13-x-2-k-x-27-0-are-in-geometric-progression-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11285/if-the-roots-of-the-quadratic-equation-x-2-35-x-c-0-are-in-the-ratio-2-3-and-c-6</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11286/for-real-values-of-x-and-a-if-the-expression-x-a-2-x-2-3-x-1-assumes-all-real-va</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11287/if-the-sum-of-two-roots-of-the-equation-x-4-x-3-8-x-2-2-x-12-0-is-zero-and-are-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11288/if-the-roots-of-the-equation-6-x-3-11-x-2-6-x-1-0-are-in-harmonic-progression-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11289/if-and-are-the-roots-of-the-equation-x-3-3-x-2-4-x-5-0-then-the-cubic-equation-w</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11290/if-k-kx-3-3-3-x-k-12-x-5-kx-3-3-x-k-x-r-3-k-k-3-then-both-the-roots-of-the-equat</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/11293/the-sum-of-the-fourth-powers-of-the-roots-of-the-equation-16-x-2-10-x-1-0-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11294/if-p-x-0-is-a-polynomial-equation-of-least-degree-with-integer-coefficients-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11295/if-and-are-the-roots-of-the-equation-x-3-a-2-b-x-c-0-then-the-roots-of-the-equat</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11296/the-value-of-4-x-3-4-x-2-7-x-127-when-x-4-5-1-2-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11297/if-one-root-of-the-equation-x-3-6-x-2-3-x-10-0-is-the-average-of-the-other-two-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11298/if-the-equation-having-the-roots-as-the-values-obtained-oy-diminishing-each-root</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/11300/for-x-r-the-minimum-value-of-x-2-2-x-5-x-2-4-x-10-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11301/if-and-are-the-roots-of-the-equation-2-6-x-3-2-3-x-2-32-0-with-1-then-2-3</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11302/if-and-are-the-roots-of-the-equation-x-3-a-2-b-x-c-0-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11303/if-and-are-the-roots-of-x-3-3-x-2-0-then-5-5-5</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11304/if-the-sum-of-the-cubes-of-the-roots-of-the-equation-x-3-a-x-2-b-x-c-0-is-zero-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11305/if-are-the-roots-of-x-3-2-x-5-0-then-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11306/if-a-and-b-are-the-roots-of-the-equation-y-2-y-1-0-then-the-value-of-a-4-b-4-a-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11307/if-x-2-x-6-is-a-factor-of-2-x-3-x-2-a-x-b-then-6-a-13-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11308/if-c-and-d-are-the-roots-of-x-2-a-x-b-0-then-a-root-of-x-2-4-c-a-x-b-2-a-c-4-c-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11309/if-the-equation-x-4-7-x-3-18-x-2-20-x-8-0-has-a-repeated-root-then-that-repeated</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11310/if-the-equation-2-x-3-5-x-2-4-x-12-0-has-a-repeated-root-then-the-constant-term</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11311/if-and-are-the-roots-of-the-equation-2-x-2-4-x-3-0-then-2-4-4-3-2-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11312/if-and-are-the-roots-of-the-equation-a-2-b-x-c-0-then-the-equation-whose-roots-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11313/in-x-4-6-x-3-9-x-2-5-x-20-x-2-x-2-f-x-a-x-p-b-x-q-then-2-a-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11314/if-one-root-of-the-equation-a-x-3-b-x-c-0-is-twice-another-root-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/11316/if-1-is-a-twice-repeated-root-of-the-equation-a-x-3-b-x-2-c-x-1-0-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11317/the-minimum-value-of-f-x-x-2-2-x-3-x-2-4-x-7-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11318/the-coefficient-of-the-highest-power-of-x-in-the-expansion-of-x-x-2-1-8-x-x-2-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11319/if-x-2-x-2-3-is-one-of-the-partial-fractions-of-3-x-3-x-2-2-x-17-x-4-x-2-12-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/11321/if-3-2-2-x-2-4-3-2-2-x-2-4-6-then-x-4-x-2-5</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/11325/if-and-are-the-roots-of-the-equation-2-x-2-6-x-k-0-then-the-maximum-value-of-whe</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/11327/let-30-and-15-be-the-roots-of-the-quadratic-equation-x-2-a-x-b-0-then-1-a-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/11331/if-are-the-roots-of-a-x-2-b-x-c-0-then-the-quadratic-equation-whose-roots-are-5</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/11337/the-sum-of-squares-of-roots-of-the-equation-x-2-3-x-1-3-2-0-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/11428/let-x-x-x-2-1-x-1-if-a-b-and-c-are-the-roots-of-the-equation-x-3-3-x-0-0-then-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/11430/if-and-945-and-946-are-the-real-roots-of-x-2-p-x-q-0-and-and-945-4-and-946-4-are</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11431/x-and-8712-and-8477-6-x-x-2-2-x-5-and-8805-6-x-x-2-x-4</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11432/let-and-952-be-an-acute-angle-such-that-the-equation-x-3-4-x-2-cos-and-952-x-cot</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11433/if-satisfies-the-equation-x-2-x-1-2-x-1-x-2-then-the-roots-of-the-equation-2-x-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11434/let-f-x-x-2-2-x-2-g-x-x-2-2-x-1-and-a-b-be-the-extreme-values-of-f-x-g-x-respect</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/11436/if-are-the-roots-of-the-equation-x-3-a-x-2-b-x-c-0-then-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11437/the-sum-of-all-the-rational-roots-of-the-equation-6-x-6-25-x-5-31-x-4-31-x-2-25</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/11443/let-a-b-and-c-be-three-positive-real-numbers-such-that-the-sum-of-any-two-of-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/11445/if-the-sum-of-any-two-roots-of-the-equation-x-3-p-x-2-q-x-r-0-is-zero-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11446/the-number-of-distinct-real-solutions-for-the-equation-x-2-2-x-8-x-2-0-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11447/if-x-is-real-then-the-sum-of-the-maximum-and-the-minimum-values-of-the-expressio</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/11451/the-sum-of-the-non-real-roots-of-p-2-p-3-p-2-p-2-12-0-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/11454/if-the-equation-whose-roots-are-p-times-the-roots-of-x-4-2-a-x-3-4-b-x-2-8-a-x-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11455/let-a-b-and-c-be-three-positive-real-numbers-such-that-the-sum-of-any-two-of-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/11457/if-a-b-and-c-are-the-roots-of-x-3-4-x-1-0-then-1-a-b-1-b-c-1-c-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11458/if-the-sum-of-any-two-roots-of-the-equation-x-3-p-x-2-q-x-r-0-is-zero-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/11460/if-and-are-the-roots-of-the-equation-x-2-4-x-5-0-then-the-quadratic-equation-who</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11461/f-x-is-a-quadratic-expression-such-that-f-x-is-negative-when-x-5-3-3-and-positiv</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/11472/the-value-of-k-for-which-the-equation-x-2-3-x-k-0-has-at-least-one-real-root-in</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/11744/in-a-poisson-distribution-with-unit-mean-x-0-x-x-p-x-x-x-is-the-mean-of-the-dist</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11745/the-standard-deviation-of-the-numbers-22-26-28-20-24-30-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11746/the-marks-obtained-by-students-a-and-b-in-3-examinations-are-given-below-marks-o</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11747/the-mean-of-five-observations-is-4-and-their-variance-is-also-4-if-three-of-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11748/the-mean-deviation-of-the-following-data-about-its-mean-is-array-l-l-l-l-l-l-i-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11749/if-the-variance-of-6-7-8-9-10-11-is-2-then-the-variance-of-12-14-16-18-20-22-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11750/consider-the-frequency-distribution-if-the-variance-of-this-distribution-is-6000</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11751/the-standard-deviation-of-the-scores-505-510-515-520-595-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11752/if-the-variance-of-the-distribution-array-cccccccc-x-i-and-4-and-8-and-11-and-17</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11753/the-standard-deviation-of-the-numbers-22-26-28-20-24-30-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11754/the-marks-obtained-by-students-a-and-b-in-3-examinations-are-given-below-the-rat</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11755/the-arithmetic-mean-and-standard-deviation-of-a-data-of-nine-numbers-are-13-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11756/the-variance-of-the-following-distribution-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11757/the-mean-and-the-standard-deviation-of-a-data-of-8-items-are-25-and-5-respective</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11758/the-mean-deviation-from-the-median-for-the-following-distribution-corrected-to-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11759/consider-the-following-data-the-coefficient-of-variation-of-the-above-distributi</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11760/the-mean-deviation-about-the-median-of-the-numbers-2-3-5-20-17-15-13-11-9-7-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11761/the-variance-of-the-following-data-is-array-cccccccc-x-i-and-6-and-10-and-14-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11762/if-0-and-the-mean-deviation-of-the-observations-k-for-k-1-2-50-about-its-median</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11763/the-mean-of-numbers-a-b-8-5-10-is-6-and-their-variance-is-6-80-then-tan-1-a-tan</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11764/if-the-coefficients-of-variation-of-two-distributions-are-60-and-70-and-their-st</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11765/the-variance-of-the-first-ten-multiples-of-3-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11766/if-the-mean-deviation-from-the-mean-of-the-observations-1-k-where-k-0-1-2-100-an</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11767/the-standard-deviation-of-the-following-distribution-is-array-l-c-c-c-c-array-l</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11768/the-mean-deviation-of-the-numbers-a-a-d-a-2-d-a-2-n-d-from-their-mean-is-equal-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11769/let-a-and-b-be-two-real-numbers-if-the-arithmetic-mean-and-the-variance-of-a-b-8</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11770/if-the-mean-of-10-observations-is-50-and-the-sum-of-the-squares-of-the-deviation</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11771/the-variance-of-the-first-50-even-natural-numbers-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11772/the-arithmetic-mean-of-the-observations-10-8-5-a-b-is-6-and-their-variance-is-6</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11773/if-the-median-of-the-data-6-7-x-2-x-18-and-21-written-in-ascending-order-is-16-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11774/if-x-x-x-n-are-n-observations-such-that-i-1-n-x-2-400-and-i-1-n-x-80-then-the-le</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11775/the-mean-of-four-observations-is-3-if-the-sum-of-the-squares-of-these-observatio</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11776/the-random-variable-takes-the-values-1-2-3-m-if-p-x-n-1-m-to-each-n-then-the-var</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11777/if-m-and-2-are-the-mean-and-variance-of-the-random-variable-x-whose-distribution</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11778/the-locus-of-the-third-vertex-of-a-right-angled-triangle-the-ends-of-whose-hypot</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11779/the-coordinate-axes-are-rotated-about-the-origin-in-the-counter-clockwise-direct</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11780/the-image-of-a-point-2-1-with-respect-to-the-line-x-y-1-0-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11781/if-a-straight-line-is-at-a-distance-of-10-units-from-the-origin-and-the-perpendi</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11782/a-straight-line-passing-through-the-origin-o-meets-the-parallel-lines-4-x-2-y-9</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11783/a-4-3-b-2-5-are-two-points-if-p-is-a-variable-point-on-the-same-side-as-that-of</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11784/by-shifting-the-origin-to-the-point-2-3-through-translation-of-axes-if-the-equat</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11785/the-points-2-3-and-4-4-3-lie-on-the-opposite-sides-of-the-line-l-5-x-6-y-k-0-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11786/if-the-incentre-of-the-triangle-formed-by-the-lines-x-2-0-x-y-1-0-x-y-3-0-is-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11787/if-a-b-c-1-2-are-the-vertices-of-a-abc-then-the-locus-of-its-centroid-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11788/if-the-axes-are-translated-to-the-orthocentre-of-the-triangle-formed-by-the-poin</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11789/the-angle-made-by-a-line-l-with-positive-x-axis-measured-in-the-positive-directi</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11790/l-and-l-are-two-lines-having-slopes-2-and-1-2-respectively-if-both-l-and-l-are-c</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11791/the-lines-l-y-x-0-and-l-2-x-y-0-intersect-the-line-l-y-2-0-at-p-and-q-respective</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11792/a-a-0-is-a-fixed-point-and-is-a-parameter-such-that-0-2-if-p-a-a-is-a-point-on-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11793/the-point-p-4-1-undergoes-the-following-transformations-in-succession-i-origin-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11794/l-ax-3-y-5-0-and-l-4-x-6-y-8-0-are-two-parallel-lines-if-p-q-are-the-intercepts</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11795/if-h-k-is-the-image-of-the-point-2-3-with-respect-to-the-line-5-x-3-y-2-then-h-k</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11796/when-the-axes-are-rotated-through-an-angle-about-origin-in-anticlockwise-directi</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11797/if-the-perpendicular-distances-from-the-points-2-3-4-a-and-on-to-the-line-3-x-4</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11798/the-equation-of-the-base-of-an-equilateral-triangle-is-x-y-2-and-its-opposite-ve</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11799/if-the-median-ad-of-the-triangle-abc-is-bisected-at-e-and-be-meets-ac-in-f-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11800/if-the-locus-of-a-point-which-is-equidistant-from-the-coordinate-axes-forms-a-tr</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11801/a-2-3-is-a-point-on-the-line-4-x-3-y-1-0-if-the-points-on-the-line-that-are-10-u</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11802/if-is-the-angle-made-by-the-perpendicular-drawn-from-origin-to-the-line-12-x-5-y</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11803/a-straight-line-passing-through-a-fixed-point-2-3-intersects-the-coordinate-axes</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11804/if-m-is-the-foot-of-the-perpendicular-drawn-from-the-origin-to-the-line-x-2-y-3</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11805/if-a-1-0-b-0-2-c-2-1-are-three-fixed-points-then-the-equation-of-the-locus-of-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11806/a-line-l-passing-through-the-point-of-intersection-of-the-lines-x-2-y-3-0-and-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11807/if-the-lines-x-y-2-0-3-x-4-y-1-0-and-5-x-k-y-7-0-are-concurrent-at-then-equation</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11808/if-the-distance-of-a-variable-point-p-from-a-point-a-2-2-is-twice-the-distance-o</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11809/p-6-4-is-a-point-on-the-line-x-y-2-0-if-a-and-b-are-two-points-on-this-line-lyin</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11810/if-the-straight-line-2-x-3-y-1-0-bisects-the-angle-between-two-other-straight-li</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11811/if-p-is-a-variable-point-which-is-at-a-distance-of-2-units-from-the-line-2-x-3-y</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11812/if-the-equation-3-x-2-4-y-2-x-y-k-0-is-the-transformed-equation-of-3-x-2-4-y-2-x</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11813/if-the-intercept-of-a-straight-line-l-made-between-the-straight-lines-5-x-y-4-0</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11814/a-line-l-passes-through-the-point-p-1-2-and-makes-an-angle-of-60-with-o-x-in-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11815/the-locus-of-the-midpoint-of-the-portion-of-the-line-x-y-p-intercepted-by-the-co</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11816/the-origin-is-shifted-to-the-point-2-3-by-translation-of-axes-and-then-the-coord</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11817/if-the-straight-line-passing-through-p-3-4-makes-an-angle-6-with-the-positive-x</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11818/the-equations-of-the-perpendicular-bisectors-of-the-sides-ab-and-ac-of-abc-are-x</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11819/a-pair-of-lines-drawn-through-the-origin-forms-a-right-angled-isosceles-triangle</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11820/the-locus-of-a-variable-point-which-forms-a-triangle-of-fixed-area-with-two-fixe</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11821/a-line-l-passing-through-the-point-p-5-4-cuts-the-line-x-y-5-0-and-x-3-y-2-0-res</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11822/if-the-reflection-of-a-point-a-2-3-in-x-axis-is-b-reflection-of-b-in-the-line-x</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11823/the-equation-of-the-locus-of-points-which-are-equidistant-from-the-points-2-3-an</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11824/the-equation-of-the-side-of-an-equilateral-triangle-is-x-y-2-and-one-vertex-is-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11825/the-orthocentre-of-the-triangle-formed-by-lines-x-y-1-0-x-y-1-0-and-3-x-4-y-5-0</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11826/the-perimeter-of-the-locus-of-the-point-p-which-divides-the-line-segment-q-a-int</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11827/p-is-a-point-on-x-y-5-0-whose-perpendicular-distance-from-2-x-3-y-3-0-is-13-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11828/for-r-x-2-y-1-3-x-2-y-11-0-and-3-x-4-y-11-x-2-y-3-0-represent-two-families-of-li</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11829/the-value-of-c-such-that-the-straight-line-joining-the-points-0-3-and-5-2-is-tan</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11830/in-a-triangle-if-the-angles-are-in-the-ratio-3-2-1-then-the-ratio-of-its-sides-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11831/in-a-triangle-abc-if-bc-5-ca-6-ab-7-then-the-length-of-the-median-drawn-from-b-o</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11832/in-abc-if-ab-bc-ca-6-4-5-then-r-r</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11833/p-is-a-variable-point-such-that-the-distance-of-p-from-a-4-0-is-twice-the-distan</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11834/let-r-if-the-line-1-x-y-1-passes-through-a-fixed-point-h-k-for-all-then-h-2-k-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11835/if-is-the-orthocentre-of-the-triangle-with-the-vertices-2-2-5-1-4-4-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11836/the-area-of-the-triangle-formed-by-the-lines-represented-by-3-x-y-15-0-and-3-x-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11837/a-2-3-b-1-1-are-two-points-if-p-is-a-variable-point-such-that-a-p-b-90-then-locu</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11838/if-the-origin-is-shifted-to-remove-the-first-degree-terms-from-the-equation-2-x</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11839/the-circumcentre-of-the-triangle-formed-by-the-lines-x-y-2-0-2-x-y-8-0-and-x-y-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11840/if-the-line-2-x-3-y-5-0-is-the-perpendicular-bisector-of-the-line-segment-joinin</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11841/if-the-line-2-x-3-y-5-0-is-the-perpendicular-bisector-of-the-line-segment-joinin</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11842/the-equation-of-straight-line-passing-through-the-point-of-intersection-of-the-l</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11843/if-o-0-0-0-a-3-0-0-b-0-4-0-form-a-triangle-then-the-incentre-of-triangle-oab-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11844/p-and-p-are-the-perpendicular-distances-from-the-origin-to-the-tangent-and-norma</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11845/if-the-line-segment-joining-the-points-1-0-and-0-1-subtends-an-angle-of-45-at-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11846/if-the-origin-is-shifted-to-a-point-p-by-the-translation-of-axes-to-remove-the-y</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11847/if-l-m-n-are-the-mid-points-of-the-sides-pq-qr-and-rp-of-pqr-respectively-then-q</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11848/point-1-2-is-changed-to-a-b-when-the-origin-is-shifted-to-the-point-2-1-by-trans</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11849/the-point-a-b-is-the-foot-of-the-perpendicular-drawn-from-the-point-3-1-to-the-l</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11850/a-ray-of-light-passing-through-the-point-2-3-reflects-on-y-axis-at-a-point-p-if</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11851/the-area-in-square-units-of-the-triangle-formed-by-the-lines-6-x-2-13-x-y-6-y-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11852/if-a-1-2-0-b-2-0-1-c-3-0-2-are-the-vertices-of-a-b-c-then-the-length-of-the-inte</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11853/the-perpendicular-distance-from-the-point-1-1-0-to-the-line-joining-the-points-0</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11854/in-h-is-orthocentre-of-abc-and-ah-x-bh-y-ch-z-then-a-b-c-x-y-z</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11855/if-the-lines-3-x-y-4-0-x-y-10-0-x-2-y-4-0-and-3-x-y-k-0-represent-the-sides-of-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11856/a-is-the-point-of-intersection-of-the-lines-3-x-y-4-0-and-x-y-0-if-a-line-having</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11857/2-x-2-3-x-y-2-y-2-0-represents-two-lines-l-and-l-2-x-2-3-x-y-2-y-2-x-7-y-3-0-rep</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11858/the-area-of-the-triangle-formed-by-the-pair-of-lines-23-x-2-48-x-y-3-y-2-0-with</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11859/if-the-ends-of-the-hypotenuse-of-a-right-angled-triangle-are-0-a-and-a-0-then-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11860/the-point-p-2-1-is-translated-to-a-point-q-parallel-to-the-line-l-x-y-4-0-by-2-3</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11861/if-o-is-the-origin-and-p-q-are-points-on-the-line-3-x-4-y-15-0-such-that-op-oq-9</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11862/the-number-of-straight-lines-that-can-be-drawn-through-the-point-3-4-which-are-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11863/let-pqr-be-a-right-angled-isosceles-triangle-right-angled-at-p-2-1-if-the-equati</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11864/in-a-b-c-if-r-r-7-8-and-r-r-3-4-then-a-b-c</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11865/if-a-straight-line-l-perpendicular-to-the-line-3-x-4-y-6-forms-a-triangle-of-are</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11866/let-a-b-c-and-d-be-non-zero-numbers-if-the-point-of-intersection-of-the-lines-4</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11867/if-the-image-of-the-point-3-8-in-the-line-x-3-y-7-is-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11868/the-square-of-the-distance-from-the-origin-to-the-point-of-intersection-of-the-p</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11869/if-all-the-normals-drawn-to-the-curve-y-1-3-x-2-3-x-2-at-the-points-of-intersect</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11870/if-a-2-3-and-b-2-3-are-two-points-then-the-equation-of-the-locus-of-a-point-p-su</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11871/in-abc-if-a-1-2-and-the-equations-of-the-medians-through-b-and-c-are-x-y-5-and-x</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11872/the-equation-of-the-line-passing-through-the-point-a-3-a-3-and-perpendicular-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11873/a-ray-of-light-incident-along-a-line-meets-another-line-7-x-y-1-0-at-the-point-0</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11874/the-transformed-equation-of-2-x-2-3-y-2-z-2-8-x-18-y-2-z-9-0-when-the-axes-are-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11875/if-t-r-1-then-the-locus-of-the-point-3-a-t-1-t-3-3-at-2-1-t-3-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11876/the-centre-of-a-square-of-side-4-units-length-is-3-7-and-one-of-the-diagonals-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11877/the-area-in-square-units-of-the-triangle-formed-by-the-lines-x-0-y-0-and-3-x-4-y</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11878/let-origin-be-the-centroid-of-an-equilateral-triangle-abc-and-one-of-its-sides-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11879/the-equation-of-the-line-common-to-the-pair-of-lines-p-2-q-2-x-2-q-2-r-2-xy-r-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11880/the-lines-l-y-x-0-and-l-2-x-y-0-intersect-the-line-l-y-2-0-at-p-and-q-respective</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11881/the-locus-of-the-point-which-is-equidistant-from-the-point-1-1-and-the-line-x-y</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11882/if-the-y-intercept-of-the-perpendicular-bisector-of-the-line-segment-joining-p-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11883/a-straight-line-l-at-a-distance-of-4-units-from-the-origin-makes-positive-interc</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11884/if-p-and-q-are-the-x-and-y-intercepts-respectively-of-the-line-passing-through-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11885/if-the-equations-x-t-2-t-1-y-t-2-t-1-represents-a-curve-c-with-parameter-t-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11886/the-circumcentre-of-the-triangle-with-vertices-2-3-2-1-4-0-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11887/if-ps-is-the-median-of-the-triangle-with-vertices-p-2-2-q-6-1-and-r-7-3-then-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11888/two-sides-of-a-rhombus-are-along-the-lines-x-y-1-0-and-7-x-y-5-0-if-its-diagonal</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11889/if-2-x-2-5-x-y-2-y-2-0-represents-two-sides-of-a-triangle-whose-centroid-is-1-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11890/let-the-curve-x-2-2-y-2-2-intersect-the-line-x-y-1-at-two-points-p-and-q-and-o-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11891/if-a-2-3-4-and-b-2-3-4-then-the-locus-of-a-point-p-such-that-pa-pb-4-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11892/f-x-is-a-continuous-function-on-r-and-y-f-x-is-a-curve-if-is-a-point-such-that-f</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11893/if-a-2-3-and-b-4-5-are-two-fixed-points-then-the-locus-of-a-point-p-such-that-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11894/the-sides-of-a-triangle-are-3-x-2-y-6-0-2-x-3-y-6-0-and-x-2-y-2-0-if-p-0-b-lies</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11895/a-point-on-the-straight-line-3-x-5-y-15-which-is-equidistant-from-the-coordinate</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11896/the-equation-of-the-line-passing-through-the-points-ct-c-t-and-ct-c-t-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11897/if-the-angle-between-the-pair-of-lines-x-2-2-2-x-y-k-y-2-0-k-0-is-45-then-the-ar</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11898/if-the-plane-56-x-4-y-9-z-2016-meets-the-coordinate-axes-in-a-b-and-c-then-the-c</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11899/if-abc-is-a-right-angled-isosceles-triangle-and-c-90-then-r-r</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11900/let-p-1-0-q-0-0-and-r-3-3-3-be-three-points-then-the-equation-of-the-bisector-of</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11901/the-diagonals-ac-and-bd-of-a-rhombus-abcd-intersect-at-the-point-3-4-if-bd-2-2-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11902/the-lines-p-p-2-1-x-y-q-0-and-p-2-1-2-x-p-2-1-y-2-q-0-are-perpendicular-to-a-lin</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11903/assertion-a-the-difference-of-the-slopes-of-the-lines-represented-by-y-2-2-xysec</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11904/the-combined-equation-of-the-lines-passing-through-the-point-3-4-and-each-making</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11905/the-equal-sides-of-an-isosceles-triangle-are-given-by-equations-7-x-y-3-0-and-x</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11906/in-abc-the-coordinates-of-the-vertex-a-are-3-1-if-the-equation-of-the-median-thr</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11907/if-a-line-a-b-of-length-r-moves-so-that-a-and-b-always-lie-respectively-on-x-axi</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11908/ali-points-inside-the-triangle-with-vertices-at-1-3-5-0-and-1-2-must-necessarily</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11909/the-line-on-which-the-lines-a-x-b-y-1-and-b-x-a-y-1-with-a-0-b-intersect-for-any</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11910/if-the-coordinates-of-the-vertices-of-a-a-b-c-are-a-7-6-4-b-5-4-6-c-3-2-0-and-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11911/in-a-triangle-abc-b-c-a-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11912/in-a-triangle-abc-if-a-2-b-c-0-then-a-2-c-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11913/if-g-2-1-2-is-the-centroid-of-tetrahedron-oabc-where-o-0-0-0-and-g-is-the-centro</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11914/in-a-b-c-if-a-is-1-2-b-and-c-lie-on-y-x-where-is-variable-then-the-locus-of-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11915/given-two-points-q-3-4-and-r-1-2-what-is-the-point-p-x-y-on-the-line-2-x-y-1-0-f</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11916/suppose-the-vertices-of-a-triangle-are-given-by-a-0-3-b-2-0-and-c-6-1-for-1-to-l</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11917/for-a-triangle-formed-by-0-0-4-0-and-3-4-the-orthocenter-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11918/suppose-the-pairs-of-straight-lines-x-2-2-a-x-y-y-2-0-and-x-2-2-b-x-y-y-2-0-are</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11919/suppose-a-triangle-of-area-27-sq-units-is-formed-by-18-x-2-9-x-y-y-2-0-and-y-c-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11920/if-d-d-d-are-the-distances-of-the-point-1-2-3-from-the-x-y-z-coordinate-axes-res</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11921/if-p-3-12-4-and-q-is-a-point-on-the-line-op-such-that-o-q-3-then-the-sum-of-all</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11922/a-point-p-x-y-is-such-that-the-sum-of-squares-of-its-distance-from-a-0-and-a-0-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11923/suppose-the-hypotenuse-and-its-opposite-vertex-of-an-isosceles-right-angled-tria</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11924/a-point-p-on-a-line-is-at-a-distance-of-4-units-from-the-origin-0-0-if-the-line</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11925/suppose-a-b-o-c-is-a-rhombus-in-the-first-quadrant-with-o-being-the-origin-if-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11926/p-q-r-s-is-a-quadrilateral-and-p-q-a-q-r-b-s-p-a-b-m-is-the-mid-point-of-q-r-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11927/if-c-is-the-mid-point-of-the-line-segment-a-b-and-p-is-any-point-outside-the-lin</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11928/on-the-locus-of-the-point-p-x-y-equidistant-from-3-0-and-0-4-if-a-and-b-are-two</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11929/if-one-side-of-an-isosceles-triangle-is-given-by-y-2-and-the-base-is-provided-by</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11930/the-straight-line-passing-through-0-0-and-the-foot-of-perpendicular-from-2-4-ont</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11931/if-p-lies-inside-the-triangle-formed-by-the-vertices-0-0-3-2-0-and-0-3-2-then-li</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11932/the-triangle-formed-by-x-2-4-x-y-y-2-0-and-x-y-4-6-0-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11933/the-equation-of-bisectors-of-the-angle-between-the-lines-given-by-3-x-2-5-x-y-4</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11934/a-variable-line-passing-through-l-m-intersects-the-coordinate-axes-at-the-points</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11935/the-triangle-with-vertices-at-2-2-2-2-and-1-1-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11936/for-the-three-points-a-2-0-b-0-2-and-p-1-1-suppose-d-is-the-algebraic-sum-of-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11937/number-of-triangle-formed-by-the-lines-x-y-3-0-2-x-y-3-0-3-x-y-2-0-and-x-y-3-0-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11938/the-length-of-the-sides-of-a-triangle-are-13-14-and-15-if-r-and-r-respectively-d</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11939/if-origin-is-the-ortho-center-of-an-equilateral-triangle-whose-vertices-are-a-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11940/a-point-p-x-y-is-such-that-its-distance-from-1-0-and-0-2-are-in-a-ratio-of-2-1-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11941/if-a-point-of-3-x-y-0-and-3-4-lie-on-the-opposite-sides-of-3-x-4-y-8-0-then-whic</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11942/if-a-particle-moving-along-x-2-y-3-0-gets-reflected-in-a-perpendicular-direction</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11943/the-family-of-lines-forming-an-isosceles-triangle-with-the-lines-3-x-4-y-2-0-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11944/the-straight-line-passing-through-1-1-and-remaining-parallel-to-the-line-common</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11945/the-midpoint-of-the-diagonal-of-a-rectangle-formed-by-x-2-5-x-6-0-and-y-2-8-y-20</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11946/if-the-vertices-of-a-triangle-abc-are-a-1-2-3-b-h-3-0-and-c-4-k-1-and-the-centro</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11947/suppose-a-point-p-moves-so-that-bp-2-ap-2-121-where-a-and-b-are-2-5-and-5-11-res</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11948/if-two-distinct-points-lying-at-a-unit-distance-from-4-x-3-y-10-0-and-passing-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11949/suppose-p-x-y-lying-on-3-x-y-2-0-or-3-x-y-2-0-is-at-a-distance-of-5-units-from-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11950/if-a-3-3-b-1-1-c-1-1-and-d-2-2-are-the-vertices-of-a-quadrilateral-the-angle-bet</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11951/suppose-the-pairs-of-straight-lines-2-x-2-a-x-y-3-y-2-0-and-2-x-2-b-x-y-3-y-2-0</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11952/the-locus-of-the-incentre-of-the-triangle-formed-by-the-lines-x-y-4-x-4-y-16-0-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11953/if-the-centroid-of-triangle-whose-vertices-are-a-1-3-2-b-5-and-4-7-c-be-the-orig</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11954/if-2-3-are-angles-made-by-a-ray-with-ox-oy-oz-axes-respectively-then-all-the-pos</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11955/the-locus-of-mid-points-of-points-of-intersection-of-x-y-1-with-the-coordinate-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11956/suppose-p-and-q-lie-on-3-x-4-y-4-0-and-5-x-y-4-0-respectively-if-the-mid-point-o</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11957/the-length-of-intercept-of-x-1-0-between-the-lines-3-x-2-y-5-and-3-x-2-y-3-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11958/suppose-that-the-three-points-a-b-and-c-in-the-plane-are-such-that-their-x-coord</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11959/suppose-p-and-q-are-the-mid-points-of-the-sides-a-b-and-b-c-of-a-triangle-where</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11960/suppose-and-8710-a-b-c-is-an-isosceles-triangle-with-and-8736-c-90-and-176-a-2-3</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11961/if-the-points-of-intersection-of-the-coordinate-axes-and-x-y-2-form-a-rhombus-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11962/the-equation-of-perpendicular-bisectors-of-sides-a-b-and-a-c-of-a-and-8710-a-b-c</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11963/if-the-pair-of-straight-lines-9-x-2-a-x-y-4-y-2-6-x-b-y-3-0-represents-two-paral</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11964/a-line-passing-through-p-2-3-and-making-an-angle-of-30-and-176-with-the-positive</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11965/the-least-distance-from-origin-to-a-point-on-the-line-y-x-3-which-lies-at-a-dist</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11966/starting-from-the-point-a-3-4-a-moving-object-touches-2-x-y-7-0-at-b-and-reaches</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11967/suppose-a-triangle-is-formed-by-x-y-10-and-the-coordinate-axes-then-the-number-o</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11968/if-the-lines-represented-by-a-x-2-2-h-x-y-b-y-2-2-g-x-2-f-y-c-0-intersect-on-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11969/for-and-945-and-8712-0-and-960-2-the-angle-between-the-lines-represented-by-x-co</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11970/a-rod-of-length-2l-slides-with-its-ends-on-two-perpendicular-lines-then-the-locu</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11971/if-the-axes-are-transformed-to-the-point-1-1-then-the-equation-3-x-2-y-2-2-x-4-y</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11972/find-the-value-of-k-if-the-line-joining-the-points-2-k-and-3-7-is-parallel-to-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11973/the-equation-of-a-line-though-the-point-1-2-whose-distance-from-the-point-3-1-ha</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11974/identify-the-point-on-the-line-2x-3y-7-0-which-is-at-a-distance-of-3-units-from</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11975/a-person-standing-at-the-junction-crossing-of-2-straight-paths-represented-by-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11976/number-of-triangles-in-which-a-b-c-a-b-c-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11977/the-equation-of-the-locus-of-a-point-which-is-equidistant-from-the-points-2-3-an</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11978/the-equation-obtained-by-transforming-x-2-y-2-6-x-10-y-2-0-to-the-parallel-axis</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11979/if-a-point-a-a-falls-between-the-lines-x-y-4-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11980/if-the-straight-lines-2-x-y-1-0-4-x-y-2-0-and-x-y-k-0-are-concurrent-then-k-equa</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/11981/in-an-isosceles-a-b-c-the-coordinates-of-vertices-b-and-c-of-the-base-b-c-are-3</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/12164/if-a-d-b-c-0-then-the-area-in-sq-units-of-the-parallelogram-formed-by-the-lines</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/12221/the-distance-from-the-origin-to-the-image-of-1-1-with-respect-to-the-line-x-y-5</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12222/the-harmonic-conjugate-of-2-3-4-with-respect-to-the-points-3-2-2-6-17-4-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/12224/the-point-2-3-is-first-reflected-in-the-straight-line-y-x-and-then-translated-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/12226/the-point-on-the-line-4-x-y-2-0-which-is-equidistant-from-the-points-5-6-and-3-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12227/if-the-lines-x-2-a-y-a-0-x-3-b-y-b-0-x-4-c-y-c-0-are-concurrent-then-a-b-and-c-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12229/the-equation-of-a-straight-line-perpendicular-to-3-x-4-y-6-and-forming-a-triangl</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12230/if-the-image-of-7-5-6-5-in-a-line-is-1-2-then-the-equation-of-the-line-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/12233/the-locus-of-the-centroid-of-the-triangle-with-vertices-at-a-a-b-b-and-1-0-is-he</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12234/the-origin-is-translated-to-1-2-the-point-7-5-in-the-old-system-undergoes-the-fo</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12235/if-p-and-q-are-the-perpendicular-distances-from-the-origin-to-the-straight-lines</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12236/if-2-x-3-y-5-is-the-perpendicular-bisector-of-the-line-segment-joining-the-point</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/12238/the-perpendicular-distance-from-the-point-1-to-the-line-joining-1-0-and-1-2-in-p</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12239/the-equation-of-a-straight-line-passing-through-the-point-1-2-and-inclined-at-45</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12240/a-point-moves-in-the-x-y-plane-such-that-the-sum-of-its-distance-from-two-mutual</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/12243/if-the-pair-of-lines-given-by-x-2-y-2-2-x-y-2-are-perpendicular-to-each-other-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/12262/the-point-on-the-line-3-x-4-y-5-which-is-equidistant-from-1-2-and-3-4-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/12274/if-a-point-p-moves-such-that-its-distances-from-the-point-a-1-1-and-the-line-x-y</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/12380/a-2-3-5-b-3-3-and-c-7-5-are-the-vertices-of-a-triangle-if-the-median-through-a-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12381/the-equation-of-the-plane-passing-through-the-point-1-2-2-and-perpendicular-to-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12382/let-l-be-the-line-passing-through-the-points-i-9-k-and-7-j-k-and-be-the-plane-pa</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12383/if-the-extremities-of-a-diagonal-of-a-square-are-1-2-3-and-2-3-5-then-the-length</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12384/coordinate-planes-and-the-planes-which-are-respectively-parallel-to-yz-zx-xy-pla</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12385/an-equation-of-a-plane-parallel-to-the-plane-x-2-y-2-z-5-0-and-which-is-at-one-u</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12386/if-l-m-n-l-m-n-are-the-direction-cosines-of-two-lines-then-1-m-1-m-2-m-n-m-n-2-n</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12387/a-point-on-the-plane-passing-through-the-points-2-1-4-0-1-0-and-0-0-1-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12388/the-coordinates-of-the-point-3-7-5-in-the-new-system-when-the-origin-is-shifted</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12389/let-a-1-1-2-b-6-11-2-c-1-2-6-be-three-points-if-l-m-n-are-the-direction-cosines</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12390/if-a-and-b-are-two-vectors-such-that-a-b-14-and-a-b-7-then-a-b-a-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12391/let-abcd-be-a-tetrahedron-in-which-the-coordinates-of-each-of-its-vertices-are-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12392/if-a-3-1-11-b-0-2-3-c-4-8-11-are-three-points-then-the-coordinates-of-the-foot-o</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12393/if-s-is-the-set-of-all-real-values-of-a-such-that-a-plane-passing-through-the-po</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12394/3-i-2-j-k-2-i-j-3-k-and-i-3-j-2-k-are-the-position-vectors-of-the-vertices-a-b-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12395/if-the-line-passing-through-the-points-5-1-a-and-3-b-1-crosses-the-yz-plane-at-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12396/abc-is-formed-by-a-1-8-4-b-0-11-4-and-c-2-3-1-if-d-is-the-foot-of-the-perpendicu</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12397/the-distance-between-two-parallel-planes-a-x-b-y-c-z-d-0-a-x-b-y-c-z-d-0-is-give</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12398/the-distance-between-a-point-p-whose-position-vector-is-5-i-j-3-k-and-the-line-r</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12399/if-the-direction-cosines-of-a-line-satisfy-the-relations-l-m-n-0-and-l-m-m-m-4-n</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12400/let-be-the-plane-passing-through-the-point-3-3-1-and-perpendicular-to-the-line-j</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12401/let-a-3-2-7-and-b-3-1-2-let-a-plane-perpendicular-to-the-line-segment-a-b-divide</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12402/if-the-centroid-of-a-triangle-with-vertices-4-p-3-1-1-2-and-3-5-8-is-given-by-mi</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12403/a-ray-makes-angles-3-and-4-with-y-and-z-axes-respectively-then-the-value-of-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12404/a-plane-meets-the-x-y-z-axes-in-a-b-c-respectively-if-the-centroid-of-the-a-b-c</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12405/if-the-point-3-4-5-divides-the-line-segment-joining-the-points-1-2-3-and-4-5-6-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12406/suppose-l-m-n-and-l-m-n-are-the-directional-cosines-of-two-lines-and-is-the-angl</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12407/let-the-plane-a-x-b-y-c-z-d-0-bisect-the-line-joining-the-points-4-3-1-and-2-3-5</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12408/let-the-centroid-of-a-triangle-formed-by-the-points-a-4-x-1-b-y-5-2-and-c-7-8-3</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12409/if-l-m-n-and-l-m-n-are-the-direction-cosines-of-two-lines-satisfying-the-relatio</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12410/if-3-4-7-is-the-foot-of-the-perpendicular-drawn-from-the-point-2-3-6-to-the-plan</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12411/if-a-b-c-are-the-direction-ratios-of-a-line-l-and-m-n-are-its-direction-cosines</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12412/if-a-b-c-are-the-intercepts-made-by-the-plane-passing-through-the-point-1-2-3-pa</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12413/if-2-4-3-4-5-are-the-intercepts-made-by-a-plane-on-x-y-z-axes-respectively-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12414/if-p-divides-the-line-segment-joining-the-points-a-1-2-1-and-b-1-0-1-externally</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12415/if-the-direction-cosines-of-a-line-are-a-83-5-83-c-83-and-c-a-4-then-c-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12416/let-the-plane-pass-through-the-point-1-0-1-and-perpendicular-to-the-planes-2-x-3</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12417/if-the-equation-of-the-plane-passing-through-the-point-a-2-1-3-and-perpendicular</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12418/if-x-coordinate-of-a-point-p-on-the-line-joining-the-points-q-2-2-1-and-r-5-2-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12419/if-2-3-c-are-the-direction-ratios-of-a-ray-passing-through-the-point-c-5-q-1-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12420/if-the-equation-of-the-plane-which-is-at-a-distance-of-1-3-units-from-the-origin</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12421/the-point-of-intersection-of-the-lines-r-and-8594-2-b-and-8594-t-6-c-and-8594-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12422/if-the-point-a-8-2-divides-the-line-segment-joining-the-points-1-4-6-and-5-2-10</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12423/if-a-b-c-are-the-direction-ratios-of-a-line-joining-the-points-4-3-5-and-2-1-8-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12424/the-x-intercept-of-a-plane-and-960-passing-through-the-point-1-1-1-is-5-2-and-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12425/the-position-vectors-of-a-and-b-are-i-j-k-and-1-3-j-1-3-k-if-b-divides-the-line</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12426/which-of-the-following-points-lie-on-the-plane-passing-through-2-i-3-j-k-3-i-2-j</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12427/if-the-lengths-of-projections-of-a-line-of-length-l-over-the-coordinate-axes-are</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12428/if-the-direction-ratios-of-two-lines-are-given-by-3lm-4ln-mn-0-and-l-2m-3n-0-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12429/the-perpendicular-distance-from-origin-to-the-plane-x-2y-2z-5-0-equals-units</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12430/if-the-origin-is-the-centroid-of-the-triangle-for-which-2-3-4-and-3-1-5-are-two</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12431/if-the-line-joining-the-points-k-2-3-and-1-1-2-is-parallel-to-the-line-joining-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12432/the-angle-between-any-two-diagonals-of-a-cube-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12433/the-plane-passing-through-the-points-1-1-1-1-1-1-and-7-3-5-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12434/r-divides-the-line-joining-two-points-p-and-q-whose-position-vectors-are-i-2-j-k</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12435/if-the-direction-cosines-of-a-straight-line-are-1-c-1-c-1-c-then-c-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12436/a-line-a-b-in-three-dimensions-makes-angles-45-and-120-with-the-positive-x-axis</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12437/a-variable-plane-x-a-y-b-z-c-1-which-is-at-a-unit-distance-from-the-origin-cuts</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12438/the-angle-between-the-lines-whose-direction-cosines-are-given-by-the-equations-l</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12439/find-the-equation-of-a-plane-given-that-the-foot-of-perpendicular-drawn-to-the-p</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12440/the-plane-passing-through-2-1-3-and-perpendicular-to-3-i-j-2-k-contains-the-poin</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12441/if-a-line-makes-angles-90-135-and-45-with-the-positive-x-y-and-z-axis-respective</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12442/if-the-line-joining-a-4-1-2-and-b-0-k-1-is-perpendicular-to-the-line-joining-c-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12443/find-the-equation-of-the-plane-which-passes-through-the-points-0-1-2-and-1-0-3-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12444/a-ray-of-light-passing-through-the-point-a-1-2-3-strikes-the-plane-x-y-z-12-at-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12445/if-the-line-joining-the-points-a-7-p-2-and-b-q-2-5-is-parallel-to-the-line-joini</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12446/the-angle-between-the-planes-2-x-y-z-6-and-x-y-2-z-3-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12447/the-equation-of-the-plane-passing-through-3-i-2-j-6-k-and-parallel-to-the-vector</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12448/the-direction-cosines-of-the-line-joining-the-points-2-4-5-and-1-2-3-are</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12449/the-sum-of-intercepts-of-the-plane-4-x-3-y-2-z-2-on-the-coordinate-axes-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12450/the-position-vectors-of-the-points-a-and-b-with-respect-to-o-are-2-i-2-j-k-and-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12451/if-the-lines-x-3-2-y-2-3-z-1-and-955-and-x-2-3-y-3-2-z-2-3-are-coplanar-then-sin</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12452/the-line-passing-through-1-1-1-and-parallel-to-the-vector-i-2-j-k-meets-the-line</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12453/let-a-and-8594-i-and-b-and-8594-j-is-the-point-of-intersection-of-the-lines-r-an</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12454/a-2-3-4-b-4-5-7-c-2-6-3-d-4-4-k-are-four-points-if-the-line-a-b-and-175-is-paral</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12455/if-the-direction-cosines-of-two-lines-are-2-3-2-3-1-3-and-5-13-12-13-0-then-iden</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/12456/x-intercept-of-the-plane-containing-the-line-of-intersection-of-the-planes-x-2-y</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/13172/let-a-b-and-c-be-any-three-non-coplanar-vectors-if-m-n-are-scalars-such-that-a-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13173/if-2-i-j-k-i-3-j-5-k-and-3-i-4-j-4-k-are-the-position-vectors-of-three-points-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13174/if-oa-2-i-j-k-o-b-3-i-k-and-o-c-2-j-3-k-are-the-position-vectors-of-the-points-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13175/let-b-3-i-2-j-k-and-c-i-j-k-be-two-vectors-if-a-is-a-vector-such-that-a-b-c-0-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13176/let-a-2-i-j-k-and-b-i-3-j-5-k-be-two-vectors-and-r-be-a-vector-along-the-vector</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13177/if-i-is-the-position-vector-of-the-centroid-g-of-triangle-abc-and-2-i-j-k-are-re</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13178/if-a-2-i-9-j-6-k-and-b-t-i-2-j-6-k-are-vectors-such-that-a-b-25-then-the-sum-of</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13179/if-a-i-3-j-13-k-and-b-2-i-4-j-3-k-are-two-vectors-then-the-component-vector-of-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13180/let-a-2-i-3-j-5-k-and-b-3-i-2-j-5-k-be-two-vectors-and-r-be-a-vector-in-the-plan</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13181/if-a-point-c-divides-the-line-segment-joining-the-points-with-the-position-vecto</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13182/if-a-2-x-y-i-3-j-9-k-and-b-2-i-j-x-y-k-are-two-collinear-vectors-then-x-3-27-y-3</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13183/let-a-i-2-j-b-2-j-3-k-c-pi-q-j-and-d-p-j-q-k-be-four-vectors-if-a-b-c-3-a-b-d-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13184/let-a-i-2-j-3-k-and-b-i-2-j-3-k-be-two-vectors-if-a-is-the-area-of-the-quadrilat</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13185/for-some-real-number-if-the-area-of-the-triangle-having-a-3-i-j-k-and-b-i-j-3-k</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13186/if-7-i-4-j-5-k-is-the-position-vector-of-the-vertex-a-of-a-tetrahedron-a-b-c-d-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13187/let-oa-i-2-j-2-k-and-ob-2-i-3-j-6-k-be-the-position-vectors-of-two-points-a-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13188/let-a-b-denote-the-angle-between-vectors-a-and-b-if-a-2-i-3-j-6-k-a-b-4-and-a-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13189/the-distance-of-a-point-a-from-the-plane-r-m-q-is-given-by-a-m-q-m-if-the-distan</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13190/a-and-b-are-two-vectors-such-that-a-is-not-parallel-to-b-if-p-x-2-y-3-a-5-x-y-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13191/let-be-the-plane-determined-by-the-vectors-i-2-j-and-3-j-2-k-let-be-the-plane-de</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13192/if-a-2-i-3-j-b-3-j-4-k-and-c-5-i-4-k-are-three-vectors-then-a-vector-which-is-pe</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13193/let-oa-2-i-3-j-k-ob-i-4-j-3-k-and-oc-3-i-j-2-k-be-the-position-vectors-of-three</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13194/if-a-and-b-are-two-non-collinear-vectors-and-the-vector-a-b-bisects-the-angle-be</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13195/o-a-b-c-d-is-a-pentagon-in-which-the-sides-o-a-and-c-b-are-parallel-and-the-side</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13196/if-the-points-p-i-2-j-q-4-i-6-j-r-5-i-7-j-s-a-i-b-j-are-the-consecutive-vertices</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13197/if-a-4-i-6-j-b-3-j-4-k-and-c-is-the-projection-vector-of-a-on-b-then-c-and-c-res</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13198/a-2-1-2-b-1-0-0-c-1-3-3-6-are-vertices-of-a-triangle-if-the-length-of-the-median</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13199/let-a-a-i-a-j-a-k-where-a-a-a-and-a-are-rational-numbers-if-a-makes-an-angle-45</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13200/if-e-e-are-two-non-collinear-unit-vectors-such-that-e-e-3-then-2-e-5-e-3-e-e</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13201/a-b-c-d-are-any-4-points-and-a-b-c-d-b-c-a-d-c-a-b-d-area-of-a-b-c-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13202/let-a-i-x-j-k-b-i-j-k-and-a-b-a-b-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13203/if-a-i-2-j-3-k-b-2-i-3-j-k-c-8-i-13-j-9-k-and-x-a-y-b-z-c-0-then-x-y-z-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13204/the-vector-x-is-perpendicular-to-the-vectors-a-3-i-2-j-2-k-b-18-i-22-j-5-k-and-m</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13205/a-b-are-two-vectors-such-that-a-3-b-2-if-x-is-unit-vector-satisfying-x-a-b-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13206/the-set-of-real-values-of-for-which-the-vectors-i-3-j-5-k-and-2-i-j-k-are-perpen</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13207/a-b-are-non-collinear-vectors-a-2-2-b-3-and-the-angle-between-a-and-b-is-45-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13208/the-vertices-of-a-triangle-are-at-i-3-j-and-2-i-5-j-and-its-orthocenter-is-at-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13209/if-3-vectors-a-b-c-are-such-that-a-0-and-a-b-2-a-c-a-1-c-1-b-4-and-angle-between</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13210/the-vectors-a-2-i-3-j-6-k-and-b-are-collinear-and-b-2-l-then-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13211/in-a-trapezium-a-b-c-d-b-c-a-d-and-x-a-c-b-d-if-x-p-a-d-then-p</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13212/in-a-a-b-c-c-b-a-c-a-b-a-b-c-and-c-d-is-the-median-through-the-vertex-c-then-c-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13213/if-a-i-j-k-c-j-k-a-b-c-a-b-3-then-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13214/let-p-be-a-real-number-and-p-2-if-a-b-c-are-variable-angles-such-that-p-2-4-a-p</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13215/if-a-p-2-5-and-b-1-q-3-are-collinear-vectors-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13216/let-a-2-i-3-j-k-b-4-i-j-c-i-3-j-7-k-if-r-x-i-y-j-z-k-r-a-9-r-b-7-r-c-6-then-x-y</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13217/if-a-b-c-d-is-a-cyclic-quadrilateral-with-r-as-the-radius-of-the-circumcircle-an</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13218/if-a-13-b-5-and-a-b-60-then-a-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13219/7-i-4-j-7-k-i-6-j-10-k-i-3-j-4-k-5-i-j-5-k-respectively-then-a-b-c-d-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13220/m-and-n-are-the-mid-points-of-the-sides-bc-and-cd-of-a-parallelogram-abcd-respec</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13221/three-vectors-a-b-c-satisfy-the-condition-a-b-c-0-if-a-1-b-3-c-4-then-a-b-b-c-c</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13222/let-o-a-4-i-3-k-o-b-14-i-2-j-5-k-o-d-bisects-a-o-b-and-o-d-6-then-o-d</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13223/a-b-c-are-non-coplanar-vectors-if-aligned-and-a-3-b-4-c-x-a-2-b-3-c-y-a-5-b-2-c</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13224/three-vectors-of-magnitudes-a-2-a-3-a-are-along-the-directions-of-the-diagonals</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13225/if-a-is-collinear-with-b-3-i-6-j-6-k-and-a-b-27-then-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13226/let-a-b-and-c-be-unit-vectors-such-that-a-is-perpendicular-to-the-plane-containi</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13227/let-f-2-i-2-j-5-k-a-1-2-5-b-1-2-3-and-b-a-f-4-i-6-j-2-k-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13228/d-e-f-are-respectively-the-points-on-the-sides-b-c-c-a-and-a-b-of-a-and-8710-a-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13229/o-a-b-c-is-a-tetrahedron-if-d-e-are-the-midpoints-of-o-a-and-b-c-respectively-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13230/if-a-and-8594-b-and-8594-c-and-8594-are-vectors-such-that-a-and-8594-b-and-8594</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13231/if-p-q-are-two-points-on-the-curve-y-2-x-2-in-the-rectangular-cartesian-coordina</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13232/in-quadrilateral-a-b-c-d-a-b-and-8594-a-and-8594-b-c-and-8594-b-and-8594-d-a-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13233/the-vectors-3-a-5-b-and-2-a-b-are-mutually-perpendicular-and-the-vectors-a-4-b-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13234/let-a-and-8594-x-i-y-j-z-k-and-x-2-y-if-a-and-8594-5-2-and-a-and-8594-makes-an-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13235/let-a-and-8594-b-and-8594-c-and-8594-be-the-position-vectors-of-the-vertices-of</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13236/let-a-b-and-c-are-3-non-zero-vectors-such-that-no-2-of-these-are-collinear-if-ve</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13237/if-a-b-and-c-are-three-vectors-such-that-a-b-2-a-b-2-and-a-b-c-0-then-c-is-equal</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13238/let-u-v-and-w-are-non-coplanar-vectors-then-the-value-of-u-2-v-w-u-v-u-v-w-u-v-w</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13239/let-u-and-v-be-two-non-zero-vectors-in-r-3-then-u-v-2-u-v-2-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13240/let-u-and-v-be-non-collinear-vectors-in-r-2-let-w-be-the-orthogonal-projection-v</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13241/if-p-q-q-r-2-2-5-r-p-then-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13242/if-c-is-the-mid-point-of-line-segment-a-b-and-p-is-any-point-not-on-the-line-a-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13243/if-is-the-angle-between-the-unit-vectors-a-and-b-then-2-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13244/the-vectors-a-lies-in-the-plane-of-vectors-b-and-c-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13245/a-and-b-are-unit-vectors-such-that-a-2-b-is-also-a-unit-vector-if-is-the-angle-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13246/if-a-b-and-c-are-non-zero-vectors-such-a-b-c-and-b-c-a-then-a-c-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13247/consider-the-vectors-u-a-i-b-j-c-k-v-a-2-i-b-2-j-c-2-k-and-w-a-3-i-b-3-j-c-3-k-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13248/a-b-c-d-e-f-is-a-regular-hexagon-the-sum-of-the-vectors-b-e-b-c-e-f-b-a-c-f-a-f</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13249/if-a-b-c-d-e-f-is-a-regular-hexagon-with-a-b-a-and-b-c-b-then-c-e-equals-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13250/if-a-is-a-vector-of-magnitude-7-b-is-a-vector-of-magnitude-8-then-the-maximum-va</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13251/the-number-of-vectors-of-unit-length-perpendicular-to-the-two-vectors-a-1-1-0-an</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13252/if-the-vectors-a-i-j-2-k-b-2-i-4-j-k-and-c-i-j-k-are-mutually-orthogonal-then-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13253/let-a-b-and-c-be-the-three-vectors-if-a-1-b-17-and-c-8-and-the-angle-between-a-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13254/if-a-t-2-i-e-t-j-k-and-b-2-i-t-2-j-t-k-and-f-t-a-b-then-f-l-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13255/a-b-c-d-is-a-parallelogram-such-that-l-is-mid-point-of-b-c-then-a-l-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13256/the-number-of-values-of-m-r-for-which-the-vectors-i-2-j-m-k-and-i-m-j-2-k-are-co</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13257/if-a-b-c-d-e-f-is-a-regular-hexagon-where-two-adjacent-sides-a-b-and-b-c-are-a-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13258/if-a-b-and-c-are-three-vectors-such-that-a-3-b-4-and-c-5-and-a-b-c-0-then-a-b-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13259/let-a-b-and-c-be-non-zero-vectors-such-that-a-b-c-1-3-b-c-a-if-is-the-acute-angl</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13260/if-a-x-2-i-x-j-3-k-and-b-x-i-4-j-2-k-and-a-b-6-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13261/if-a-b-and-c-be-3-non-coplanar-vectors-and-a-b-b-2-c-c-2-a-0-then-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13262/if-three-consecutive-vertices-of-a-parallelogram-are-a-4-3-5-b-0-6-0-c-8-1-4-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13263/let-a-b-c-d-e-f-be-a-regular-hexagon-with-the-vertices-a-b-c-d-e-f-counter-clock</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13264/let-a-b-and-c-is-three-points-on-a-circle-of-radius-r-if-o-is-the-centre-of-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13265/the-figure-formed-by-the-four-points-i-j-k-2-i-3-j-5-j-2-k-and-k-j-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13266/let-a-i-2-j-if-b-is-a-vector-in-x-y-plane-such-that-a-b-b-15-and-a-b-6-then-b-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13267/the-area-of-the-parallelogram-for-which-the-vectors-i-j-2-k-and-3-i-2-j-k-are-ad</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13268/let-a-b-and-c-be-unit-vectors-such-that-a-b-0-a-c-and-the-acute-angle-between-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13269/let-u-and-v-are-unit-vectors-such-that-u-v-0-if-r-is-any-vector-coplanar-with-u</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13270/let-u-and-v-be-two-vectors-then-u-v-u-v-if-and-only-if</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13271/in-o-a-c-if-b-is-the-mid-point-of-side-a-c-and-o-a-a-o-b-b-then-o-c-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13272/let-a-b-c-d-e-f-be-a-regular-hexagon-with-the-vertices-a-b-c-d-e-and-f-counter-c</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13273/if-35-i-14-j-77-k-2-i-7-j-5-k-and-5-i-2-j-k-are-coplanar-then-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13274/if-a-b-c-and-d-are-vectors-in-which-d-1-and-given-a-b-c-s-d-b-c-d-a-a-d-4-then-s</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13275/let-x-r-and-x-0-then-the-vectors-a-2-x-s-and-b-x-s-x-include-an-acute-angle-if</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13276/if-a-and-8594-i-j-k-b-and-8594-i-j-2-k-and-c-and-8594-x-i-x-2-j-k-and-if-the-vec</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13277/let-u-and-8594-2-i-j-and-v-and-8594-3-i-5-j-consider-three-points-p-q-and-r-havi</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13278/the-point-of-intersection-of-the-lines-joining-points-i-2-j-2-i-j-and-i-2-i-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13279/the-value-of-a-and-8594-and-215-b-and-8594-2-a-and-8594-and-183-b-and-8594-2-2-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13280/let-a-and-8594-i-j-b-and-8594-j-k-and-c-and-8594-k-i-if-d-and-8594-is-a-unit-vec</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13281/let-u-and-8594-and-v-and-8594-be-two-non-zero-vectors-with-the-intermediate-angl</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13282/given-a-and-8594-3-i-j-b-and-8594-2-i-j-3-k-and-b-and-8594-b-1-and-8594-b-2-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13283/let-u-and-8594-2-i-3-j-k-v-and-8594-3-i-2-j-and-w-and-8594-i-j-4-k-then-which-of</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13284/if-a-and-8594-1-1-0-b-and-8594-1-1-1-then-unit-vector-in-the-plane-of-a-and-8594</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13285/which-of-the-following-vector-is-equally-inclined-with-the-coordinate-axes</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13286/if-i-4-j-3-k-i-2-j-3-k-3-i-2-j-k-are-position-vectors-of-a-b-c-respectively-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13287/if-a-and-8594-and-b-and-8594-are-two-vectors-such-that-a-and-8594-and-183-b-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13288/let-a-and-8594-b-and-8594-c-and-8594-be-three-unit-vectors-and-a-and-8594-and-18</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13289/let-x-y-are-real-numbers-if-a-and-8594-sin-x-i-sin-y-j-and-b-and-8594-cos-x-i-co</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13290/if-the-points-2-4-1-3-6-1-and-4-5-1-are-three-consecutive-vertices-of-a-parallel</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13291/a-vector-makes-equal-angles-and-945-with-x-and-y-axes-and-90-and-176-with-z-axis</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13292/if-d-e-and-f-are-respectively-mid-points-of-a-b-a-c-and-b-c-in-and-8710-a-b-c-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13293/if-the-volume-of-the-parallelopiped-formed-by-the-vectors-i-a-j-k-j-a-k-and-a-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13294/if-a-and-8594-3-2-k-b-and-8594-2-i-2-j-k-2-then-angle-between-a-and-8594-b-and-8</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13295/if-a-and-8594-i-and-729-j-and-729-k-b-and-8594-i-and-729-3-j-and-729-5-k-and-c-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13296/if-a-and-8594-2-i-j-3-k-b-and-8594-i-3-j-k-and-c-and-8594-3-i-j-2-k-then-the-val</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13297/if-a-and-8594-and-b-and-8594-are-two-vectors-such-that-a-and-8594-2-b-and-8594-3</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13298/let-u-v-and-w-be-non-coplanar-vectors-then-the-points-corresponding-to-which-of</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13299/let-a-b-c-be-a-triangle-let-u-a-b-and-v-a-c-if-d-is-a-middle-point-of-b-c-then-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13300/a-vector-in-the-direction-of-v-2-i-3-j-k-with-magnitude-7-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13301/if-is-the-angle-of-a-regular-pentagon-then-i-j-k</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13302/if-a-b-c-are-unit-vectors-such-that-a-b-a-c-0-and-the-angle-between-b-and-c-is-3</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13303/if-a-b-c-are-unit-vectors-such-that-a-b-3-c-0-then-the-angle-between-a-and-b-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13304/let-u-and-v-be-two-vectors-then-u-v-u-v-if-and-only-if</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13305/the-area-of-the-parallelogram-whose-diagonals-are-2-i-j-k-and-i-3-j-k-is-equal-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13306/number-of-unit-vectors-of-the-form-a-i-b-j-c-k-where-a-b-c-and-8712-w-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13307/the-scalar-product-of-the-vector-a-and-8594-i-j-k-with-a-unit-vector-along-the-s</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13308/if-p-q-r-s-t-is-a-pentagon-then-the-resultant-of-forces-p-q-and-175-p-t-and-175</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13309/let-u-and-v-be-two-vectors-in-r-2-if-u-v-2-2-u-2-v-2-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13310/if-a-b-and-c-are-position-vectors-of-the-vertices-of-a-b-c-then-a-c-b-a-b-a-c-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13311/if-p-q-p-r-and-p-q-p-r-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13312/if-a-and-b-are-two-unit-vectors-and-is-the-angle-between-them-then-the-unit-vect</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13313/if-a-b-c-are-coterminous-edges-of-a-parallelopiped-such-that-array-lll-a-a-and-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13314/if-a-b-and-c-are-three-vectors-such-that-a-b-c-b-c-a-and-a-b-c-are-mutually-perp</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13315/let-a-b-c-d-e-f-be-a-regular-hexagon-with-the-vertices-a-b-c-d-e-f-counterclock</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13316/if-p-3-i-5-j-k-and-q-i-2-j-3-k-are-two-sides-of-a-triangle-then-its-area-is-equa</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13317/given-a-b-c-such-that-a-is-2-i-j-k-b-is-i-3-j-5-k-and-c-is-3-i-4-j-4-k-then-a-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13318/if-a-2-i-3-j-4-k-b-i-4-j-2-k-c-3-i-j-4-k-then-array-lll-a-b-and-b-c-c-a-array</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13319/if-a-and-b-are-unit-vectors-such-that-a-b-is-also-a-unit-vector-then-the-angle-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13320/let-u-2-i-2-j-k-and-v-i-2-j-2-k-then-angle-between-u-and-v-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13321/for-a-right-angled-triangle-having-the-lengths-of-two-sides-as-2-2-and-5-find-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13322/let-u-i-2-j-and-v-3-i-5-j-consider-three-points-p-q-and-r-having-position-vector</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13323/if-the-magnitude-of-the-vector-product-of-the-vector-i-j-k-with-a-unit-vector-al</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/13344/a-b-c-is-a-right-angled-triangle-in-which-a-b-b-c-a-c-b-c-if-the-position-vector</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13345/if-are-distinct-real-numbers-and-0-then-the-points-with-position-vectors-i-j-k-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/13349/for-a-non-zero-real-number-x-if-the-points-with-position-vectors-x-u-i-x-j-x-k-x</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13350/if-p-is-a-point-lying-on-the-line-passing-through-the-point-a-i-j-3-k-and-parall</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/13356/if-a-and-175-b-and-175-c-and-175-are-non-zero-non-collinear-vectors-and-a-and-17</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/13380/if-a-b-c-are-three-non-coplanar-vectors-then-match-the-items-of-list-i-with-thos</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13381/a-b-and-c-are-three-unit-vectors-such-that-no-two-of-them-are-collinear-if-b-2-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13382/if-a-and-b-are-two-unit-vectors-such-that-a-b-is-also-a-unit-vector-then-a-b-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/13398/let-a-b-and-c-be-three-non-coplanar-vectors-the-vector-equation-of-a-line-which</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13399/in-p-q-r-m-is-the-mid-point-of-q-r-and-c-is-the-mid-point-of-p-m-if-q-c-when-ext</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13400/if-a-i-2-j-3-k-b-2-i-j-k-c-i-3-j-2-k-then-a-b-b-c-b-c-c-a-c-a-a-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13401/if-a-i-2-j-3-k-b-i-2-j-k-c-i-2-j-2-k-n-is-perpendicular-to-both-a-and-b-and-is-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13402/if-a-b-and-c-are-mutually-perpendicular-vectors-of-the-same-magnitude-then-the-c</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13403/it-a-b-and-c-are-non-coplanar-vectors-and-the-four-points-with-position-vectors</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13404/in-abc-if-s-is-the-circumcentre-and-o-is-the-orthocentre-then-o-a-o-b-o-c</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13405/let-a-b-and-c-be-non-coplanar-vectors-if-p-q-r-and-s-are-four-points-with-positi</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13406/let-a-b-c-be-such-that-a-o-b-o-a-c-b-and-b-c-a-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13407/if-a-b-and-c-are-vectors-such-that-a-b-2-c-3-1-b-and-c-are-perpendicular-and-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13408/if-the-vectors-p-q-and-r-are-such-that-q-r-r-p-3-r-then-p-q-q-r-r-p</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13409/if-p-q-r-are-three-mutually-perpendicular-vectors-of-equal-magnitude-and-if-a-ve</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13410/if-a-b-and-c-are-non-zero-vectors-such-that-a-and-b-are-not-perpendicular-to-eac</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13411/the-triad-x-y-z-of-real-number-such-that-3-i-j-2-k-2-i-3-j-k-x-i-2-j-2-k-y-2-i-j</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13412/if-the-volume-of-the-tetrahedron-formed-by-the-coterminous-edges-a-b-and-c-is-4</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13413/if-a-b-are-two-non-parallel-unit-vectors-and-the-vector-a-b-bisects-the-internal</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13414/if-oa-3-i-j-k-ab-2-6-and-the-direction-ratios-of-ab-are-1-1-2-then-ob</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13415/let-a-b-c-be-three-vectors-such-that-a-c-1-b-4-b-c-15-if-a-b-2-c-then-the-value</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13416/let-u-v-w-be-vectors-such-that-u-1-v-2-w-3-if-the-projection-of-v-on-u-is-equal</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13417/if-the-vectors-a-b-c-satisfy-the-condition-a-c-b-c-then-b-a-c-a-b-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13418/for-two-given-vectors-a-and-b-if-the-vectors-a-b-are-such-that-a-b-a-a-b-b-and-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13419/a-point-c-with-position-vector-3-a-4-b-5-c-3-where-a-b-and-c-are-non-coplanar-ve</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13420/the-line-passing-through-the-point-2-a-b-and-parallel-to-the-vector-b-c-and-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13421/if-a-and-b-are-not-perpendicular-to-each-other-r-a-b-a-and-r-c-0-then-r</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13422/if-the-two-diagonals-of-a-parallelogram-are-i-2-j-3-k-and-2-i-j-2-k-then-the-are</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13423/the-minimum-volume-of-the-parallalopiped-formed-by-the-vectors-i-a-j-k-j-a-k-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13424/if-a-2-i-j-3-k-b-i-2-j-k-c-i-j-4-k-d-i-j-p-k-where-p-is-a-positive-real-number-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13425/a-vector-of-magnitude-51-which-makes-equal-angles-with-the-vectors-a-1-3-i-2-j-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13426/a-unit-vector-orthogonal-to-the-vector-3-i-4-j-5-k-and-coplanar-with-the-vectors</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13427/let-a-and-b-be-two-non-collinear-unit-vectors-if-u-a-a-b-b-and-v-a-b-then-v</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13428/if-a-4-7-8-b-2-3-4-and-c-2-5-7-are-the-position-vectors-of-the-vertices-of-a-tri</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13429/given-a-2-i-j-2-k-and-b-i-j-if-c-is-a-vector-such-that-a-c-c-c-a-2-2-and-the-ang</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13430/if-in-a-right-angled-triangle-abc-the-hypotenuse-a-b-p-then-a-b-a-c-b-c-b-a-c-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13431/let-a-2-i-j-k-and-b-i-3-k-if-c-is-a-unit-vector-then-the-maximum-value-of-array</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13432/let-a-4-i-5-j-k-b-i-4-j-5-k-c-3-i-j-k-and-let-be-a-vector-perpendicular-to-both</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13433/if-a-2-i-3-j-5-k-b-m-i-n-j-12-k-and-a-b-0-then-m-n-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13434/if-a-3-b-4-and-the-angle-between-a-and-b-is-120-then-4-a-3-b-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13435/if-a-b-c-are-non-zero-vectors-such-that-a-b-c-1-3-b-c-a-c-a-and-is-the-angle-bet</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13436/if-a-b-c-0-and-atleast-one-of-the-scalars-a-b-c-is-non-zero-then-the-vectors-are</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13437/if-a-b-and-c-are-unit-vectors-such-that-a-b-c-0-then-the-a-b-b-c-c-a-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13438/if-a-2-i-k-b-i-j-k-c-4-i-3-j-7-k-then-the-vector-r-satisfying-r-b-c-b-and-r-a-0</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13439/if-a-b-and-c-are-three-vectors-such-that-a-1-b-2-c-3-and-a-b-b-c-c-a-0-then-a-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13440/if-a-b-b-c-c-a-a-b-c-2-then-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13441/the-shortest-distance-between-the-skew-lines-r-i-2-j-3-k-t-i-3-j-2-k-and-r-4-i-5</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13442/if-x-y-and-z-are-non-zero-real-numbers-and-a-x-i-2-j-b-y-j-3-k-and-c-x-i-y-j-z-j</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13443/if-a-b-and-c-are-vectors-with-magnitudes-2-3-and-4-respectively-then-the-best-up</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13444/the-angle-between-the-lines-r-2-i-3-j-k-i-4-j-3-k-and-r-i-j-2-k-i-2-j-3-k-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13445/if-a-b-and-c-are-non-coplanar-vectors-and-if-d-is-such-that-d-1-x-a-b-c-and-d-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13446/three-non-zero-non-collinear-vectors-a-b-and-c-are-such-that-a-3-b-is-collinear</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13447/the-points-whose-position-vectors-are-2-i-3-j-4-k-3-i-4-j-2-k-and-4-i-2-j-3-k-ar</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13448/if-a-0-b-0-c-0-a-b-0-and-b-c-0-then-a-c-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13449/a-unit-vector-coplanar-with-i-j-3-k-and-i-3-j-k-and-perpendicular-to-i-j-k-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13450/if-a-and-b-are-two-non-zero-perpendicular-vectors-then-a-vector-y-satisfying-equ</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13451/a-i-j-2-k-a-i-j-2-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13452/let-a-b-and-c-be-three-non-coplanar-vectors-and-let-p-q-and-r-be-the-vectors-def</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13453/the-point-if-intersection-of-the-lines-l-r-t-i-6-j-2-k-t-i-2-j-k-l-r-u-4-j-k-u-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13454/the-vectors-a-b-3-i-2-j-2-k-and-b-c-i-2-k-are-the-adjacent-sides-of-a-parallelog</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13455/if-p-th-q-th-r-th-terms-of-a-geometric-progression-are-the-positive-numbers-a-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13456/if-the-vectors-i-2-x-j-3-y-k-and-i-3-x-j-2-y-k-are-orthogonal-to-each-other-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13457/for-any-vector-r-i-r-i-j-r-j-k-r-k-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13458/if-the-vectors-ab-3-i-4-k-and-ac-5-i-2-j-4-k-are-the-sides-of-a-a-b-c-then-the-l</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13459/if-a-1-b-2-and-the-angle-between-a-and-b-is-120-then-a-3-b-3-a-b-2-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13460/let-v-2-i-j-k-and-w-i-3-k-if-u-is-any-unit-vector-then-the-m-59-aximum-value-of</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13461/if-three-unit-vectors-a-b-c-satisfy-a-b-c-0-then-the-angle-between-a-and-b-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13462/a-2-b-c-a-b-a-b-c-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13463/if-u-a-b-v-a-b-a-b-2-then-u-v-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13464/if-the-angle-between-the-vectors-a-2-x-2-i-4-x-j-k-and-b-7-i-2-j-x-k-is-such-tha</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13465/let-o-a-o-b-o-c-be-the-co-terminal-edges-of-a-rectangular-parallelopiped-of-volu</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13466/if-m-m-m-and-m-are-respectively-the-magnitudes-of-the-vectors-a-2-i-j-k-a-3-i-4</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13467/suppose-a-i-7-j-3-k-b-i-j-2-k-if-the-angle-between-a-and-b-is-greater-than-90-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13468/the-volume-of-the-tetrahedron-having-the-edges-i-2-j-k-i-j-k-i-j-k-as-coterminou</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13469/the-position-vectors-of-p-and-q-are-respectively-a-and-b-if-r-is-a-point-on-pq-s</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13470/if-the-points-with-position-vectors-60-i-3-j-40-i-8-j-and-a-i-52-j-are-collinear</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13471/if-the-position-vectors-of-a-b-and-c-are-respectively-2-i-j-k-i-3-j-5-k-and-3-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13472/if-a-i-j-k-b-i-j-k-c-i-j-k-and-d-i-j-k-then-observe-the-following-the-correct-ma</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13473/let-a-be-a-unit-vector-b-2-i-j-k-and-c-i-3-k-then-maximum-value-of-a-b-c-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13474/if-the-points-whose-position-vectors-are-2-i-j-k-6-i-j-2-k-and-14-i-5-j-p-k-are</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13475/the-volume-in-cubic-units-of-the-tetrahedron-with-edges-i-j-k-i-j-k-and-i-2-j-k</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/13730/a-capacitor-is-made-of-a-flat-plate-of-area-a-and-a-second-plate-of-stair-like-s</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13731/four-capacitors-marked-with-capacitances-and-break-down-voltages-are-connected-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13732/two-identical-condensers-are-joined-as-shown-in-the-figure-when-the-switch-s-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13733/four-capacitors-of-capacitances-2-f-3-f-4-f-and-x-f-are-connected-to-a-battery-o</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13734/the-plates-of-a-parallel-plate-capacitor-are-charged-upto-100-v-a-2-mm-thick-ins</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13735/in-the-circuit-shown-in-figure-if-the-point-r-is-earthed-and-point-p-is-given-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13736/four-capacitors-marked-with-capacitances-and-breakdown-voltages-are-connected-as</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13737/one-plate-of-a-parallel-plate-capacitor-is-connected-to-a-spring-as-shown-in-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13738/a-parallel-plate-capacitor-has-a-capacity-80-10-f-when-air-is-present-between-it</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13739/three-uncharged-capacitors-of-capacities-c-c-and-c-are-connected-as-shown-in-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13740/a-fully-charged-capacitor-of-capacity-c-is-discharged-through-a-small-resistance</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13741/in-the-diagram-the-area-of-each-plate-is-2-m-2-and-d-2-10-m-an-electric-charge-o</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13742/in-the-circuit-given-the-charge-on-the-capacitor-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13743/the-equivalent-capacitance-between-the-points-a-and-b-of-the-network-shown-in-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13744/four-metallic-plates-a-b-c-and-d-of-same-size-with-same-separations-between-them</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13745/a-capacitor-of-capacitance-20-f-is-charged-by-a-battery-of-potential-24-3-v-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13746/five-identical-conducting-plates-each-of-face-area-a-are-placed-parallel-to-each</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13747/the-energy-of-a-parallel-plate-capacitor-when-connected-to-a-battery-is-e-with-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13748/two-metal-plates-each-of-area-a-form-a-parallel-plate-capacitor-with-air-in-betw</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13749/a-parallel-plate-capacitor-has-a-capacity-80-10-f-when-air-is-present-between-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13750/a-fully-charged-capacitor-has-a-capacitance-c-it-is-discharged-through-a-small-c</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13751/two-identical-condensers-m-and-n-are-connected-in-series-with-a-battery-the-spac</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13752/the-potential-difference-between-two-parallel-plates-is-10-4-v-if-the-plates-are</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13753/two-capacitors-of-capacities-1-f-and-c-f-are-connected-in-series-and-the-combina</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13754/a-capacitor-of-capacity-0-1-f-connected-in-series-to-a-resistor-of-10-m-is-charg</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13755/a-oil-drop-having-a-mass-4-8-10-g-and-charge-2-4-10-c-stands-still-between-two-c</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13756/a-4-f-capacitor-is-charged-by-a-200-v-battery-it-is-then-disconnected-from-the-s</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13757/the-plates-of-a-parallel-plate-capacitor-are-charged-upto-200-volts-a-dielectirc</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13758/a-parallel-plate-capacitor-of-capacity-c-is-charged-to-a-potential-v-i-the-energ</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13759/a-parallel-plate-capacitor-of-capacity-100-f-is-charged-by-a-battery-of-50-volts</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13760/the-time-in-seconds-required-to-produce-a-potential-difference-of-20-v-across-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13761/a-20-f-capacitor-is-charged-to-5-v-and-isolated-it-is-then-connected-in-parallel</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13762/a-body-of-capacity-4-f-is-charged-to-80-v-and-another-body-of-capacity-6-f-is-ch</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13763/a-body-falls-freely-on-to-a-hard-horizontal-surface-if-the-coefficient-of-restit</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13764/two-bodies-of-masses-m-and-4m-initially-at-rest-start-moving-towards-each-other</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13765/a-body-of-mass-2-kg-is-moving-towards-north-with-a-velocity-of-20-m-s-and-anothe</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13766/a-body-of-mass-m-moving-along-a-straight-line-collides-with-a-stationary-body-of</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13767/a-disc-of-mass-0-2-kg-is-kept-floating-in-air-without-falling-by-vertically-firi</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13768/a-body-moving-along-a-straight-line-collides-another-body-of-same-mass-moving-in</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13769/the-coordinates-of-the-centre-of-mass-of-a-uniform-l-shaped-plate-of-mass-3-kg-s</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13770/two-balls-each-of-mass-250-g-moving-in-opposite-directions-each-with-a-speed-16</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13771/three-blocks-a-b-and-c-are-arranged-as-shown-in-the-figure-such-that-the-distanc</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13772/the-linear-momentum-of-a-body-of-mass-8-kg-is-24-kg-m-s-if-a-constant-force-of-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13773/a-block-of-mass-10-kg-moving-with-a-speed-of-5-i-m-s-on-a-frictionless-horizonta</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13774/a-steel-sphere-of-radius-1-2-cm-collides-a-second-steel-sphere-at-rest-if-the-co</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13775/if-two-bodies-of-masses-2-kg-and-3-kg-are-moving-at-right-angles-with-velocities</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13776/a-soccer-ball-of-mass-250-g-is-moving-horizontally-to-the-left-with-a-speed-22-m</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13777/a-body-of-mass-30-kg-moving-with-a-velocity-20-ms-undergoes-one-dimensional-elas</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13778/two-blocks-of-equal-masses-are-tied-with-a-light-string-passing-over-a-massless</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13779/a-light-body-of-momentum-p-l-and-a-heavy-body-of-momentum-p-h-both-have-the-same</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13780/a-ball-falls-freely-from-rest-from-a-height-of-6-25-m-on-to-a-hard-horizontal-su</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13781/a-body-of-mass-2-kg-collides-head-on-with-another-body-of-mass-4-kg-if-the-relat</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13782/a-ball-falls-freely-from-rest-on-to-a-hard-horizontal-floor-and-repeatedly-bounc</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13783/in-an-inelastic-collision-after-collision-the-kinetic-energy</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13784/two-bodies-of-masses-12-kg-and-6-kg-are-projected-simultaneously-with-velocities</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13785/which-of-the-following-statements-regarding-centre-of-mass-is-not-true</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13786/a-particle-of-mass-10-g-is-moving-towards-east-with-a-velocity-of-10-ms-and-anot</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13787/a-freely-falling-body-has-attained-a-velocity-of-2-ms-now-if-the-weight-of-the-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13788/a-bomb-at-rest-explodes-into-three-pieces-of-equal-masses-if-two-pieces-move-per</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13789/two-particles-of-masses-1-g-and-2-g-move-towards-each-other-with-velocities-10-m</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13790/a-ball-moving-with-velocity-2-m-s-collides-head-on-with-another-stationary-ball</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13791/a-circular-plate-a-of-radius-1-5-r-is-removed-from-one-edge-of-a-uniform-circula</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13792/two-particles-of-masses-5-g-and-3-g-are-separated-by-a-distance-of-40-cm-the-cen</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13793/a-body-falls-freely-from-a-height-of-100-m-on-to-the-ground-and-rebounds-to-a-ma</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13794/a-cricket-ball-hits-the-ground-with-a-speed-of-5-m-s-making-an-angle-30-with-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13795/a-circular-portion-of-radius-r-has-been-removed-from-one-edge-of-a-circular-disc</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13796/two-wooden-blocks-of-mass-m-and-m-rest-on-a-frictionless-table-a-bullet-of-mass</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13797/masses-m-1-2-1-2-m-1-2-2-1-3-m-1-2-n-1-1-n-m-are-placed-at-x-1-2-3-n-respectivel</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13798/the-centre-of-mass-of-a-homogenous-semi-circular-plate-of-radius-r-is-located-at</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13799/ball-a-of-mass-1-kg-moving-along-a-straight-line-with-a-velocity-of-4-ms-hits-an</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13800/two-balls-a-and-b-of-masses-m-and-2-m-respectively-collide-each-other-if-the-bal</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13801/a-ball-of-mass-0-5-kg-moving-horizontally-at-10-m-s-1-strikes-a-vertical-wall-an</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13802/masses-m-1-3-n-1-n-are-placed-at-x-n-when-n-2-3-4-and-8230-and-8734-if-the-total</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13803/assertion-a-in-an-elastic-collision-of-two-billiard-balls-the-total-ke-is-conser</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13804/a-bullet-of-mass-30-g-moving-with-700-ms-collides-with-a-block-of-mass-4-kg-hang</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13805/a-body-of-mass-3-kg-is-moving-with-a-velocity-of-8-ms-collides-head-on-with-anot</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13806/what-is-the-nature-of-the-graph-between-momentum-of-a-body-and-its-kinetic-energ</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13807/a-force-time-f-t-graph-for-a-linear-motionis-shown-in-following-figure-the-segme</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13808/a-bullet-of-mass-m-is-fired-from-a-rifle-of-mass-m-if-v-be-the-velocity-of-the-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13809/in-perfectly-inelastic-collisions-the-relative-velocity-of-the-bodies</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13810/a-shell-of-mass-m-moving-with-velocity-v-suddenly-breaks-into-two-pieces-if-one</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/13812/the-coefficient-of-restitution-for-a-perfect-elastic-collision-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13813/a-ball-of-mass-3-kg-moving-with-a-speed-of-100-m-s-1-strikes-a-wall-at-an-angle</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13814/a-metal-ball-of-mass-2-kg-moving-with-a-velocity-of-36-kmph-has-a-head-on-collis</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13815/a-particle-of-mass-and-39-m-and-39-moving-with-a-velocity-and-39-v-and-39-makes</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13816/the-sum-of-moments-of-all-the-particles-in-a-system-about-its-center-of-mass-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13817/a-free-body-of-mass-8-kg-is-moving-at-2-m-s-along-a-straight-line-it-splits-into</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13818/two-objects-of-masses-m-and-m-possess-equal-kinetic-energies-if-p-and-p-are-thei</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13819/a-body-whose-momentum-is-constant-must-have-constant</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13820/a-steel-ball-of-radius-2-cm-is-at-rest-on-a-frictionless-surface-another-steel-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13821/a-bullet-of-mass-m-and-velocity-v-when-fired-at-a-sand-bag-of-mass-m-suspended-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13822/two-atoms-of-oxygen-are-located-at-r-and-r-their-centre-of-mass-is-at</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13823/a-bullet-of-mass-0-01-kg-travelling-at-a-speed-of-500-ms-strikes-a-block-of-mass</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13824/a-bomb-of-mass-9-kg-explodes-into-two-pieces-of-mass-3-kg-and-6-kg-the-velocity</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13825/when-a-moving-body-collides-with-a-stationary-body-of-n-times-its-mass-then-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13826/a-uniform-circular-disc-has-radius-r-a-square-portion-of-diagonal-r-is-cut-from</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13827/four-identical-spheres-each-of-radius-10-cm-and-equal-mass-1-kg-each-are-placed</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13828/two-balls-x-2-kg-and-y-4-kg-approach-each-other-with-equal-speeds-of-10-ms-if-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13829/in-a-rocket-fuel-burns-at-the-rate-of-1-kg-s-this-fuel-is-ejected-from-the-rocke</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13830/the-kinetic-energy-of-a-body-is-increased-by-4-times-its-momentum-will</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13831/a-bullet-strikes-against-a-wooden-block-and-is-embedded-in-it-the-nature-of-coll</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13832/a-bomb-at-rest-explodes-into-three-parts-of-equal-mass-if-the-momentum-of-two-pa</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13833/at-high-altitude-a-body-explodes-which-is-at-rest-into-two-equal-fragments-with</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13834/a-mass-m-is-in-rest-on-an-inclined-plane-of-mass-m-which-is-further-resting-on-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13835/when-two-bodies-collide-elastically-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13836/an-explosion-blows-a-stationary-rock-into-three-parts-two-parts-of-masses-1-kg-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13837/a-body-a-moving-with-momentum-p-collides-one-dimensionally-with-another-stationa</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13838/in-the-figure-shown-the-blocks-have-equal-masses-friction-mass-of-the-string-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13839/the-position-time-x-t-graph-of-a-moving-body-of-mass-2-kg-is-shown-in-the-figure</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13840/three-identical-spheres-each-of-diameter-2-3-m-are-kept-on-a-horizontal-surface</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13841/two-particles-p-and-q-each-of-mass-3-m-lie-at-rest-on-the-x-axis-at-points-a-0-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13842/a-particle-of-mass-4-m-which-is-initially-at-rest-explodes-into-three-pieces-of</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13843/a-bullet-of-mass-10-g-pierces-through-a-plate-a-of-mass-500-g-and-then-gets-embe</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13844/a-ball-moving-horizontally-with-a-velocity-2-ms-strikes-the-bob-of-a-seconds-pen</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13845/a-ball-of-mass-2-kg-collides-with-another-ball-of-mass-m-at-rest-if-the-collisio</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13846/a-moving-hydrogen-atom-makes-a-head-on-collision-with-a-stationary-hydrogen-atom</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13847/a-ball-falls-freely-from-a-height-of-180-m-on-to-a-hard-horizontal-floor-and-rep</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13848/a-circular-disc-of-radius-r-is-removed-from-one-end-of-a-bigger-circular-disc-of</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13849/a-rocket-with-an-initial-mass-m-is-going-up-with-a-constant-acceleration-a-by-ex</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13850/a-particle-of-mass-4-m-which-is-initially-at-rest-explodes-into-three-pieces-of</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13851/a-bullet-of-mass-10-g-pierces-through-a-plate-a-of-mass-500-g-and-then-gets-embe</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13852/a-canon-shell-fired-breaks-into-two-equal-parts-at-its-highest-point-if-one-part</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13853/two-particles-of-masses-in-the-ratio-1-2-are-placed-along-a-vertical-line-the-li</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13854/two-identical-balls-a-and-b-of-equal-mass-are-lying-on-a-smooth-surface-as-shown</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13855/three-circular-discs-of-same-material-and-same-thickness-of-radii-r-2-r-and-3-r</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13856/three-uniform-thin-aluminium-rods-each-of-length-2-m-form-an-equilateral-triangl</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13857/two-spheres-a-and-b-of-equal-mass-lie-at-rest-at-the-opposite-ends-of-a-diameter</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13858/a-uniform-square-plate-has-a-side-of-length-2-r-a-circular-piece-of-maximum-poss</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13859/three-identical-uniform-thin-rods-each-of-mass-m-and-length-l-are-arranged-in-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13860/a-ball-of-mass-2-g-moving-with-a-velocity-of-2-ms-collides-with-another-ball-of</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13861/a-1-kg-ball-moving-with-a-speed-of-6-ms-collides-headon-with-a-0-5-kg-ball-movin</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13862/a-ball-is-thrown-vertically-down-from-a-height-of-40-m-from-the-ground-with-an-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13863/two-smooth-and-similar-right-angled-prisms-are-arranged-on-a-smooth-horizontal-p</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13864/a-ball-p-moving-with-a-speed-of-v-ms-collides-directly-with-another-identical-ba</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13865/two-bodies-of-mass-4-kg-and-5-kg-are-moving-along-east-and-north-directions-with</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13866/a-mass-of-2-9-kg-is-suspended-from-a-string-of-length-50-cm-and-is-at-rest-anoth</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13867/choose-correct-statement-a-the-position-of-centre-of-mass-of-a-system-is-depende</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13868/a-ball-a-of-mass-m-moving-along-positive-x-direction-with-kinetic-energy-k-and-m</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13869/a-ball-is-let-fall-from-a-height-h-it-makes-n-collisions-with-the-earth-after-n</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13870/a-circular-disc-of-radius-r-is-removed-from-a-bigger-circular-disc-of-radius-2-r</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13871/a-bomb-moving-with-velocity-40-i-50-j-25-k-m-s-explodes-into-two-pieces-of-mass</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13872/a-body-of-mass-m-4-kg-moves-at-5-i-m-s-and-another-body-of-mass-m-2-kg-moves-at</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13873/a-ball-falls-from-a-height-h-and-rebounds-after-striking-the-floor-the-coefficie</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13874/a-body-of-mass-5-kg-makes-an-elastic-collision-with-another-body-at-rest-and-con</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13875/a-particle-of-mass-4-m-explodes-into-three-pieces-of-masses-m-m-and-2-m-the-equa</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13876/a-bullet-of-mass-0-02-kg-travelling-horizontally-with-velocity-250-ms-strikes-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13877/a-ball-is-dropped-from-a-height-h-on-a-floor-of-coefficient-of-restitution-e-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13878/two-particles-a-and-b-initially-at-rest-move-towards-each-other-under-mutual-for</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13879/a-rifle-of-20-kg-mass-can-fire-4-bullets-per-second-the-mass-of-each-bullet-is-3</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13880/two-bodies-of-6-kg-and-4-kg-masses-have-their-velocity-5-i-2-j-10-k-and-10-i-2-j</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13881/in-two-separate-collisions-the-coefficient-of-restitutions-e-and-e-are-in-the-ra</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13882/a-man-of-50-kg-is-standing-at-one-end-on-a-boat-of-length-25-m-and-mass-200-kg-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13883/the-centre-of-mass-of-three-particles-of-masses-1-kg-2-kg-and-3-kg-is-at-2-2-2-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13884/consider-the-following-statements-a-and-b-and-identify-the-correct-answer-a-in-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13885/at-a-given-instant-of-time-two-particles-are-having-the-position-vectors-4-i-4-j</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13886/a-2-kg-ball-moving-at-24-ms-undergoes-inelastic-head-on-collision-with-a-4-kg-ba</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13887/two-particles-of-equal-mass-have-velocities-v-4-i-and-v-4-j-ms-first-particle-ha</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13888/two-particles-having-position-vectors-r-3-i-5-j-metres-and-r-5-i-3-j-metres-are</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13889/two-objects-of-masses-200-g-and-500-g-possess-velocities-10-i-m-s-and-3-i-5-j-m</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13890/particles-of-masses-m-2-m-3-m-n-m-grams-are-placed-on-the-same-line-at-distance</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13891/a-particle-falls-from-a-height-h-upon-a-fixed-horizontal-plane-and-rebounds-if-e</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13892/the-velocities-of-three-particles-of-masses-20-g-30-g-and-50-g-are-10-i-10-j-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13893/in-amplitude-modulation-if-a-message-signal-of-5-khz-is-modulated-by-a-carrier-w</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13894/the-heights-of-tansmitting-and-receiving-antennas-are-respectively-1-20000-and-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/13895/the-layer-of-the-atmosphere-that-reflects-low-frequency-lf-electromagnetic-waves</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/14027/a-8-resistor-is-connected-to-a-battery-that-has-an-internal-resistance-of-0-2-if</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/14030/a-galvanometer-has-a-coil-of-resistance-100-showing-a-full-scale-deflection-at-5</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/19818/consider-the-gaseous-equilibrium-2-ab-2-g-2-ab-g-b-2-g-the-expression-relating-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/19842/56-g-of-nitrogen-and-8-g-of-hydrogen-gas-are-heated-in-a-closed-vessel-at-equili</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/19850/in-a-lime-kiln-to-get-higher-yield-of-co-the-measure-that-can-be-taken-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/19853/a-first-order-reaction-is-50-complete-in-30-minutes-at-300-k-and-in-10-minutes-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/19858/60-of-a-first-order-reaction-was-completed-in-60-min-then-50-of-the-same-reactio</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/19859/identify-the-correct-values-to-be-plotted-in-the-graph-the-slope-of-which-can-be</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/19862/the-initial-amount-of-2-radioactive-elements-x-and-y-is-1-g-each-and-their-half</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/19864/in-the-following-reaction-x-a-y-b-d-a-d-t-d-b-d-t-0-3010-the-relation-between-x</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/19866/the-half-life-of-a-first-order-reaction-is-p-and-its-3-4-th-life-period-is-q-p-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/19868/the-hydrogenation-of-ethyne-is-carried-out-at-600-k-the-same-reaction-when-carri</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/19869/i-and-ii-are-2-chemical-reactions-carried-out-at-tk-with-identical-pre-exponenti</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/19873/during-a-chemical-reaction-x-y-the-rates-of-reaction-starting-with-initial-conce</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/19874/choose-the-correct-statement</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/19875/when-the-temperature-of-a-reaction-a-b-c-is-increased-from-300-k-to-310-k-the-ra</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/19876/the-order-of-a-reaction-w-x-y-z-with-respect-to-w-is-3-and-with-respect-to-x-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/19877/x-2-y-is-a-first-order-reaction-where-1-0-mol-l-of-the-reactant-yields-0-4-mol-l</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/19878/two-chemical-reactions-of-the-same-order-have-equal-frequency-factor-value-their</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/19886/the-rate-of-appearance-of-bromine-is-related-to-the-disappearance-of-bromide-ion</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/19887/given-below-a-first-order-reaction-in-the-gas-phase-a-g-b-g-c-g-if-the-initial-p</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/19888/for-the-reaction-a-3-b-2-c-d-the-concentration-of-a-changes-from-0-0150-to-0-012</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/19890/the-activation-energy-for-the-reaction-a-b-c-at-a-temperature-tk-was-0-04606-rt</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/19897/the-rate-constant-for-the-reaction-a-b-c-at-500-k-is-given-as-0-004-s-at-what-te</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/19899/given-below-are-4-graphs-a-b-c-and-d-identify-the-2-graphs-that-represent-a-zero</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/25950/let-1-60-61-1-62-63-1-118-119-then-the-value-of-cosec-1-2-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/25959/for-any-two-points-m-and-n-in-the-x-y-plane-let-m-n-denote-the-vector-from-m-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/25972/consider-the-cube-in-the-first-octant-with-sides-o-p-o-q-and-or-of-length-1-alon</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/32928/let-f-x-be-a-polynomial-of-degree-6-in-x-in-which-the-coefficient-of-x-6-is-unit</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/32929/for-which-of-the-following-curves-the-line-x-3-y-2-3-is-the-tangent-at-the-point</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/32932/if-the-area-of-the-triangle-formed-by-the-x-axis-the-normal-and-the-tangent-to-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/32933/the-function-f-x-4-x-3-3-x-2-6-2-sin-x-2-x-1-cos-x</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/32935/the-minimum-value-of-and-945-for-which-the-equation-4-sin-x-1-1-sin-x-and-945-ha</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/32936/the-set-of-all-real-values-and-955-for-which-the-function-f-x-1-cos-2-x-and-955</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/32937/for-all-twice-differentiable-functions-f-r-and-8594-r-with-f-0-f-1-f-and-39-0-0</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/32938/if-the-tangent-to-the-curve-y-f-x-x-log-e-x-x-and-62-0-at-a-point-c-f-c-is-paral</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/32940/let-a-d-and-b-c-be-two-vertical-poles-at-a-and-160-and-and-160-b-respectively-on</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/32941/if-x-1-is-a-critical-point-of-the-function-f-x-3-x-2-a-x-2-a-e-x-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/32942/which-of-the-following-points-lies-on-the-tangent-to-the-curve-x-4-e-y-2-y-1-3-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/32944/the-area-in-sq-units-of-the-largest-rectangle-a-b-c-d-whose-vertices-a-and-b-lie</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/32945/let-f-be-a-twice-differentiable-function-on-1-6-if-f-2-8-f-and-39-2-5-f-and-39-x</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/32946/suppose-f-x-is-a-polynomial-of-degree-four-having-critical-points-at-1-0-1-if-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/32949/the-function-f-x-3-x-7-x-2-3-x-and-8712-r-is-increasing-for-all-x-lying-in</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/33611/let-a-b-be-a-chord-of-length-12-of-the-circle-x-2-2-y-1-2-169-4-if-tangents-draw</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33612/let-a-line-l-pass-through-the-point-of-intersection-of-the-lines-b-x-10-y-8-0-an</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33613/let-the-mirror-image-of-a-circle-c-1-x-2-y-2-2-x-6-y-and-945-0-in-line-y-x-1-be</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33614/let-the-tangents-at-two-points-a-and-b-on-the-circle-x-2-y-2-4-x-3-0-meet-at-ori</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33615/let-c-be-the-centre-of-the-circle-x-2-y-2-x-2-y-11-4-and-p-be-a-point-on-the-cir</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33616/a-circle-c-1-passes-through-the-origin-o-and-has-diameter-4-on-the-positive-x-ax</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33617/if-the-circle-x-2-y-2-2-g-x-6-y-19-c-0-g-c-and-8712-and-8477-passes-through-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33618/let-the-abscissae-of-the-two-points-p-and-q-on-a-circle-be-the-roots-of-x-2-4-x</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33619/a-point-p-moves-so-that-the-sum-of-squares-of-its-distances-from-the-points-1-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33620/if-the-circles-x-2-y-2-6-x-8-y-16-0-and-x-2-y-2-2-3-3-x-2-4-6-y-k-6-3-8-6-k-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33621/let-the-locus-of-the-centre-and-945-and-946-and-946-and-62-0-of-the-circle-which</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33622/let-a-triangle-a-b-c-be-inscribed-in-the-circle-x-2-2-x-y-y-2-0-such-that-and-87</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33623/let-the-tangent-to-the-circle-c-1-x-2-y-2-2-at-the-point-m-1-1-intersect-the-cir</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33624/if-one-of-the-diameters-of-the-circle-x-2-y-2-2-2-x-6-2-y-14-0-is-a-chord-of-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33625/if-the-tangents-drawn-at-the-point-o-0-0-and-p-1-5-2-on-the-circle-x-2-y-2-2-x-4</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33626/let-the-lines-y-2-x-11-7-7-and-2-y-x-2-11-6-7-be-normal-to-a-circle-c-x-h-2-y-k</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33627/the-set-of-values-of-k-for-which-the-circle-c-4-x-2-4-y-2-12-x-8-y-k-0-lies-insi</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33628/let-a-circle-c-of-radius-5-lie-below-the-x-axis-the-line-l-1-4-x-3-y-2-passes-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33629/a-rectangle-r-with-end-points-of-the-one-of-its-sides-as-1-2-and-3-6-is-inscribe</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33630/let-c-be-a-circle-passing-through-the-points-a-2-1-and-b-3-4-the-line-segment-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33631/a-circle-touches-both-the-y-axis-and-the-line-x-y-0-then-the-locus-of-its-center</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33632/let-a-circle-c-touch-the-lines-l-1-4-x-3-y-k-1-0-and-l-2-4-x-3-y-k-2-0-k-1-k-2-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33633/let-the-abscissae-of-the-two-points-p-and-q-be-the-roots-of-2-x-2-r-x-p-0-and-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33634/let-a-circle-c-x-h-2-y-k-2-r-2-k-and-62-0-touch-the-x-axis-at-1-0-if-the-line-x</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33635/let-b-be-the-centre-of-the-circle-x-2-y-2-2-x-4-y-1-0-let-the-tangents-at-two-po</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33636/if-the-variable-line-3-x-4-y-and-945-lies-between-the-two-circles-x-1-2-y-1-2-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33637/two-circles-each-of-radius-5-units-touch-each-other-at-the-point-1-2-if-the-equa</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33638/let-the-equation-x-2-y-2-p-x-1-p-y-5-0-represent-circles-of-varying-radius-r-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33639/a-circle-c-touches-the-line-x-2-y-at-the-point-2-1-and-intersects-the-circle-c-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33640/the-locus-of-a-point-which-moves-such-that-the-sum-of-squares-of-its-distances-f</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33641/consider-a-circle-c-which-touches-the-y-axis-at-0-6-and-cuts-off-an-intercept-6</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33642/two-tangents-are-drawn-from-the-point-p-1-1-to-the-circle-x-2-y-2-2-x-6-y-6-0-if</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33643/let-p-and-q-be-two-distinct-points-on-a-circle-which-has-center-at-c-2-3-and-whi</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33644/let-a-x-y-and-8712-r-and-215-r-and-8739-2-x-2-2-y-2-2-x-2-y-1-b-x-y-and-8712-r-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33645/let-the-circle-s-36-x-2-36-y-2-108-x-120-y-c-0-be-such-that-it-neither-intersect</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33646/let-r-1-and-r-2-be-the-radii-of-the-largest-and-smallest-circles-respectively-wh</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33647/let-s-1-x-2-y-2-9-and-s-2-x-2-2-y-2-1-then-the-locus-of-center-of-a-variable-cir</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33648/choose-the-correct-statement-about-two-circles-whose-equations-are-given-below-x</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33649/for-the-four-circles-m-n-o-and-p-following-four-equations-are-given-circle-m-x-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33650/two-tangents-are-drawn-from-a-point-p-to-the-circle-x-2-y-2-2-x-4-y-4-0-such-tha</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33651/let-the-tangent-to-the-circle-x-2-y-2-25-at-the-point-r-3-4-meet-x-axis-and-y-ax</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33652/the-line-2-x-y-1-0-is-a-tangent-to-the-circle-at-the-point-2-5-and-the-centre-of</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33653/choose-the-incorrect-statement-about-the-two-circles-whose-equations-are-given-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33654/the-minimum-distance-between-any-two-points-p-1-and-p-2-while-considering-point</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33655/let-the-lengths-of-intercepts-on-x-axis-and-y-axis-made-by-the-circle-x-2-y-2-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33656/let-a-b-c-d-be-a-square-of-side-of-unit-length-let-a-circle-c-1-centered-at-a-wi</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33657/if-the-locus-of-the-mid-point-of-the-line-segment-from-the-point-3-2-to-a-point</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33658/let-a-1-4-and-b-1-5-be-two-points-let-p-be-a-point-on-the-circle-x-1-2-y-1-2-1-s</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33659/in-the-circle-given-below-let-o-a-1-unit-o-b-13-unit-and-p-q-and-8869-o-b-then-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33660/if-one-of-the-diameters-of-the-circle-x-2-y-2-2-x-6-y-6-0-is-a-chord-of-another</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33661/if-the-length-of-the-chord-of-the-circle-x-2-y-2-r-2-r-and-62-0-along-the-line-y</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33662/the-circle-passing-through-the-intersection-of-the-circles-x-2-y-2-6-x-0-and-x-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33663/the-diameter-of-the-circle-whose-centre-lies-on-the-line-x-y-2-in-the-first-quad</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33664/the-numbers-of-integral-values-of-k-for-which-the-line-3-x-4-y-k-intersects-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33665/a-circle-touches-the-y-axis-at-the-point-0-4-and-passes-through-the-point-2-0-wh</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33666/if-a-line-y-m-x-c-is-a-tangent-to-the-circle-x-3-2-y-2-1-and-it-is-perpendicular</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33667/let-the-tangents-drawn-from-the-origin-to-the-circle-x-2-y-2-8-x-4-y-16-0-touch</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33668/a-circle-touching-the-x-axis-at-3-0-and-making-an-intercept-of-length-8-on-the-y</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33669/if-the-angle-of-intersection-at-a-point-where-the-two-circles-with-radii-5-c-m-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33670/the-locus-of-the-centres-of-the-circles-which-touch-the-circle-x-2-y-2-1-externa</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33671/the-line-x-y-touches-a-circle-at-the-point-1-1-if-the-circle-also-passes-through</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33672/if-the-circles-x-2-y-2-5-k-x-2-y-k-0-and-2-x-2-y-2-2-k-x-3-y-1-0-k-and-8712-r-in</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33673/a-rectangle-is-inscribed-in-a-circle-with-a-diameter-lying-along-the-line-3-y-x</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33674/the-common-tangent-to-the-circles-x-2-y-2-4-and-x-2-y-2-6-x-8-y-24-0-also-passes</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33675/if-a-tangent-to-the-circle-x-2-y-2-1-intersects-the-coordinate-axes-at-distinct</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33676/the-tangent-and-the-normal-lines-at-the-point-3-and-8201-1-to-the-circle-x-2-y-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33677/the-sum-of-the-squares-of-the-lengths-of-the-chords-intercepted-on-the-circle-x</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/33679/let-c-1-and-c-2-be-the-centres-of-the-circles-x-2-y-2-2-x-2-y-2-0-and-x-2-y-2-6</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33680/if-a-variable-line-3-x-4-y-and-955-0-is-such-that-the-two-circles-x-2-y-2-2-x-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33681/a-circle-cuts-a-chord-of-length-4-a-on-the-x-axis-and-passes-through-a-point-on</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33682/a-square-is-inscribed-in-the-circle-x-y-6-x-8-y-103-0-with-its-sides-parallel-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33683/two-circles-with-equal-radii-are-intersecting-at-the-points-0-1-and-0-1-the-tang</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33684/the-straight-line-x-2-y-1-meets-the-coordinate-axes-at-a-and-b-a-circle-is-drawn</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33685/if-the-area-of-an-equilateral-triangle-inscribed-in-the-circle-x-2-y-2-10-x-12-y</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/33687/if-the-circles-x-2-y-2-16-x-20-y-164-r-2-and-8201-and-x-4-2-y-7-2-36-intersect-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33688/three-circles-of-radii-a-b-c-a-and-60-b-and-60-c-touch-each-other-externally-if</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33689/if-a-circle-c-whose-radius-is-3-touches-externally-the-circle-x-2-y-2-2-x-4-y-4</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33690/the-tangent-to-the-circle-c-x-2-y-2-2-x-1-0-at-the-point-2-1-cuts-off-a-chord-of</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33691/a-circle-passes-through-the-points-2-3-and-4-5-if-its-centre-lies-on-the-line-y</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33692/a-circle-passes-through-the-points-2-3-and-4-5-if-its-centre-lies-on-the-line-y</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33693/a-line-drawn-through-the-point-p-4-7-cuts-the-circle-x-2-y-2-9-at-the-points-a-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33694/if-two-parallel-chords-of-a-circle-having-diameter-4-units-lie-on-the-opposite-s</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33695/if-the-common-tangents-to-the-parabola-x-2-4-y-and-the-circle-x-2-y-2-4-intersec</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33696/if-a-point-p-0-2-and-q-is-any-point-on-the-circle-x-2-y-2-5-x-y-5-0-then-the-max</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33697/the-radius-of-a-circle-having-minimum-area-which-touches-the-curve-y-4-x-2-and-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33698/equation-of-the-tangent-to-the-circle-at-the-point-1-1-whose-center-is-the-point</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33699/a-circle-passes-through-2-4-and-touches-the-y-axis-at-0-2-which-one-of-the-follo</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33700/the-centres-of-those-circles-which-touch-the-circle-x-2-y-2-8-x-8-y-4-0-external</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33701/if-one-of-the-diameters-of-the-circle-given-by-the-equation-x-2-y-2-4-x-6-y-12-0</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33702/if-a-circle-passing-through-the-point-1-0-touches-y-axis-at-0-2-then-the-x-inter</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33703/if-the-incentre-of-an-equilateral-triangle-is-1-1-and-the-equation-of-its-one-si</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33704/if-y-3-x-0-is-the-equation-of-a-chord-of-the-circle-x-2-y-2-30-x-0-then-the-equa</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33705/let-the-tangents-drawn-to-the-circle-x-2-y-2-16-from-the-point-p-0-h-meet-the-x</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33706/the-number-of-common-tangents-to-the-circles-x-2-y-2-4-x-6-y-1-2-0-and-x-2-y-2-6</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33707/the-equation-of-the-circle-described-on-the-chord-3-x-and-8289-y-and-8289-5-0-of</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33708/for-the-two-circles-x-2-y-2-16-and-x-2-y-2-2-y-0-there-is-are</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33709/the-set-of-all-real-values-of-for-which-exactly-two-common-tangents-can-be-drawn</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33710/let-l-be-the-length-of-the-common-chord-of-the-curves-x-2-y-2-9-and-y-2-8-x-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33711/if-the-point-1-4-lies-inside-the-circle-x-2-y-2-6-x-10-y-p-0-and-the-circle-does</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33712/let-c-be-the-circle-with-center-at-1-1-and-radius-1-if-t-is-the-circle-centered</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33713/statement-1-the-only-circle-having-radius-10-and-a-diameter-along-line-2-x-y-5-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33714/if-a-circle-of-unit-radius-is-divided-into-two-parts-by-an-arc-of-another-circle</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33715/if-the-circle-x-2-y-2-6-x-8-y-25-a-2-0-touches-the-axis-of-x-then-a-equals</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33716/if-a-circle-c-passing-through-4-0-touches-the-circle-x-2-y-2-4-x-6-y-12-0-extern</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33717/if-each-of-the-lines-5-x-8-y-13-and-4-x-y-3-contains-a-diameter-of-the-circle-x</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33718/the-circle-passing-through-1-2-and-touching-the-axis-of-x-at-3-0-also-passes-thr</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33719/given-a-circle-2-x-2-2-y-2-5-and-a-parabola-y-2-4-5-x-statement-i-an-equation-of</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33720/the-number-of-common-tangents-of-the-circles-given-by-x-2-y-2-8-x-2-y-1-0-and-x</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33721/if-the-line-y-m-x-1-meets-the-circle-x-2-y-2-3-x-0-in-two-points-equidistant-fro</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33722/the-equation-of-the-circle-passing-through-the-point-1-2-and-through-the-points</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33723/the-length-of-the-diameter-of-the-circle-which-touches-the-x-axis-at-the-point-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33724/the-two-circles-x-2-y-2-a-x-and-x-2-y-2-c-2-c-0-touch-each-other-if</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33725/the-circle-x-2-y-2-4-x-8-y-5-intersects-the-line-3-x-4-y-m-at-two-distinct-point</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33726/if-p-and-q-are-the-points-of-intersection-of-the-circles-x-2-y-2-3-x-7-y-2-p-5-0</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33727/the-point-diametrically-opposite-to-the-point-p-1-0-on-the-circle-x-2-y-2-2-x-4</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33728/consider-a-family-of-circles-which-are-passing-through-the-point-1-1-and-are-tan</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33729/if-the-lines-3-x-4-y-7-0-and-2-x-3-y-5-0-are-two-diameters-of-a-circle-of-area-4</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33730/let-c-be-the-circle-with-centre-0-0-and-radius-3-units-the-equation-of-the-locus</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33731/if-the-circles-x-2-y-2-2-a-x-c-y-a-0-and-x-2-y-2-3-a-x-d-y-1-0-intersect-in-two</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33732/a-circle-touches-the-x-axis-and-also-touches-the-circle-with-centre-at-0-3-and-r</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33733/if-a-circle-passes-through-the-point-a-b-and-cuts-the-circle-x-2-y-2-p-2-orthogo</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33734/if-the-pair-of-lines-a-x-2-2-a-b-x-y-b-y-2-0-lie-along-diameters-of-a-circle-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33735/if-a-circle-passes-through-the-point-a-b-and-cuts-the-circle-x-2-y-2-4-orthogona</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33736/if-the-lines-2-x-3-y-1-0-and-3-x-y-4-0-lie-along-diameters-of-a-circle-of-circum</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33737/the-intercept-on-the-line-y-x-by-the-circle-x-2-y-2-2-x-0-is-a-b-equation-of-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33738/if-the-two-circles-x-1-2-y-3-2-r-2-and-x-2-y-2-8-x-2-y-8-0-intersect-in-two-dist</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33739/the-lines-2-x-3-y-5-and-3-x-4-y-7-are-diameters-of-a-circle-having-area-as-154-s</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33740/locus-of-mid-point-of-the-portion-between-the-axes-of-x-y-p-where-p-is-constant</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33741/if-the-chord-y-m-x-1-of-the-circle-x-2-y-2-1-subtends-an-angle-of-measure-45-0-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33742/the-centres-of-a-set-of-circles-each-of-radius-3-lie-on-the-circle-x-2-y-2-25-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33743/the-centre-of-the-circle-passing-through-0-0-and-1-0-and-touching-the-circle-x-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33744/two-common-tangents-to-the-circle-x-2-y-2-2-a-2-and-parabola-y-2-8-a-x-are</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33745/the-number-of-values-of-z-c-satisfying-the-equations-z-4-8i-10-and-z-3-5i-z-5-11</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33746/let-s-z-c-z-2-6-iz-3-0-then-z-s-z-8-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33747/let-the-set-of-all-values-of-k-r-such-that-the-equation-z-z-2-i-k-2-3i-0-z-c-has</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33748/let-z-z-c-be-the-distinct-solutions-of-the-equation-z-2-4z-1-12i-0-then-z-2-z-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33749/let-s-z-c-z-2-4z-16-0-then-z-s-z-3-i-2-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33750/let-z-be-a-complex-number-such-that-z-2-z-2-and-z-3-z-i-4-then-z-2-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33751/let-the-circles-c-z-r-and-c-z-3-4i-5-z-c-be-such-that-c-lies-within-c-if-z-moves</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33752/let-x-and-y-be-real-numbers-such-that-50-2x-1-3i-y-1-2i-31-17i-i-1-then-the-valu</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33753/let-a-z-c-z-2-4-and-b-z-c-z-2-z-2-5-then-the-max-z-z-z-a-and-z-b-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33754/let-z-be-a-complex-number-such-that-z-6-5-and-z-2-6-i-5-then-the-value-of-z-3-z</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33755/let-z-1-i-1-2-i-1-3-i-1-n-i-where-i-1-if-z-44200-then-n-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33756/if-z-3-2-i-2-i-1-then-z-i-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33757/let-s-z-3-2-z-3-1-i-7-be-a-set-of-complex-numbers-then-z-s-z-1-2-5-3-i-is-equal</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33758/let-s-z-c-4-z-z-0-then-z-s-z-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33759/let-1-i-3-2-and-1-i-3-2-i-1-if-7-7-9-9-7-7-7-9-7-14-7-7-m-then-m-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33760/let-z-be-the-complex-number-satisfying-z-5-3-and-having-maximum-positive-princip</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33761/if-x-x-1-0-then-the-value-of-x-1-x-x-1-x-x-1-x-x-1-x-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33762/let-a-0-2-1-10-re-2-i-3-i-0-then-a-2-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33763/if-the-locus-of-z-c-such-that-re-z-1-2-z-i-re-z-1-2-z-i-2-is-a-circle-of-radius</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33764/among-the-statements-s1-the-set-z-c-i-z-1-and-z-i-z-i-is-purely-real-contains-ex</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33765/let-the-product-of-8-i-7-4-i-and-1-8-i-4-7-i-be-i-i-1-let-p-and-q-be-the-maximum</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33766/if-is-a-root-of-the-equation-x-2-x-1-0-and-k-1-n-k-1-k-2-20-then-n-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33767/let-a-z-c-z-2-i-3-b-z-c-re-z-i-z-2-and-s-a-b-then-z-s-z-2-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33768/if-z-z-z-c-are-the-vertices-of-an-equilateral-triangle-whose-centroid-is-z-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33769/let-z-c-be-such-that-z-2-3-i-z-2-i-2-3-i-then-the-sum-of-all-possible-values-of</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33770/let-z-be-a-complex-number-such-that-z-1-if-2-k-2-z-k-z-kz-k-r-then-the-maximum-d</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33771/let-integers-a-b-3-3-be-such-that-a-b-0-then-the-number-of-all-possible-ordered</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33772/let-z-8-2-i-1-and-z-2-6-i-2-z-z-c-then-the-minimum-value-of-z-z-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33773/if-i-and-i-are-the-roots-of-x-2-3-2-i-x-2-i-2-0-i-1-then-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33774/let-o-be-the-origin-the-point-a-be-z-3-2-2-i-the-point-b-z-be-such-that-3-z-z-an</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33775/if-and-are-the-roots-of-the-equation-2-z-2-3-z-2-i-0-where-i-1-then-16-re-lm-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33776/the-number-of-complex-numbers-z-satisfying-z-1-and-z-z-z-z-1-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33777/let-be-the-roots-of-the-equation-x-2-a-x-b-0-with-im-im-let-p-n-n-n-if-p-5-7-i-p</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33778/let-z-i-2-z-i-1-3-z-c-be-the-equation-of-a-circle-with-center-at-c-if-the-area-o</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33779/let-the-curve-z-1-i-z-1-i-4-z-c-divide-the-region-z-3-1-into-two-parts-of-areas</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33780/let-z-z-and-z-be-three-complex-numbers-on-the-circle-z-1-with-z-4-z-0-and-z-4-if</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33781/let-z-be-a-complex-number-such-that-the-real-part-of-z-2-i-z-2-i-is-zero-then-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33782/the-sum-of-the-square-of-the-modulus-of-the-elements-in-the-set-z-a-ib-a-b-z-z-c</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33783/the-sum-of-all-possible-values-of-2-for-which-1-i-1-2-i-is-purely-imaginary-is-e</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33784/let-z-be-a-complex-number-such-that-z-2-1-and-im-z-1-z-2-1-5-then-the-value-of-r</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33785/if-z-z-are-two-distinct-complex-number-such-that-z-2-z-1-2-z-z-2-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33786/let-s-z-c-z-5-s-z-c-im-z-1-3-i-1-3-i-0-and-s-z-c-re-z-0-then-the-area-of-the-reg</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33787/consider-the-following-two-statements-statement-i-for-any-two-non-zero-complex-n</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33788/the-area-in-sq-units-of-the-region-s-z-c-z-1-2-z-z-i-z-z-2-im-z-0-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33789/let-and-be-the-sum-and-the-product-of-all-the-non-zero-solutions-of-the-equation</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33790/if-z-is-a-complex-number-such-that-z-1-then-the-minimum-value-of-z-1-2-3-4-i-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33791/let-p-z-z-2-3-i-1-and-q-z-z-1-i-z-1-i-8-let-in-p-q-z-3-2-i-be-maximum-and-minimu</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33792/let-s-z-c-z-1-1-and-2-1-z-z-i-z-z-2-2-let-z-1-z-2-s-be-such-that-z-1-max-z-s-z-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33793/let-z-1-and-z-2-be-two-complex-number-such-that-z-1-z-2-5-and-z-1-3-z-2-3-20-15</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33794/if-denotes-the-number-of-solutions-of-1-i-x-2-x-and-z-arg-z-where-z-4-1-i-4-1-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33795/if-z-is-a-complex-number-then-the-number-of-common-roots-of-the-equation-z-1985</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33796/if-z-x-i-y-x-y-0-satisfies-the-equation-z-2-i-z-0-then-z-2-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33797/let-r-and-respectively-be-the-modulus-and-amplitude-of-the-complex-number-z-2-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33798/let-be-the-roots-of-the-equation-x-2-6-x-3-0-such-that-im-im-let-a-b-be-integers</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33799/if-z-1-2-2-i-is-such-that-z-1-z-1-i-i-1-and-r-then-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33800/let-be-the-roots-of-the-equation-x-2-x-2-0-with-im-im-then-6-4-4-5-2-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33801/let-the-complex-numbers-and-1-lie-on-the-circles-z-z-0-2-4-and-z-z-0-2-16-respec</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33802/if-s-z-c-z-i-z-i-z-1-then-n-s-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33803/if-satisfies-the-equation-x-2-x-1-0-and-1-7-a-b-c-2-a-b-c-0-then-5-3-a-2-b-c-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33804/if-the-set-re-z-z-and-175-z-z-and-175-2-3-z-5-z-and-175-z-and-8712-and-8450-re-z</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33805/let-s-z-and-8712-and-8450-z-and-175-i-z-2-re-z-and-175-then-and-8721-z-and-8712</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33806/let-w-z-z-and-175-k-1-z-k-2-i-z-and-955-1-i-k-1-k-2-and-8712-and-8477-let-r-e-w</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33807/let-c-be-the-circle-in-the-complex-plane-with-centre-z-0-1-2-1-3-i-and-radius-r</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33808/for-a-and-8712-and-8450-let-a-z-and-8712-and-8450-re-a-z-and-175-and-62-im-a-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33809/let-s-z-and-8712-and-8450-i-2-i-z-2-8-i-z-15-z-2-3-i-z-2-and-8712-and-8477-and-9</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33810/let-w-1-be-the-point-obtained-by-the-rotation-of-z-1-5-4-i-about-the-origin-thro</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33811/let-s-z-x-i-y-2-z-3-i-4-z-2-i-is-a-real-number-then-which-of-the-following-is-no</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33812/let-the-complex-number-z-x-i-y-be-such-that-2-z-3-i-2-z-i-is-purely-imaginary-if</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33813/let-a-and-952-and-8712-0-2-and-960-1-2-i-sin-and-952-1-i-sin-and-952-is-purely-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33814/if-for-z-and-945-i-and-946-z-2-z-4-1-i-then-and-945-and-946-and-and-945-and-946</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33815/let-a-and-8800-b-be-two-non-zero-real-numbers-then-the-number-of-elements-in-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33816/for-and-945-and-946-z-and-8712-and-8450-and-and-955-and-62-1-if-and-955-1-is-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33817/let-a-b-be-two-real-numbers-such-that-a-b-and-60-0-if-the-complex-number-1-a-i-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33818/if-the-center-and-radius-of-the-circle-z-2-z-3-2-are-respectively-and-945-and-94</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33819/the-complex-number-z-i-1-cos-and-960-3-i-sin-and-960-3-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33820/for-all-z-and-8712-c-on-the-curve-c-1-z-4-let-the-locus-of-the-point-z-1-z-be-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33821/let-z-1-i-and-z-1-1-i-z-and-175-z-and-175-1-z-1-z-and-183-then-12-and-960-arg-z</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33822/let-and-945-8-14-i-a-z-and-8712-and-8450-and-945-z-and-945-and-175-z-and-175-z-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33823/for-two-non-zero-complex-number-z-1-and-z-2-if-re-z-1-z-2-0-and-re-z-1-z-2-0-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33824/let-z-be-a-complex-number-such-that-z-2-i-z-i-2-z-and-8800-i-then-z-lies-on-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33825/let-z-1-2-3-i-and-z-2-3-4-i-the-set-s-z-and-8712-c-z-z-1-2-z-z-2-2-z-1-z-2-2-rep</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33826/the-value-of-1-sin-2-and-960-9-i-cos-2-and-960-9-1-sin-2-and-960-9-i-cos-2-and-9</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33827/let-p-q-and-8712-and-8477-and-1-3-i-200-2-199-p-i-q-i-1-then-p-q-q-2-and-p-q-q-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33828/if-z-and-8800-0-be-a-complex-number-such-that-z-1-z-2-then-the-maximum-value-of</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33829/let-s-z-x-i-y-z-1-i-and-8805-z-z-and-60-2-z-i-z-1-then-the-set-of-all-values-of</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33830/if-z-2-3-i-then-z-5-z-and-175-5-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33831/let-z-a-i-b-b-and-8800-0-be-complex-numbers-satisfying-z-2-z-and-175-and-183-2-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33832/let-s-1-z-1-and-8712-c-z-1-3-1-2-and-s-2-z-2-and-8712-c-z-2-z-2-1-z-2-z-2-1-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33833/let-s-be-the-set-of-all-and-945-and-946-and-960-and-60-and-945-and-946-and-60-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33834/let-the-minimum-value-v-0-of-v-z-2-z-3-2-z-6-i-2-z-and-8712-and-8450-is-attained</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33835/let-s-z-and-8712-and-8450-z-2-z-and-175-0-then-and-8721-z-and-8712-s-re-z-im-z-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33836/if-z-x-i-y-satisfies-z-2-0-and-z-i-z-5-i-0-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33837/let-o-be-the-origin-and-a-be-the-point-z-1-1-2-i-if-b-is-the-point-z-2-re-z-2-an</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33838/for-z-and-8712-and-8450-if-the-minimum-value-of-z-3-2-z-p-2-i-is-5-2-then-a-valu</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33839/if-and-945-and-946-and-947-and-948-are-the-roots-of-the-equation-x-4-x-3-x-2-x-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33840/for-n-and-8712-n-let-s-n-z-and-8712-c-z-3-2-i-n-4-and-t-n-z-and-8712-c-z-2-3-i-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33841/let-z-represent-the-principal-argument-of-the-complex-number-z-the-z-3-and-arg-z</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33842/let-and-945-and-and-946-be-the-roots-of-the-equation-x-2-2-i-1-0-then-the-value</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33843/let-s-z-and-8712-c-z-2-and-8804-1-z-1-i-z-and-175-1-i-and-8804-2-let-z-4-i-attai</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33844/sum-of-squares-of-modulus-of-all-the-complex-numbers-z-satisfying-z-and-175-i-z</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33845/the-number-of-elements-in-the-set-z-a-i-b-and-8712-and-8450-a-b-and-8712-and-848</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33846/the-number-of-points-of-intersection-z-4-3-i-2-and-z-z-4-6-z-and-8712-c-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33847/let-for-some-real-numbers-and-945-and-and-946-a-and-945-i-and-946-if-the-system</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33848/the-area-of-the-polygon-whose-vertices-are-the-non-real-roots-of-the-equation-z</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33849/if-z-2-z-1-0-z-and-8712-c-then-and-8721-n-1-15-z-n-1-a-1-z-n-2-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33850/let-a-z-and-8712-c-z-1-z-1-and-60-1-and-b-z-and-8712-c-arg-z-1-z-1-2-and-960-3-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33851/let-z-1-and-z-2-be-two-complex-numbers-such-that-z-and-175-1-i-z-and-175-2-and-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33852/let-a-circle-c-in-complex-plane-pass-through-the-points-z-1-3-4-i-z-2-4-3-i-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33853/let-s-z-and-8712-and-8450-z-3-and-8804-1-and-z-4-3-i-z-and-175-4-3-i-and-8804-24</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33854/let-a-z-and-8712-c-1-and-10877-z-1-i-and-10877-2-and-b-z-and-8712-a-z-1-i-1-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33855/if-for-the-complex-numbers-z-satisfying-z-2-2-i-and-8804-1-the-maximum-value-of</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33856/if-z-is-a-complex-number-such-that-z-i-z-1-is-purely-imaginary-then-the-minimum</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33857/a-point-z-moves-in-the-complex-plane-such-that-arg-z-2-z-2-and-960-4-then-the-mi</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33858/let-z-1-and-z-2-be-two-complex-numbers-such-that-arg-z-1-z-2-and-960-4-and-z-1-z</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33859/if-s-z-and-8712-c-z-i-z-2-i-and-8712-r-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33860/if-3-i-100-2-99-p-i-q-then-p-and-q-are-roots-of-the-equation</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33861/the-least-positive-integer-n-such-that-2-i-n-1-i-n-2-i-1-is-a-positive-integer-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33862/the-equation-a-r-g-z-1-z-1-and-960-4-represents-a-circle-with</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33863/let-z-1-i-3-2-i-1-then-the-value-of-21-z-1-z-3-z-2-1-z-2-3-z-3-1-z-3-3-and-8230</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33864/let-and-8450-be-the-set-of-all-complex-numbers-let-s-1-z-and-8712-and-8450-z-2-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33865/if-the-real-part-of-the-complex-number-z-3-2-i-cos-and-952-1-3-i-cos-and-952-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33866/let-c-be-the-set-of-all-complex-numbers-let-s-1-z-and-8712-c-z-and-8211-3-and-82</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33867/the-equation-of-a-circle-is-re-z-2-2-im-z-2-2-re-z-0-where-z-x-i-y-a-line-which</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33868/let-n-denote-the-number-of-solutions-of-the-equation-z-2-3-z-and-175-0-where-z-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33869/if-the-real-part-of-the-complex-number-1-cos-and-952-2-i-sin-and-952-1-is-1-5-fo</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33870/if-z-and-and-969-are-two-complex-numbers-such-that-z-and-969-1-and-arg-z-arg-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33871/let-a-complex-number-be-w-1-3-i-let-another-complex-number-z-be-such-that-z-w-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33872/if-f-x-and-g-x-are-two-polynomials-such-that-the-polynomial-p-x-f-x-3-x-g-x-3-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33873/if-the-equation-a-z-2-and-945-and-175-z-and-945-z-and-175-and-175-d-0-represents</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33874/let-z-1-z-2-be-the-roots-of-the-equation-z-2-a-z-12-0-and-z-1-z-2-form-an-equila</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33875/let-s-1-s-2-and-s-3-be-three-sets-defined-as-s-1-z-and-8712-and-8450-z-1-and-880</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33876/the-area-of-the-triangle-with-vertices-p-z-q-i-z-and-r-z-i-z-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33877/the-least-value-of-z-where-z-is-complex-number-which-satisfies-the-inequality-e</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33878/let-a-complex-number-z-z-and-8800-1-satisfy-log-1-2-z-11-z-1-2-and-8804-2-then-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33879/let-z-and-w-be-two-complex-numbers-such-that-w-z-z-and-175-2-z-2-z-i-z-3-i-1-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33880/let-z-be-those-complex-numbers-which-satisfy-z-5-and-8804-4-and-z-1-i-z-and-175</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33881/let-the-lines-2-i-z-2-i-z-and-175-and-2-i-z-i-2-z-and-175-4-i-0-here-i-2-1-be-no</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33882/let-i-1-if-1-i-3-21-1-i-24-1-i-3-21-1-i-24-k-and-n-k-be-the-greatest-integral-pa</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33883/if-the-least-and-the-largest-real-values-of-and-945-for-which-the-equation-z-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33884/let-z-x-iy-be-a-non-zero-complex-number-such-that-z-2-i-z-2-where-i-1-then-z-lie</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33885/the-region-represented-by-z-x-i-y-and-8712-c-z-re-z-and-8804-1-is-also-given-by</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33886/the-value-of-1-i-3-1-i-30-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33887/if-the-four-complex-numbers-z-z-and-175-z-and-175-2-re-z-and-175-and-z-2-re-z-re</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33888/if-a-and-b-are-real-numbers-such-that-2-and-945-4-a-b-and-945-where-and-945-1-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33889/let-u-2-z-i-z-k-i-z-x-i-y-and-k-and-62-0-if-the-curve-represented-by-re-u-im-u-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33890/if-z-1-z-2-are-complex-numbers-such-that-re-z-1-z-1-1-and-re-z-2-z-2-1-and-arg-z</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33891/if-1-i-1-i-m-2-1-i-i-1-n-3-1-and-160-and-160-m-and-160-n-and-8712-n-then-the-gre</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33892/the-imaginary-part-of-3-2-54-1-2-3-2-54-1-2-can-be</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33893/the-value-of-1-sin-2-and-960-9-i-cos-2-and-960-9-1-sin-2-and-960-9-and-8722-i-co</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33894/if-z-is-a-complex-number-satisfying-r-e-z-i-m-z-4-then-z-cannot-be</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33895/let-z-be-a-complex-number-such-that-z-i-z-2-i-1-and-z-5-2-then-the-value-of-z-3</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33896/let-and-945-1-i-3-2-if-a-1-and-945-and-8721-k-0-100-and-945-2-k-and-b-and-8721-k</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33897/if-the-equation-x-2-b-x-45-0-b-and-8712-r-has-conjugate-complex-roots-and-they-s</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33898/if-3-i-s-i-n-and-952-4-i-c-o-s-and-952-and-952-and-8712-0-2-and-960-is-a-real-nu</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33899/if-r-e-z-1-2-z-i-1-where-z-x-i-y-then-the-point-x-y-lies-on-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33900/let-z-and-8712-c-with-i-m-z-10-and-it-satisfies-2-and-8201-z-n-2-and-8201-z-n-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33901/the-equation-z-i-z-1-i-1-represents</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33902/if-z-and-and-969-are-two-complex-numbers-such-that-z-and-969-1-and-a-r-g-z-a-r-g</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33903/if-a-and-62-0-and-z-1-i-2-a-i-has-magnitude-2-5-then-z-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33904/let-z-and-8712-c-be-such-that-z-and-60-1-if-and-969-5-3-z-5-1-z-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33905/all-the-points-in-the-set-s-and-945-i-and-945-i-and-945-and-8712-r-i-1-lie-on-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33906/if-z-3-2-i-2-i-1-then-1-i-z-z-5-i-z-8-9-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33907/if-and-945-and-and-946-be-the-roots-of-the-equation-x-2-2-x-2-0-then-the-least-v</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33908/let-z-1-and-z-2-be-two-complex-numbers-satisfying-z-1-9-and-z-2-3-4-i-4-then-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33909/if-z-and-945-z-and-945-and-945-and-8712-r-is-a-purely-imaginary-number-and-z-2-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33910/let-z-be-a-complex-number-such-that-z-z-3-i-where-i-1-then-z-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33911/let-2-1-3-i-x-i-y-27-i-1-where-x-and-y-are-real-numbers-then-y-x-equals</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33912/let-z-3-2-i-2-5-3-2-i-2-5-if-r-z-and-i-z-respectively-denote-the-real-and-imagin</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33913/let-z-1-and-z-2-be-any-two-non-zero-complex-numbers-such-that-3-z-1-4-z-2-if-z-3</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33914/let-z-0-be-a-root-of-quadratic-equation-x-2-x-1-0-if-z-3-6-i-z-0-81-3-i-z-0-93-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33915/let-a-and-952-and-8712-and-960-2-and-960-3-2-i-and-8201-s-i-n-and-952-1-2-i-s-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33916/the-least-positive-integer-n-for-which-1-i-3-1-i-3-n-1-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33917/if-z-3-2-i-4-then-the-difference-between-the-greatest-value-and-the-least-value</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33918/the-set-of-all-r-for-which-w-1-1-8-z-1-z-is-a-purely-imaginary-number-for-all-z</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33919/the-set-of-all-and-945-and-8712-r-for-which-w-1-1-8-and-945-z-1-z-is-a-purely-im</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33920/if-c-are-the-distinct-roots-of-the-equation-x-2-x-1-0-then-101-107-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33921/the-equation-i-m-i-z-2-z-i-1-0-z-and-8712-c-z-and-8800-i-represents-a-part-of-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33922/let-z-and-8712-c-the-set-of-complex-numbers-then-the-equation-2-z-3-i-z-i-0-repr</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33923/let-and-969-be-a-complex-number-such-that-2-and-969-1-z-where-z-3-if-1-1-1-1-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33924/let-z-1-a-i-be-a-complex-number-a-and-62-0-such-that-z-3-is-a-real-number-then-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33925/the-point-represented-by-2-i-in-the-argand-plane-moves-1-unit-eastwards-then-2-u</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33926/a-value-of-and-952-for-which-2-3-i-sin-and-952-1-2-i-sin-and-952-is-purely-imagi</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33927/if-z-is-a-non-real-complex-number-then-the-minimum-value-of-i-m-z-5-i-m-z-5-is-w</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33928/the-largest-value-of-r-for-which-the-region-represented-by-the-set-and-969-and-8</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33929/if-2-3-i-is-one-of-the-roots-of-the-equation-2-x-3-9-x-2-k-x-13-0-k-and-8712-r-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33930/a-complex-number-z-is-said-to-be-unimodular-if-z-1-let-z-1-and-z-2-are-complex-n</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33931/for-all-complex-numbers-z-of-the-form-1-i-and-945-and-945-and-8712-r-if-z-2-x-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33932/let-z-i-be-any-complex-number-such-that-z-i-z-i-is-a-purely-imaginary-number-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33933/if-z-z-and-z-z-are-2-pairs-of-complex-conjugate-numbers-then-z-z-z-z-equals</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33934/let-w-i-m-w-and-8800-0-be-a-complex-number-then-the-set-of-all-complex-numbers-z</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33935/if-z-is-a-complex-number-such-that-z-and-8805-2-then-the-minimum-value-of-z-1-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33936/let-z-satisfy-z-1-and-z-1-z-statement-1-z-is-a-real-number-statement-2-principal</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33937/let-a-im-1-z-2-2-i-z-where-z-is-any-non-zero-complex-number-the-set-a-a-z-1-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33938/if-a-complex-number-z-statisfies-the-equation-x-2-z-1-i-0-then-z-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33939/if-z-0-and-z-be-two-complex-numbers-such-that-z-z-is-a-purely-imaginary-number-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33940/if-z-is-a-complex-number-of-unit-modulus-and-argument-and-952-then-arg-1-z-1-z-c</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33941/z-z-2-z-z-2-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33942/let-z-and-w-be-complex-numbers-such-that-z-w-and-z-denotes-the-principal-argumen</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33943/the-area-of-the-triangle-whose-vertices-are-complex-numbers-z-i-z-z-i-z-in-the-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33944/let-z-and-z-be-any-two-complex-number-statement-1-z-z-z-z-statement-2-z-z-z-z</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33945/if-z-1-and-z-2-z-1-is-real-then-the-point-represented-by-the-complex-number-z-li</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33946/let-be-real-and-z-be-a-complex-number-if-z-2-z-0-has-two-distinct-roots-on-the-l</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33947/if-1-is-a-cube-root-of-unity-and-1-7-a-b-then-a-b-equals</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33948/the-number-of-complex-numbers-z-such-that-z-1-z-1-z-i-equals</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33949/if-z-4-z-2-then-the-maximum-value-of-z-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33950/the-conjugate-of-a-complex-number-is-1-i-1-then-the-complex-number-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33951/if-z-4-3-then-the-maximum-value-of-z-1-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33952/if-z-2-z-1-0-where-z-is-a-complex-number-then-the-value-of-z-1-z-2-z-2-1-z-2-2-z</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33953/if-the-cube-roots-of-unity-are-1-2-then-the-roots-of-the-equation-x-1-3-8-0-are</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33954/if-z-and-z-are-two-non-zero-complex-numbers-such-that-z-z-z-z-then-z-z-is-equal</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33955/if-z-z-1-3-i-and-1-then-z-lies-on</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33956/let-z-w-be-complex-numbers-such-that-z-i-w-0-and-z-w-then-arg-z-equals</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33957/if-z-x-i-y-and-z-1-3-p-i-q-then-x-p-y-q-p-2-q-2-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33958/if-z-2-1-z-2-1-then-z-lies-on</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33959/if-z-and-are-two-non-zero-complex-numbers-such-that-z-1-and-arg-z-arg-2-then-z-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33960/let-z-and-z-be-two-roots-of-the-equation-x-2-a-z-b-0-being-complex-further-assum</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33961/if-1-i-1-i-x-1-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33962/z-and-w-are-two-non-zero-complex-no-s-such-that-z-w-and-arg-z-arg-w-then-z-equal</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33963/if-z-4-z-2-its-solution-is-given-by</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33964/the-locus-of-the-centre-of-a-circle-which-touches-the-circle-z-z-a-and-z-z-b-ext</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33965/for-the-function-f-x-e-x-x-x-r-consider-the-following-statements-statement-i-f-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33966/let-f-x-cases-1-3-and-x-2-b-1-x-2x-2-and-x-2-cases-if-f-is-continuous-at-x-2-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33967/let-f-x-cases-x-3-8-and-x-then-the-number-of-points-where-the-function-g-f-is-di</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33968/let-f-x-cases-e-x-1-and-x-0-x-2-5x-6-and-x-0-cases-and-g-x-f-x-f-x-if-the-number</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33969/the-number-of-points-at-which-the-function-f-x-6x-2-3x-2-x-1-x-2-1-4-x-is-not-di</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33970/the-number-of-points-in-the-interval-2-4-at-which-the-function-f-x-x-2-x-1-2-whe</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33971/let-f-x-0-x-x-2-x-1-1-x-2-x-1-x-r-consider-the-following-two-statements-i-f-x-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33972/let-t-denote-the-greatest-integer-less-than-or-equal-to-t-if-the-function-f-x-ar</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33973/if-the-function-f-x-e-x-e-x-x-1-e-x-x-x-x-x-is-continuous-at-x-0-then-the-value</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33974/let-r-be-such-that-the-function-f-x-cases-2-x-2-2-x-and-x-be-differentiable-at-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33975/if-f-x-array-cc-a-x-x-2-x-x-x-and-x-0-b-and-x-0-array-is-continuous-at-x-0-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33976/let-f-x-cases-a-x-2-a-x-3-4-x-4-x-3-and-x-3-2-1-2-b-and-x-3-2-1-2-cases-be-conti</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33977/let-denote-the-greatest-integer-function-and-let-f-x-2-x-x-let-s-x-2-2-the-funct</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33978/the-number-of-points-of-discontinuity-of-the-function-f-x-x-2-2-x-x-0-4-where-de</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33979/let-m-and-n-be-the-number-of-points-at-which-the-function-f-x-x-x-3-x-5-x-x-r-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33980/let-f-x-cases-1-ax-1-x-and-x-0-1-b-and-x-0-x-4-1-2-2-x-c-1-3-2-and-cases-be-cont</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33981/let-the-function-f-x-x-2-1-x-2-a-x-2-x-be-not-differentiable-at-the-two-points-x</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33982/let-f-x-array-lc-3-x-and-x-0-1-x-x-x-2-x-and-0-x-2-5-and-x-2-array-where-denotes</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33983/let-x-denote-the-greatest-integer-function-and-let-m-and-n-respectively-be-the-n</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33984/if-the-function-f-x-array-l-2-x-k-1-x-k-1-x-x-0-4-x-0-2-x-e-2-k-x-2-k-x-x-0-arra</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33985/let-f-x-be-a-real-differentiable-function-such-that-f-0-1-and-f-x-y-f-x-f-y-f-x</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33986/let-the-function-f-x-cases-3-a-x-2-2-and-x-1-a-2-b-x-and-x-1-cases-be-differenti</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33987/let-f-0-r-be-a-function-given-by-f-x-array-cc-8-7-8-x-7-x-and-0-where-a-b-z-if-f</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33988/for-a-b-0-let-f-x-array-cc-a-1-x-b-x-x-and-x-0-array-be-a-continous-function-at</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33989/let-t-denote-the-greatest-integer-less-than-or-equal-to-t-let-f-0-r-be-a-functio</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33990/let-f-1-2-r-be-given-by-f-x-2-x-2-x-x-2-x-where-t-denotes-the-greatest-integer-l</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33991/if-the-function-f-x-3-x-x-3-x-x-3-x-r-is-continuous-at-x-0-then-f-0-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33992/if-the-function-f-x-cases-72-x-9-x-8-x-1-2-1-x-and-x-0-a-e-2-e-3-and-x-0-cases-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/33993/let-f-r-r-be-a-function-given-by-f-x-array-ll-1-2-x-x-2-and-x-0-array-where-r-if</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/34085/let-f-be-a-differentiable-function-from-r-to-r-such-that-f-x-f-y-and-8804-2-x-y</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/34897/if-y-2-2-3-4-2-5-2-then-at-2-y-y-y-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34898/let-f-x-x-5-2-e-x-4-for-all-x-r-consider-a-function-g-x-such-that-g-f-x-x-for-al</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34899/if-y-x-1-x-2-x-x-x-x-x-1-15-3-cos-2-x-5-cos-3-x-then-96-y-6-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34900/let-y-log-e-1-x-2-1-x-2-1-x-1-then-at-x-1-2-the-value-of-225-y-y-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34901/suppose-f-x-2-x-2-x-tan-x-tan-1-x-2-x-1-7-x-2-3-x-1-3-then-the-value-of-f-0-is-e</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34902/let-f-x-x-3-x-2-f-1-x-f-2-f-3-x-r-then-f-10-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34903/let-for-a-differentiable-function-f-0-r-f-x-f-y-log-e-x-y-x-y-x-y-0-then-n-1-20</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34904/let-f-x-sin-x-cos-2-sin-x-cos-x-x-and-8712-0-and-960-and-960-4-then-f-7-and-960</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34905/if-2-x-y-3-y-x-20-then-d-y-d-x-at-2-2-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34906/if-y-x-x-x-x-and-62-0-then-y-and-34-2-2-y-and-39-2-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34907/let-y-f-x-sin-3-and-960-3-cos-and-960-3-2-4-x-3-5-x-2-1-3-2-then-at-x-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34908/let-y-x-1-x-1-x-2-1-x-4-1-x-8-1-x-16-then-y-and-39-y-and-34-at-x-1-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34909/let-x-t-2-2-cos-t-sin-2-t-and-y-t-2-2-sin-t-sin-2-t-t-and-8712-0-and-960-2-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34910/for-the-curve-c-x-2-y-2-3-x-2-y-2-1-5-0-the-value-of-3-y-and-39-y-3-y-and-39-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34911/the-value-of-log-e-2-d-dx-log-cos-x-cosec-x-at-x-and-960-4-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34912/if-y-x-x-x-x-x-and-62-0-then-d-2-x-d-y-2-20-at-x-1-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34913/if-cos-1-y-2-log-e-x-5-5-y-and-60-2-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34914/let-f-and-8477-and-8594-and-8477-satisfy-f-x-y-2-x-f-y-4-y-f-x-and-8704-x-y-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34915/let-f-r-and-8594-r-be-defined-as-f-x-x-3-x-5-if-g-x-is-a-function-such-that-f-g</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34916/if-y-tan-1-sec-x-3-tan-x-3-and-960-2-and-60-x-3-and-60-3-and-960-2-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34917/if-y-x-cot-1-1-sin-x-1-sin-x-1-sin-x-1-sin-x-x-and-8712-and-960-2-and-960-then-d</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34918/if-y-1-4-y-1-4-2-x-and-x-2-1-d-2-y-d-x-2-and-945-x-d-y-d-x-and-946-y-0-then-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34919/let-f-x-cos-2-tan-1-sin-cot-1-1-x-x-0-and-60-x-and-60-1-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34920/if-y-y-x-is-an-implicit-function-of-x-such-that-log-e-x-y-4-x-y-then-d-2-y-d-x-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34921/if-f-x-sin-cos-1-1-2-2-x-1-2-2-x-and-its-first-derivative-with-respect-to-x-is-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34922/let-f-s-and-8594-s-where-s-0-and-8734-be-a-twice-differentiable-function-such-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34923/the-derivative-of-tan-1-1-x-2-1-x-with-respect-to-tan-1-2-x-1-x-2-1-2-x-2-at-x-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34924/if-a-2-b-cos-x-a-2-b-cos-y-a-2-b-2-where-a-and-62-b-and-62-0-then-d-x-d-y-at-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34925/if-y-2-log-e-cos-2-x-y-x-and-8712-and-960-2-and-960-2-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34926/if-x-2-sin-and-952-sin-2-and-952-and-y-2-cos-and-952-cos-2-and-952-and-952-and-8</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34927/let-f-and-g-be-differentiable-functions-on-r-such-that-f-o-g-is-the-identity-fun</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34928/let-f-be-any-function-continuous-on-a-b-and-twice-differentiable-on-a-b-if-all-x</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34929/let-f-x-sin-tan-1-x-sin-cot-1-x-2-1-x-and-62-1-if-d-y-d-x-1-2-d-d-x-sin-1-f-x-an</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34930/let-y-y-x-be-a-function-of-x-satisfying-y-1-x-2-k-x-1-y-2-where-k-is-a-constant</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34931/if-y-and-945-2-t-a-n-and-945-c-o-t-and-945-1-t-a-n-2-and-945-1-s-i-n-2-and-945-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34932/let-x-k-y-k-a-k-a-k-and-62-0-and-d-y-d-x-y-x-1-3-0-then-k-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34933/the-derivative-of-t-a-n-1-s-i-n-x-c-o-s-x-s-i-n-x-c-o-s-x-with-respect-to-x-2-wh</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34934/if-e-y-x-y-e-the-ordered-pair-d-y-d-x-d-2-y-d-x-2-at-x-0-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34935/if-f-1-1-f-and-39-1-3-then-the-derivative-of-f-f-f-x-f-x-2-at-x-1-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34936/if-2-y-cot-1-3-cos-x-sin-x-cos-x-3-sin-x-2-and-8704-x-and-8712-0-and-960-2-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34937/let-f-be-a-differentiable-function-such-that-f-1-2-and-f-x-f-x-for-all-x-and-871</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34938/for-x-and-62-1-if-2-x-2-y-4-e-2-x-2-y-then-1-log-e-and-8289-2-x-2-d-y-d-x-is-equ</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34939/if-x-e-e-x-x-y-4-y-0-then-d-y-d-x-at-x-e-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34940/let-f-r-and-8594-r-be-a-function-such-that-f-x-x-3-x-2-f-1-x-f-2-f-3-and-8704-x</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34941/if-x-3-t-a-n-t-and-y-3-s-e-c-t-then-the-value-of-d-2-y-d-x-2-at-t-and-960-4-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34942/if-x-2-cosec-1-t-and-y-2-sec-1-t-t-and-8805-1-then-d-y-d-x-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34943/if-f-x-2-3-x-1-9-x-then-f-1-2-equals</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34944/if-x-2-y-2-y-4-then-the-value-of-d-2-y-d-x-2-at-the-point-2-0-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34945/if-x-2-y-2-sin-y-4-then-the-value-of-d-2-y-d-x-2-at-the-point-2-0-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34946/if-2-x-y-1-5-y-1-5-and-x-2-1-d-2-y-d-x-2-and-955-x-d-y-d-x-k-y-0-then-and-955-k</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34947/if-y-x-x-2-1-15-x-x-2-1-15-then-x-2-1-d-2-y-d-x-2-x-d-y-d-x-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34948/if-for-x-and-8712-0-1-4-the-derivative-of-tan-1-and-8289-6-x-x-1-9-x-3-is-x-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34949/let-f-and-g-be-two-differentiable-functions-on-r-such-that-f-x-0-and-g-x-0-for-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34950/if-y-e-n-x-then-d-2-y-d-x-2-d-2-x-d-y-2-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34951/if-f-x-x-and-f-x-x-f-x-g-x-0-then-g-x-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34952/for-a-0-t-0-2-let-x-a-t-and-y-a-t-then-1-d-y-d-x-2-equals</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34953/let-f-x-x-2-x-x-2-2-x-x-0-2-then-d-d-x-f-x-wherever-it-is-defined-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34954/if-y-sec-tan-1-x-then-d-y-d-x-at-x-1-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34955/if-f-x-x-and-y-f-2-x-3-3-2-x-then-d-y-d-x-equals</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34956/d-2-x-d-y-2-equals</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34957/let-f-1-1-r-be-a-differentiable-function-with-f-0-1-and-f-0-1-let-g-x-f-2-f-x-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34958/let-y-be-an-implicit-function-of-x-defined-by-x-2-x-2-x-x-y-1-0-then-y-1-equals</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34959/if-x-m-y-n-x-y-m-n-then-d-y-d-x-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34960/suppose-f-x-is-differentiable-x-1-and-h-0-1-h-f-1-h-5-then-f-1-equals</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34961/if-x-e-y-e-y-10-x-0-then-d-y-d-x-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34962/if-y-x-1-x-2-n-then-1-x-2-d-2-y-d-x-2-x-d-y-d-x-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34963/let-x-2-f-a-2-7a-3-y-2-f-3a-15-1-represent-an-ellipse-with-major-axis-along-y-ax</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34964/the-eccentricity-of-an-ellipse-e-with-centre-at-the-origin-o-is-3-2-and-its-dire</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34965/let-x-9-be-a-directrix-of-an-ellipse-e-whose-centre-is-at-the-origin-and-eccentr</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34966/let-a-focus-of-the-ellipse-e-x-2-a-2-y-2-b-2-1-be-s-4-0-and-its-eccentricity-be</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34967/let-a-be-the-point-3-0-and-circles-with-variable-diameter-ab-touch-the-circle-x</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34968/let-an-ellipse-x-2-a-2-y-2-b-2-1-a-b-pass-through-the-point-4-3-and-have-eccentr</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34969/an-ellipse-has-its-center-at-1-2-one-focus-at-3-2-and-one-vertex-at-5-2-then-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34970/let-the-ellipse-e-x-144-y-169-1-and-the-hyperbola-h-x-16-y-1-have-the-same-foci</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/34973/let-each-of-the-two-ellipses-e-x-a-y-b-1-a-b-and-e-x-a-y-b-1-a-b-have-eccentrici</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/34981/let-for-two-distinct-values-of-p-the-lines-y-x-p-touch-the-ellipse-e-x-2-4-2-y-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34982/the-length-of-the-latus-rectum-of-the-ellipse-whose-foci-are-2-5-and-2-3-and-ecc</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34983/let-c-be-the-circle-x-2-y-1-2-2-e-and-e-be-two-ellipses-whose-centres-lie-at-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/34985/a-line-passing-through-the-point-p-5-5-intersects-the-ellipse-x-2-36-y-2-25-1-at</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34986/if-the-length-of-the-minor-axis-of-an-ellipse-is-equal-to-one-fourth-of-the-dist</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34987/if-s-and-s-are-the-foci-of-the-ellipse-x-2-18-y-2-9-1-and-p-be-a-point-on-the-el</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/34988/if-x-y-109-is-the-equation-of-the-chord-of-the-ellipse-x-2-9-y-2-4-1-whose-mid-p</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/34990/if-the-midpoint-of-a-chord-of-the-ellipse-x-2-9-y-2-4-1-is-2-4-3-and-the-length</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/34993/let-the-product-of-the-focal-distances-of-the-point-3-1-2-on-the-ellipse-x-2-a-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/34995/let-f-x-x-2-9-g-x-x-x-9-and-a-f-g-10-b-g-f-3-if-e-and-l-denote-the-eccentricity</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/35000/if-the-length-of-the-minor-axis-of-ellipse-is-equal-to-half-of-the-distance-betw</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/35003/let-an-ellipse-with-centre-1-0-and-latus-rectum-of-length-1-2-have-its-major-axi</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/35012/let-c-be-the-largest-circle-centred-at-2-0-and-inscribed-in-the-ellipse-x-2-36-y</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/35972/if-a-array-ll-2-and-3-3-and-5-array-then-the-determinant-of-the-matrix-a-3-a-a-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/35973/let-a-be-a-3-3-matrix-such-that-a-a-t-o-if-a-array-c-1-1-0-array-array-l-3-3-2-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/35974/for-the-matrices-a-array-ll-3-and-4-1-and-1-array-and-b-array-ll-29-and-49-13-an</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/35975/for-some-r-let-a-array-ll-and-2-1-and-2-array-and-b-array-ll-1-and-1-1-and-array</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/35976/let-be-a-solution-of-x-2-x-1-0-and-for-some-a-and-b-in-r-array-lll-4-and-a-and-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/35977/let-a-array-ccc-2-and-2-p-and-2-p-q-4-and-6-2-p-and-8-3-p-2-q-6-and-12-3-p-and-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/35978/the-number-of-singular-matrices-of-order-2-whose-elements-are-from-the-set-2-3-6</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/35979/let-a-be-a-3-3-matrix-such-that-aligned-and-adj-adj-adj-a-81-if-and-s-n-z-adj-ad</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/35980/let-the-matrix-a-array-lll-1-and-0-and-0-1-and-0-and-1-0-and-1-and-0-array-satis</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/35981/let-a-array-ccc-and-0-and-0-and-1-and-0-and-0-and-array-if-for-some-0-a-2-a-t-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/35982/let-i-be-the-identity-matrix-of-order-3-3-and-for-the-matrix-a-array-ccc-and-2-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/35983/let-a-be-a-matrix-of-order-3-3-and-a-5-if-2-adj-3-a-adj-2-a-2-3-5-n-then-is-equa</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/35984/let-a-be-a-3-3-real-matrix-such-that-a-2-a-2-i-4-a-i-o-where-i-and-o-are-the-ide</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/35985/let-a-array-cc-and-1-6-and-array-0-such-that-det-a-0-and-1-if-i-denotes-2-2-iden</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/35986/let-a-r-and-a-be-a-matrix-of-order-3-3-such-that-det-a-4-and-a-i-array-lll-1-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/35987/let-a-a-i-j-be-a-matrix-of-order-3-3-with-a-i-j-2-i-j-if-the-sum-of-all-the-elem</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/35988/let-a-a-i-j-array-cc-128-and-5-8-and-25-array-if-a-i-j-is-the-cofactor-of-a-i-j</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/35989/let-s-m-z-a-m-2-a-m-3-i-a-where-a-array-cc-2-and-1-1-and-0-array-then-n-s-is-equ</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/35990/let-a-array-cc-1-2-and-2-0-and-1-array-and-p-array-cc-and-and-array-0-if-b-pap-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/35991/let-m-denote-the-set-of-all-real-matrices-of-order-3-3-and-let-s-3-2-1-1-2-let-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/35992/let-a-be-a-3-3-matrix-such-that-x-t-a-x-o-for-all-nonzero-3-1-matrices-x-array-l</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/35993/let-a-a-i-j-be-3-3-matrix-such-that-a-array-l-0-1-0-array-array-l-0-0-1-array-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/35994/if-a-b-and-adj-a-adj-b-are-non-singular-matrices-of-same-order-then-the-inverse</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/35995/for-a-3-3-matrix-m-let-trace-m-denote-the-sum-of-all-the-diagonal-elements-of-m</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/35996/let-a-be-a-square-matrix-of-order-3-such-that-det-a-2-and-det-3-adj-6-adj-3-a-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/35997/let-b-array-ll-1-and-3-1-and-5-array-and-a-be-a-2-2-matrix-such-that-a-b-a-if-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/35998/let-a-be-a-non-singular-matrix-of-order-3-if-det-3-adj-2-adj-det-a-a-3-2-and-det</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/35999/let-a-array-lll-2-and-a-and-0-1-and-3-and-1-0-and-5-and-b-array-if-a-3-4-a-2-a-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36000/let-a-array-cc-2-and-1-1-and-1-array-if-the-sum-of-the-diagonal-elements-of-a-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36001/if-a-is-a-square-matrix-of-order-3-such-that-det-a-3-and-det-adj-4-adj-3-adj-3-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36002/let-0-and-a-array-rrr-and-and-3-and-and-and-and-2-array-if-b-array-rrr-3-and-9-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36003/let-a-and-b-be-two-square-matrices-of-order-3-such-that-a-3-and-b-2-then-a-t-a-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36004/let-a-array-ll-1-and-2-0-and-1-array-and-b-i-adj-a-adj-a-2-adj-a-then-the-sum-of</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36005/let-a-be-a-2-2-symmetric-matrix-such-that-a-array-l-1-1-array-array-l-3-7-array</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36006/let-0-and-a-array-lll-1-and-2-and-1-and-0-and-1-0-and-1-and-2-array-if-det-adj-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36007/let-a-be-a-3-3-matrix-of-non-negative-real-elements-such-that-a-array-l-1-1-1-ar</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36008/let-a-i-2-2-m-m-t-where-m-is-real-matrix-of-order-2-1-such-that-the-relation-m-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36009/if-a-2-1-1-2-b-1-0-1-1-c-a-b-a-t-and-x-a-t-c-2-a-then-det-x-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36010/let-a-be-a-3-3-matrix-and-det-a-2-if-n-det-a-d-j-a-d-j-a-d-j-a-2024-times-then-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36011/let-r-x-0-0-0-y-0-0-0-z-be-a-non-zero-3-3-matrix-where-x-sin-y-sin-2-3-z-sin-4-3</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36012/let-a-2-1-2-6-2-11-3-3-2-and-p-1-2-0-5-0-2-7-1-5-the-sum-of-the-prime-factors-of</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36013/let-a-1-0-0-0-0-and-2-a-3-2-21-where-z-then-a-value-of-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36014/let-a-be-a-square-matrix-such-that-aa-t-i-then-1-2-a-a-a-t-2-a-a-t-2-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36015/let-a-be-a-2-2-real-matrix-and-i-be-the-identity-matrix-of-order-2-if-the-roots</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36016/let-a-2-0-1-1-1-0-1-0-1-b-b-1-b-2-b-3-where-b-1-b-2-b-3-are-column-matrices-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36017/consider-the-matrix-f-x-cos-x-sin-x-0-sin-x-cos-x-0-0-0-1-given-below-are-two-st</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36018/let-the-determinant-of-a-square-matrix-a-of-order-m-be-m-n-where-m-and-n-satisfy</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36019/let-for-a-1-2-3-and-945-3-1-1-1-2-a-2-if-2-adj-2-adj-2-a-32-n-then-3-n-and-945-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36020/the-number-of-symmetric-matrices-of-order-3-with-all-the-entries-from-the-set-0</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36021/let-b-1-3-and-945-1-2-3-and-945-and-945-4-and-945-and-62-2-be-the-adjoint-of-a-m</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36022/let-a-1-1-51-0-1-if-b-1-2-1-1-a-1-2-1-1-then-the-sum-of-all-the-elements-of-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36023/let-a-0-1-2-a-0-3-1-c-0-where-a-c-and-8712-r-if-a-3-a-and-the-positive-value-of</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36024/let-a-be-a-2-and-215-2-matrix-with-real-entries-such-that-a-and-39-and-945-a-1-w</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36025/if-a-1-5-6-7-5-6-7-6-7-8-7-8-9-then-adj-adj-2-a-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36026/if-a-is-a-3-and-215-3-matrix-and-a-2-then-3-adj-3-a-a-2-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36027/if-a-1-5-and-955-10-a-1-and-945-a-and-946-i-and-and-945-and-946-2-then-4-and-945</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36028/let-2-1-0-1-2-1-0-1-2-if-a-d-j-a-d-j-a-d-j-2-a-16-n-then-n-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36029/let-p-3-2-1-2-1-2-3-2-a-1-1-0-1-and-q-p-a-p-t-if-p-t-q-2007-p-a-b-c-d-then-2-a-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36030/let-p-be-a-square-matrix-such-that-p-2-i-p-for-and-945-and-946-and-947-and-948-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36031/let-a-a-i-j-2-and-215-2-where-a-and-8800-i-j-0-for-all-i-j-and-a-2-i-let-a-be-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36032/if-a-1-2-1-3-3-1-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36033/let-a-a-i-j-and-183-a-i-j-and-8712-z-and-8745-0-4-1-and-8804-i-j-and-8804-2-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36034/let-a-be-a-n-and-215-n-matrix-such-that-a-2-if-the-determinant-of-the-matrix-adj</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36035/let-a-1-0-0-0-4-1-0-12-3-then-the-sum-of-the-diagonal-elements-of-the-matrix-a-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36036/if-p-is-a-3-and-215-3-real-matrix-such-that-p-t-a-p-a-1-i-where-a-and-62-1-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36037/let-a-m-n-p-q-d-a-and-8800-0-and-a-d-adj-a-0-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36038/the-set-of-all-values-of-t-and-8712-and-8477-for-which-the-matrix-e-t-e-t-sin-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36039/let-a-be-a-symmetric-matrix-such-that-a-2-and-2-1-3-3-2-a-1-2-and-945-and-946-if</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36040/let-and-945-and-and-946-be-real-numbers-consider-a-3-and-215-3-matrix-a-such-tha</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36041/let-a-b-c-be-3-and-215-3-matrices-such-that-a-is-symmetric-and-b-and-c-are-skew</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36042/let-a-1-10-3-10-3-10-1-10-and-b-1-i-0-1-where-i-1-if-m-a-t-ba-then-the-inverse-o</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36043/let-x-y-z-and-62-1-and-a-1-log-x-y-log-x-z-log-y-x-2-log-y-z-log-z-x-log-z-y-3-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36044/the-number-of-square-matrices-of-order-5-with-entries-from-the-set-0-1-such-that</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36045/let-a-be-a-3-and-215-3-matrix-such-that-a-d-j-a-d-j-a-d-j-a-12-4-then-a-1-a-d-j</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36046/if-a-and-b-are-two-non-zero-n-and-215-n-matrices-such-that-a-2-b-a-2-b-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36047/which-of-the-following-matrices-can-not-be-obtained-from-the-matrix-1-2-1-1-by-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36048/let-x-1-1-1-and-a-1-2-3-0-1-6-0-0-1-for-k-and-8712-and-8469-if-x-a-k-x-33-then-k</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36049/let-a-and-b-be-two-3-and-215-3-non-zero-real-matrices-such-that-a-b-is-a-zero-ma</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36050/the-number-of-matrices-of-order-3-and-215-3-whose-entries-are-either-0-or-1-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36051/let-a-and-b-be-any-two-3-and-215-3-symmetric-and-skew-symmetric-matrices-respect</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36052/let-the-matrix-a-0-1-0-1-0-0-0-0-1-and-the-matrix-b-0-a-49-2-a-98-if-b-n-adj-b-n</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36053/let-a-1-1-2-and-945-and-b-and-946-1-1-0-and-945-and-946-and-8712-r-let-and-945-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36054/let-a-4-2-and-945-and-946-if-a-2-and-947-a-18-i-o-then-det-a-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36055/consider-a-matrix-a-and-945-and-946-and-947-and-945-2-and-946-2-and-947-2-and-94</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36056/let-a-1-2-2-5-let-and-945-and-946-and-8712-and-8477-be-such-that-and-945-a-2-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36057/let-s-be-the-set-containing-all-3-and-215-3-matrices-with-entries-from-1-0-1-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36058/let-a-1-1-1-and-b-9-2-10-2-11-2-12-2-13-2-14-2-15-2-16-2-17-2-then-the-value-of</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36059/the-number-of-matrices-a-a-b-c-d-where-a-b-c-d-and-8712-1-0-1-2-3-and-8230-and-8</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36060/let-a-be-a-2-2-matrix-with-det-a-1-and-det-a-i-adj-a-i-4-then-the-sum-of-the-dia</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36061/let-a-1-a-a-0-1-b-0-0-1-a-b-and-8712-and-8477-if-for-some-n-and-8712-n-a-n-1-48</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36062/let-a-2-1-1-1-0-1-1-1-0-and-b-a-i-if-and-969-3-i-1-2-then-the-number-of-elements</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36063/let-a-2-1-0-2-if-b-i-c-1-5-adj-a-c-2-5-adj-a-2-c-5-5-adj-a-5-then-the-sum-of-all</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36064/let-m-0-and-945-and-945-0-where-and-945-is-a-non-zero-real-number-and-n-and-8721</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36065/the-probability-that-a-randomly-chosen-2-and-215-2-matrix-with-all-the-entries-f</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36066/let-a-a-i-j-be-a-square-matrix-of-order-3-such-that-a-i-j-2-j-i-for-all-i-j-1-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36067/let-a-1-i-1-i-0-where-i-1-then-the-number-of-elements-in-the-set-n-and-8712-1-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36068/let-a-be-a-matrix-of-order-3-and-215-3-and-det-a-2-then-det-det-a-adj-5-adj-a-3</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36069/let-a-and-b-be-two-3-and-215-3-matrices-such-that-a-b-i-and-a-1-8-then-a-d-j-b-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36070/let-a-be-a-matrix-of-order-2-and-215-2-whose-entries-are-from-the-set-0-1-2-3-4</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36071/the-positive-value-of-the-determinant-of-the-matrix-a-whose-a-d-j-a-d-j-a-14-28</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36072/let-x-0-1-0-0-0-1-0-0-0-y-and-945-l-and-946-x-and-947-x-2-and-z-and-945-2-i-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36073/let-a-be-a-3-and-215-3-invertible-matrix-if-adj-24-a-adj-3-adj-2-a-then-a-2-is-e</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36074/let-a-2-2-1-1-and-b-1-2-1-2-then-the-number-of-elements-in-the-set-n-m-n-m-and-8</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36075/let-a-0-2-2-0-if-m-and-n-are-two-matrices-given-by-m-and-8721-k-1-10-a-2-k-and-n</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36076/let-a-be-a-3-and-215-3-matrix-having-entries-from-the-set-1-0-1-the-number-of-al</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36077/let-s-1-a-0-b-a-b-and-8712-1-2-3-and-8230-100-and-let-t-n-a-and-8712-s-a-n-n-1-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36078/let-s-n-1-and-10877-n-and-10877-50-and-n-is-odd-let-a-and-8712-s-and-a-1-0-a-1-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36079/the-number-of-elements-in-the-set-a-a-b-0-d-and-160-a-and-160-b-and-160-d-and-87</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36080/if-the-matrix-a-0-2-k-1-satisfies-a-a-3-3-i-2-i-then-the-value-of-k-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36081/let-a-1-0-0-0-1-1-1-0-0-then-a-2025-a-2020-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36082/let-a-be-a-3-and-215-3-real-matrix-if-det-2-adj-2-adj-adj-2-a-2-41-then-the-valu</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36083/if-a-1-5-2-5-2-5-1-5-b-1-0-i-1-i-1-and-q-a-t-b-a-then-the-inverse-of-the-matrix</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36084/let-a-and-b-be-two-3-and-215-3-real-matrices-such-that-a-2-b-2-is-invertible-mat</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36085/if-a-1-1-1-0-1-1-0-0-1-and-m-a-a-2-a-3-and-8230-a-20-then-the-sum-of-all-the-ele</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36086/let-a-1-2-1-4-if-a-1-and-945-i-and-946-a-and-945-and-946-and-8712-r-i-is-a-2-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36087/if-p-1-0-1-2-1-then-p-50-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36088/let-m-a-a-b-c-d-a-b-c-d-and-8712-and-177-3-and-177-2-and-177-1-0-define-f-m-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36089/let-s-n-and-8712-n-0-i-1-0-n-a-b-c-d-a-b-c-d-and-8704-a-b-c-d-and-8712-r-where-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36090/let-a-a-i-j-be-a-real-matrix-of-order-3-and-215-3-such-that-a-i-1-a-i-2-a-i-3-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36091/let-a-0-1-0-1-0-0-0-0-1-then-the-number-of-3-and-215-3-matrices-b-with-entries-f</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36092/let-a-a-i-j-be-a-3-and-215-3-matrix-where-a-i-j-1-j-i-and-160-and-160-and-160-if</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36093/let-a-2-3-a-0-a-and-8712-r-be-written-as-p-q-where-p-is-a-symmetric-matrix-and-q</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36094/let-a-1-1-0-0-1-1-0-0-1-and-b-7-a-20-20-a-7-2-i-where-i-is-an-identity-matrix-of</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36095/let-i-be-an-identity-matrix-of-order-2-and-215-2-and-p-2-1-5-3-then-the-value-of</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36096/let-a-2-b-1-2-0-6-3-3-5-3-1-and-2-a-b-2-1-5-2-1-6-0-1-2-if-t-r-a-denotes-the-sum</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36097/let-a-a-b-c-d-and-b-and-945-and-946-and-8800-0-0-such-that-a-b-b-and-a-d-2021-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36098/if-a-0-sin-and-945-sin-and-945-0-and-det-a-2-1-2-i-0-then-a-possible-value-of-an</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36099/if-a-2-3-0-1-then-the-value-of-det-a-4-det-a-10-adj-2-a-10-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36100/let-a-a-1-a-2-and-b-b-1-b-2-be-two-2-and-215-1-matrices-with-real-entries-such-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36101/let-a-i-i-i-i-i-1-then-the-system-of-linear-equations-a-8-x-y-8-64-has</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36102/let-p-30-20-56-90-140-112-120-60-14-and-a-2-7-and-969-2-1-and-969-1-0-and-969-an</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36103/the-total-number-of-3-and-215-3-matrices-a-having-enteries-from-the-set-0-1-2-3</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36104/if-the-matrix-a-1-0-0-0-2-0-3-0-1-satisfies-the-equation-a-20-and-945-a-19-and-9</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36105/let-a-be-a-symmetric-matrix-of-order-2-with-integer-entries-if-the-sum-of-the-di</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36106/if-for-the-matrix-a-1-and-945-and-945-and-946-a-a-t-i-2-then-the-value-of-and-94</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36107/if-a-0-tan-and-952-2-tan-and-952-2-0-and-i-2-a-i-2-a-1-a-b-b-a-then-13-a-2-b-2-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36108/let-a-x-y-z-y-z-x-z-x-y-where-x-y-and-z-are-real-numbers-such-that-x-y-z-and-62</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36109/let-p-3-1-2-2-0-and-945-3-5-0-where-and-945-and-8712-r-suppose-q-q-i-j-is-a-matr</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36110/let-m-be-any-3-and-215-3-matrix-with-entries-from-the-set-0-1-2-the-maximum-numb</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36111/let-and-952-and-960-5-and-a-cosand-952-sinand-952-sinand-952-cosand-952-if-b-a-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36112/if-a-cos-and-952-isin-and-952-isin-and-952-cos-and-952-and-952-and-960-24-and-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36113/let-a-be-a-3-and-215-3-matrix-such-that-adj-a-2-1-1-1-0-2-1-2-1-and-b-adj-a-d-j</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36114/let-a-x-1-1-0-x-and-949-r-and-a-4-a-i-j-if-a-11-109-then-a-22-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36115/let-a-x-x-y-z-t-p-x-0-and-x-2-y-2-z-2-1-where-p-1-2-1-2-3-4-1-9-1-then-the-set-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36116/let-a-b-c-and-8712-r-be-all-non-zero-and-satisfies-a-3-b-3-c-3-2-if-the-matrix-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36117/let-a-be-a-2-and-215-2-real-matrix-with-entries-from-0-1-and-a-and-8800-0-consid</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36118/if-a-1-1-2-1-3-4-1-1-3-b-a-d-j-a-and-c-3-a-then-a-d-j-b-c-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36119/if-a-2-2-9-4-and-i-1-0-0-1-then-10-and-8201-a-1-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36120/the-number-of-all-3-and-215-3-matrices-a-with-entries-from-the-set-1-0-1-such-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36121/let-and-945-be-a-root-of-the-equation-x-2-x-1-0-and-the-matrix-a-1-3-1-1-1-1-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36122/if-b-5-2-and-945-1-0-2-1-and-945-3-1-is-the-inverse-of-a-3-and-215-3-matix-a-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36123/if-a-is-a-symmetric-matrix-and-b-is-skew-symmetric-matrix-such-that-a-b-2-3-5-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36124/the-total-number-of-matrices-a-0-2-y-1-2-x-y-1-2-x-y-1-x-y-and-8712-r-x-and-8800</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36125/if-1-1-0-1-1-2-0-1-1-3-0-1-and-8230-1-n-1-0-1-1-78-0-1-then-the-inverse-of-1-n-0</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36126/let-a-cos-and-945-sin-and-945-sin-and-945-cos-and-945-a-and-8712-r-such-that-a-3</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36127/let-p-1-0-0-3-1-0-9-3-1-and-q-q-i-j-be-two-3-and-215-3-matrices-such-that-q-p-5</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36128/let-a-array-ccc-0-and-2-q-and-r-p-and-q-and-r-p-and-q-and-r-array-if-aa-t-i-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36129/if-a-e-t-e-t-c-o-s-t-e-t-sin-and-8289-t-e-t-e-t-cos-and-8289-t-e-t-sin-and-8289</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36130/if-a-c-o-s-and-952-s-i-n-and-952-s-i-n-and-952-c-o-s-and-952-then-the-matrix-a-5</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36131/let-a-1-0-0-1-1-0-1-1-1-and-b-a-20-then-the-sum-of-the-elements-of-the-first-col</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36132/suppose-a-is-any-3-3-non-singular-matrix-and-a-3-i-a-5-i-o-where-i-i-and-o-o-if</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36133/let-a-be-a-matrix-such-that-a-array-ll-1-and-2-0-and-3-array-is-a-scalar-matrix</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36134/let-a-be-a-matrix-such-that-a-and-183-1-2-0-3-is-a-scalar-matrix-and-3-a-108-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36135/for-two-3-and-215-3-matrices-a-and-b-let-a-b-2-b-and-3-a-2-b-i-3-where-b-and-824</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36136/let-a-be-any-3-and-215-3-invertible-matrix-then-which-one-of-the-following-is-no</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36137/if-a-2-3-4-1-then-adj-3-a-2-12-a-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36138/let-a-be-a-3-and-215-3-matrix-such-that-a-2-5-a-7-i-o-statement-i-a-1-1-7-5-i-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36139/if-a-4-1-3-1-then-the-determinant-of-the-matrix-a-2016-2-a-2015-a-2014-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36140/if-p-3-2-1-2-1-2-3-2-a-1-1-0-1-and-q-p-a-p-t-then-p-t-q-2015-p-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36141/if-a-5-a-b-3-2-and-a-a-d-j-a-a-a-t-then-5-a-b-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36142/if-a-is-a-3-and-215-3-matrix-such-that-5-a-d-j-a-5-then-a-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36143/if-a-0-1-1-0-then-which-one-of-the-following-statements-is-not-correct</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36144/if-a-1-2-2-2-1-2-a-2-b-is-a-matrix-satisfying-the-equation-a-a-t-9-i-where-i-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36145/let-a-and-b-be-any-two-3-and-215-3-matrices-if-a-is-symmetric-and-b-is-skew-symm</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36146/if-a-array-ccc-1-and-2-and-x-3-and-1-and-2-array-and-b-array-c-y-x-1-array-be-su</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36147/let-a-be-a-3-3-matrix-such-that-a-array-lll-1-and-2-and-3-0-and-2-and-3-0-and-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36148/let-for-i-1-2-3-p-i-x-be-a-polynomial-of-degree-2-in-x-p-i-x-and-p-i-x-be-the-fi</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36149/if-b-is-a-3-and-215-3-matrix-such-that-b-2-0-then-d-e-t-i-b-50-50-b-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36150/if-a-is-a-3-and-215-3-non-singular-matrix-such-that-a-a-and-39-a-and-39-a-and-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36151/a-common-tangent-to-the-conics-x-2-6-y-and-2-x-2-4-y-2-9-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36152/let-a-other-than-i-or-i-be-a-2-2-real-matrix-such-that-a-2-i-i-being-the-unit-ma</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36153/if-p-q-r-are-3-real-numbers-satisfying-the-matrix-equation-p-q-r-array-lll-3-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36154/the-matrix-a-2-4-a-5-i-where-i-is-identity-matrix-and-a-array-cc-1-and-2-4-and-3</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36155/if-p-1-and-945-3-1-3-3-2-4-4-is-the-adjoint-of-a-3-and-215-3-matrix-a-and-a-4-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36156/if-a-array-ccc-1-and-0-and-0-2-and-1-and-0-3-and-2-and-1-array-and-b-array-ccc-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36157/if-a-t-denotes-the-transpose-of-the-matrix-a-array-lll-0-and-0-and-a-0-and-b-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36158/let-a-and-b-be-real-matrices-of-the-form-array-ll-and-0-0-and-array-and-array-ll</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36159/if-a-array-c-1-0-0-array-b-array-c-1-0-0-array-be-two-matrices-then-a-b-t-is-a-n</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36160/let-a-array-lll-1-and-0-and-0-2-and-1-and-0-3-and-2-and-1-array-if-u-and-u-are-c</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36161/let-p-and-q-be-3-3-matrices-with-p-q-if-p-3-q-3-and-p-2-q-q-2-p-then-determinant</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36162/let-a-and-b-be-two-symmetric-matrices-of-order-3-this-question-has-statement-1-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36163/the-number-of-3-3-non-singular-matrices-with-four-entries-as-1-and-all-other-ent</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36164/let-a-be-a-2-2-matrix-with-non-zero-entries-and-let-a-2-1-where-1-is-2-2-identit</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36165/let-a-be-a-2-2-matrix-statement-1-adj-adj-a-a-statement-2-adj-a-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36166/let-a-be-a-2-2-matrix-with-real-entries-let-i-be-the-2-2-identity-matrix-denote</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36167/let-a-be-a-square-matrix-all-of-whose-entries-are-integers-then-which-one-of-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36168/let-a-array-ccc-5-and-5-and-0-and-and-5-0-and-0-and-5-array-if-a-2-25-then-equal</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36169/if-a-and-b-are-square-matrices-of-size-n-n-such-that-a-2-b-2-a-b-a-b-then-which</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36170/let-a-array-ll-1-and-2-3-and-4-array-and-b-array-ll-a-and-0-0-and-b-array-a-b-n</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36171/if-a-2-a-i-0-then-the-inverse-of-a-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36172/let-a-array-ccc-0-and-0-and-1-0-and-1-and-0-1-and-0-and-0-array-the-only-correct</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36173/let-a-array-ccc-1-and-1-and-1-2-and-1-and-3-1-and-1-and-1-array-10-b-array-ccc-4</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36174/if-a-array-ll-a-and-b-b-and-a-array-and-a-array-ll-and-and-array-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36175/let-o-be-the-vertex-of-the-parabola-y-2-4x-and-its-chords-op-and-oq-are-perpendi</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36176/let-chord-pq-of-length-3-13-of-the-parabola-y-2-12x-be-such-that-the-ordinates-o</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36177/let-the-point-p-be-the-vertex-of-the-parabola-y-x-2-6x-12-if-a-line-passing-thro</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36178/let-the-directrix-of-the-parabola-p-y-2-8x-cut-x-axis-at-the-point-a-let-b-1-be</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36179/let-a-b-and-c-be-the-vertices-of-a-variable-right-angled-triangle-inscribed-in-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36180/consider-the-parabola-p-y-2-4kx-and-the-ellipse-e-x-2-a-2-y-2-b-2-1-let-the-line</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36181/let-the-parabola-y-x-2-px-q-passing-through-the-point-1-1-be-such-that-the-dista</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36182/let-a-be-the-focus-of-the-parabola-y-8-x-let-the-line-y-m-x-c-intersect-the-para</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36183/let-the-image-of-parabola-x-4-y-in-the-line-x-y-1-be-y-a-b-x-c-a-b-c-n-then-a-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36184/an-equilateral-triangle-oab-is-inscribed-in-the-parabola-y-4-x-with-the-vertex-o</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36185/let-the-locus-of-the-mid-point-of-the-chord-through-the-origin-o-of-the-parabola</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36186/if-the-chord-joining-the-points-p-x-y-and-p-x-y-on-the-parabola-y-12-x-subtends</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36187/let-y-12-x-be-the-parabola-with-its-vertex-at-o-let-p-be-a-point-on-the-parabola</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36188/let-one-end-of-a-focal-chord-of-the-parabola-y-16-x-be-16-16-if-p-divides-this-f</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36189/let-o-be-the-vertex-of-the-parabola-x-4-y-and-q-be-any-point-on-it-let-the-locus</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36190/let-r-be-the-radius-of-the-circle-which-touches-x-axis-at-point-a-0-a-0-and-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36191/let-p-be-the-parabola-whose-focus-is-2-1-and-directrix-is-2-x-y-2-0-then-the-sum</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36192/the-axis-of-a-parabola-is-the-line-y-x-and-its-vertex-and-focus-are-in-the-first</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36193/a-line-passing-through-the-point-a-2-0-touches-the-parabola-p-y-2-x-2-at-the-poi</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36194/the-radius-of-the-smallest-circle-which-touches-the-parabolas-y-x-2-2-and-x-y-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36195/let-the-point-p-of-the-focal-chord-p-q-of-the-parabola-y-2-16-x-be-1-4-if-the-fo</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36196/let-the-focal-chord-p-q-of-the-parabola-y-2-4-x-make-an-angle-of-60-with-the-pos</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36197/let-y-2-12-x-be-the-parabola-and-s-be-its-focus-let-pq-be-a-focal-chord-of-the-p</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36198/two-parabolas-have-the-same-focus-4-3-and-their-directrices-are-the-x-axis-and-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36199/let-a-and-b-be-the-two-points-of-intersection-of-the-line-y-5-0-and-the-mirror-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36200/let-a-b-c-d-be-a-trapezium-whose-vertices-lie-on-the-parabola-y-2-4-x-let-the-si</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36201/if-the-equation-of-the-parabola-with-vertex-v-3-2-3-and-the-directrix-x-2-y-0-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36202/let-the-shortest-distance-from-a-0-a-0-to-the-parabola-y-2-4-x-be-4-then-the-equ</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36203/the-focus-of-the-parabola-y-2-4-x-16-is-the-centre-of-the-circle-c-of-radius-5-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36204/if-the-line-3-x-2-y-12-0-intersects-the-parabola-4-y-3-x-2-at-the-points-a-and-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36205/let-p-4-4-3-be-a-point-on-the-parabola-y-2-4-a-x-and-pq-be-a-focal-chord-of-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36206/let-the-parabola-y-x-2-p-x-3-meet-the-coordinate-axes-at-the-points-p-q-and-r-if</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36207/let-a-b-and-c-be-three-points-on-the-parabola-y-2-6-x-and-let-the-line-segment-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36208/consider-the-circle-c-x-2-y-2-4-and-the-parabola-p-y-2-8-x-if-the-set-of-all-val</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36209/let-a-conic-c-pass-through-the-point-4-2-and-p-x-y-x-3-be-any-point-on-c-let-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36210/let-l-l-be-the-lines-passing-through-the-point-p-0-1-and-touching-the-parabola-9</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36211/let-a-line-perpendicular-to-the-line-2-x-y-10-touch-the-parabola-y-2-4-x-9-at-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36212/suppose-a-b-is-a-focal-chord-of-the-parabola-y-2-12-x-of-length-l-and-slope-m-3</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36213/let-pq-be-a-chord-of-the-parabola-y-2-12-x-and-the-midpoint-of-pq-be-at-4-1-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36214/let-the-length-of-the-focal-chord-pq-of-the-parabola-y-2-12-x-be-15-units-if-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36215/the-maximum-area-of-a-triangle-whose-one-vertex-is-at-0-0-and-the-other-two-vert</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36216/let-p-be-a-point-on-the-parabola-y-2-4-x-if-p-also-lies-on-the-chord-of-the-para</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36217/if-the-shortest-distance-of-the-parabola-y-2-4-x-from-the-centre-of-the-circle-x</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36218/let-p-q-be-a-focal-chord-of-the-parabola-y-2-36-x-of-length-100-making-an-acute</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36219/let-a-common-tangent-to-the-curves-y-2-4-x-and-x-4-2-y-2-16-touch-the-curves-at</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36220/the-ordinates-of-the-points-p-and-q-on-the-parabola-with-focus-3-0-and-directrix</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36221/let-r-be-the-focus-of-the-parabola-y-2-20-x-and-the-line-y-m-x-c-intersect-the-p</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36222/if-the-x-intercept-of-a-focal-chord-of-the-parabola-y-2-8-x-4-y-4-is-3-then-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36223/let-s-be-the-set-of-all-a-and-8712-n-such-that-the-area-of-the-triangle-formed-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36224/the-parabolas-a-x-2-2-b-x-c-y-0-and-d-2-2-e-x-f-y-0-intersect-on-the-line-y-1-if</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36225/let-a-be-a-point-on-the-x-axis-common-tangents-are-drawn-from-a-to-the-curves-x</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36226/if-p-h-k-be-point-on-the-parabola-x-4-y-2-which-is-nearest-to-the-point-q-0-33-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36227/a-triangle-is-formed-by-the-tangents-at-the-point-2-2-on-the-curves-y-2-2-x-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36228/the-equations-of-two-sides-of-a-variable-triangle-are-x-0-and-y-3-and-its-third</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/36230/the-equations-of-sides-a-b-and-a-c-of-a-triangle-a-b-c-are-and-955-1-x-and-955-y</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36231/let-a-tangent-to-the-curve-y-2-24-x-meet-the-curve-x-y-2-at-the-points-a-and-b-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36232/two-tangent-lines-l-1-and-l-2-are-drawn-from-the-point-2-0-to-the-parabola-2-y-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36233/if-the-tangents-drawn-at-the-points-p-and-q-on-the-parabola-y-2-2-x-3-intersect</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36234/if-the-length-of-the-latus-rectum-of-a-parabola-whose-focus-is-a-a-and-the-tange</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/36236/the-equation-of-a-common-tangent-to-the-parabolas-y-x-2-and-y-x-2-2-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36237/the-tangents-at-the-points-a-1-3-and-b-1-1-on-the-parabola-y-2-2-x-2-y-1-meet-at</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36238/the-sum-of-diameters-of-the-circles-that-touch-i-the-parabola-75-x-2-64-5-y-3-at</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36239/let-p-y-2-4-a-x-a-and-62-0-be-a-parabola-with-focus-s-let-the-tangents-to-the-pa</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36240/if-vertex-of-parabola-is-2-1-and-equation-of-its-directrix-is-4-x-3-y-21-then-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36241/if-the-equation-of-the-parabola-whose-vertex-is-at-5-4-and-the-directrix-is-3-x</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36242/a-circle-of-radius-2-unit-passes-through-the-vertex-and-the-focus-of-the-parabol</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36243/let-the-normal-at-the-point-p-on-the-parabola-y-2-6-x-pass-through-the-point-5-8</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/36245/if-y-m-1-x-c-1-and-y-m-2-x-c-2-m-1-and-8800-m-2-are-two-common-tangents-of-circl</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36246/let-x-2-t-y-t-2-3-be-a-conic-let-s-be-the-focus-and-b-be-the-point-on-the-axis-o</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36247/let-p-1-be-a-parabola-with-vertex-3-2-and-focus-4-4-and-p-2-be-its-mirror-image</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36248/a-particle-is-moving-in-the-x-y-plane-along-a-curve-c-passing-through-the-point</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36249/let-x-2-y-2-a-x-b-y-c-0-be-a-circle-passing-through-0-6-and-touching-the-parabol</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/36251/consider-the-parabola-with-vertex-1-2-3-4-and-the-directrix-y-1-2-let-p-be-the-p</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/36253/the-length-of-the-latus-rectum-of-a-parabola-whose-vertex-and-focus-are-on-the-p</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/36920/let-and-945-and-and-946-be-the-roots-of-x-2-6-x-2-0-if-a-n-and-945-n-and-946-n-f</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36921/if-and-945-and-946-and-8712-r-are-such-that-1-2-i-here-i-2-1-is-a-root-of-z-2-an</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36922/the-integer-k-for-which-the-inequality-x-2-2-3-k-1-x-8-k-2-7-and-62-0-is-valid-f</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36923/the-number-of-the-real-roots-of-the-equation-x-1-2-x-5-27-4-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36924/let-p-and-q-be-two-positive-numbers-such-that-p-q-2-and-p-4-q-4-272-then-p-and-q</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36925/if-and-945-and-and-946-are-the-roots-of-the-equation-2-x-2-x-1-1-then-and-946-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36926/if-and-945-and-and-946-be-two-roots-of-the-equation-x-2-64-x-256-0-then-the-valu</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36927/if-and-945-and-and-946-are-the-roots-of-the-equation-7-x-2-3-x-2-0-then-the-valu</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36928/the-product-of-the-roots-of-the-equation-9-x-2-18-x-5-0-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36929/let-and-955-and-8800-0-be-in-r-if-and-945-and-and-946-are-the-roots-of-the-equat</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36930/let-t-denote-the-greatest-integer-and-8804-t-then-the-equation-in-x-x-2-2-x-2-7</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36931/let-and-945-and-and-946-be-the-roots-of-x-2-3-x-p-0-and-and-947-and-and-948-be-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36932/the-set-of-all-real-values-of-and-955-for-which-the-quadratic-equation-and-955-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36933/consider-the-two-sets-a-m-and-8712-r-both-the-roots-of-x-2-m-1-x-m-4-0-are-real</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36934/if-and-945-and-and-946-are-the-roots-of-the-equation-x-2-p-x-2-0-and-1-and-945-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36935/let-f-x-be-a-quadratic-polynomial-such-that-f-and-8211-1-f-2-0-if-one-of-the-roo</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36936/let-and-945-and-and-946-be-the-roots-of-the-equation-5-x-2-6-x-2-0-if-s-n-and-94</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36937/let-a-b-and-8712-r-a-and-8800-0-be-such-that-the-equation-a-x-2-2-b-x-5-0-has-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36938/the-number-of-real-roots-of-the-equation-e-4-x-e-3-x-4-e-2-x-e-x-1-0-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36939/let-s-be-the-set-of-all-real-roots-of-the-equation-3-x-3-x-1-2-3-x-1-3-x-2-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36940/the-least-positive-value-of-andlsquo-a-andrsquo-for-which-the-equation-2-x-2-a-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36941/let-and-945-and-and-946-be-the-roots-of-the-equation-x-2-x-1-0-if-p-k-and-945-k</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36942/let-and-945-and-and-946-be-two-real-roots-of-the-equation-k-1-t-a-n-2-x-2-and-89</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36943/if-and-945-and-946-and-and-947-are-three-consecutive-terms-of-a-non-constant-g-p</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36944/if-and-945-and-and-946-are-the-roots-of-the-equation-375-x-2-25-x-2-0-then-l-i-m</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36945/the-number-of-real-roots-of-the-equation-5-2-x-1-2-x-2-x-2-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36946/if-and-945-and-and-946-are-the-roots-of-the-quadratic-equation-x-2-x-s-i-n-and-9</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36947/if-m-is-chosen-in-the-quadratic-equation-m-2-1-x-2-3-x-m-2-1-2-0-such-that-the-s</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36948/let-p-q-and-8712-q-if-2-3-is-a-root-of-the-quadratic-equation-x-2-p-x-q-0-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36949/if-three-distinct-numbers-a-b-c-are-in-g-p-and-the-equations-a-x-2-2-b-x-c-0-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36950/the-number-of-integral-values-of-m-for-which-the-equation-1-m-2-x-2-2-1-3-m-x-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36951/the-sum-of-the-solutions-of-the-equation-x-2-x-x-4-2-0-x-and-62-0-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36952/the-number-of-integral-values-of-m-for-which-the-quadratic-expression-1-2-m-x-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36953/if-and-955-be-the-ratio-of-the-roots-of-the-quadratic-equation-in-x-3-m-2-x-2-m</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36954/let-and-be-the-roots-of-the-quadratic-equation-x-x-1-0-0-45-and-then-n-0-n-1-n-n</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36955/if-one-real-root-of-the-quadratic-equation-81-x-k-x-256-0-is-cube-of-the-other-r</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36956/the-value-of-and-955-such-that-sum-of-the-squares-of-the-roots-of-the-quadratic</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36957/consider-the-quadratic-equation-c-5-x-2-2-c-x-c-4-0-c-and-8800-5-let-s-be-the-se</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36958/the-number-of-all-possible-positive-integral-value-of-and-945-for-which-the-root</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36959/if-both-the-roots-of-the-quadratic-equation-x-2-m-x-4-0-are-real-and-distinct-an</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36960/let-and-945-and-and-946-be-the-roots-of-the-equation-x-2-2-x-2-0-then-and-945-15</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36961/let-p-q-and-r-be-real-numbers-p-and-8800-q-r-and-8800-0-such-that-the-roots-of-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36962/if-an-angle-a-of-a-and-916-a-b-c-satisfies-5-cos-a-3-0-then-the-roots-of-the-qua</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36963/if-r-is-such-that-the-sum-of-the-cubes-of-the-roots-of-the-equation-x-2-2-x-10-0</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36964/if-and-955-and-8712-r-is-such-that-the-sum-of-the-cubes-of-the-roots-of-the-equa</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36965/if-tan-and-8289-a-and-tan-and-8289-b-are-the-roots-of-the-quadratic-equation-3-x</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36966/the-sum-of-all-the-real-values-of-x-satisfying-the-equation-2-x-1-x-2-5-x-50-1-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36967/let-p-x-be-a-quadratic-polynomial-such-that-p-0-1-if-p-x-leaves-remainder-4-when</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36968/if-for-a-positive-integer-n-the-quadratic-equation-x-x-1-x-1-x-2-x-n-1-and-175-x</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36969/if-x-is-a-solution-of-the-equation-2-x-1-2-x-1-1-x-and-8805-1-2-then-4-x-2-1-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36970/if-the-equations-x-2-b-x-1-0-and-x-2-x-b-0-have-a-common-root-different-from-1-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36971/the-sum-of-all-real-values-of-x-satisfying-the-equation-x-2-5-x-5-x-2-4-x-60-1-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36972/if-the-two-roots-of-the-equation-a-1-x-4-x-2-1-a-1-x-2-x-1-2-0-are-real-and-dist</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36973/let-and-945-and-and-946-be-the-roots-of-equation-x-2-6-x-2-0-if-a-n-and-945-n-an</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36974/the-equation-3-x-2-x-5-x-3-where-x-and-8289-is-real-has</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36975/the-sum-of-the-roots-of-the-equation-x-2-2-x-3-4-0-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36976/if-and-are-roots-of-the-equation-x-2-4-2-k-x-2-e-4-k-1-0-for-some-k-and-2-2-66-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36977/if-1-and-945-1-and-946-are-the-roots-of-the-equation-a-x-2-b-x-1-0-a-and-8800-0</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36978/if-equations-a-x-2-b-x-c-0-a-b-c-and-8712-r-a-and-8800-0-and-2-x-2-3-x-4-0-have</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36979/if-a-and-8712-r-and-the-equation-3-x-x-2-2-x-x-a-2-0-where-x-denotes-the-greates</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36980/let-and-945-and-and-946-be-the-roots-of-equation-p-x-2-q-x-r-0-p-and-8800-0-if-p</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36981/if-p-and-q-are-non-zero-real-numbers-and-3-3-p-q-then-a-quadratic-equation-whose</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36982/if-and-are-roots-of-the-equation-x-2-p-x-3-p-4-0-such-that-10-then-p-belongs-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36983/the-values-of-a-for-which-one-root-of-the-equation-x-2-a-1-x-a-2-a-8-0-exceeds-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36984/the-real-number-k-for-which-the-equation-2-x-3-3-x-k-0-has-two-distinct-real-roo</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36985/if-the-equations-x-2-2-x-3-0-and-a-x-2-b-x-c-0-a-b-c-and-8712-r-have-a-common-ro</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36986/if-a-b-c-r-and-1-is-a-root-of-equation-a-x-2-b-x-c-0-then-the-curve-y-4-a-x-2-3</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36987/let-p-q-r-r-and-r-p-0-if-the-quadratic-equation-p-x-2-q-x-r-0-has-two-complex-ro</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36988/consider-a-quadratic-equation-a-x-2-b-x-c-0-where-2-a-3-b-6-c-0-and-let-g-x-a-x</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36989/if-a-b-c-d-and-p-are-distinct-real-numbers-such-that-a-2-b-2-c-2-p-2-2-p-a-b-b-c</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36990/if-the-sum-of-the-square-of-the-roots-of-the-equation-x-2-2-x-1-0-is-least-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36991/the-value-of-k-for-which-the-equation-k-2-x-2-8-x-k-4-0-has-both-roots-real-dist</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36992/if-and-are-the-roots-of-the-equation-x-2-x-1-0-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36993/if-the-roots-of-the-equation-b-x-2-c-x-a-0-be-imaginary-then-for-all-real-values</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/36994/the-quadratic-equations-x-2-6-x-a-0-and-x-2-c-x-6-0-have-one-root-in-common-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/37071/if-the-first-term-of-an-a-p-is-3-and-the-sum-of-its-first-four-terms-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37072/suppose-that-the-number-of-terms-in-an-a-p-is-2-k-k-n-if-the-sum-of-all-odd-term</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37073/let-a-a-a-be-a-g-p-of-increasing-positive-terms-if-a-a-28-and-a-a-29-then-a-is-e</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37074/if-r-1-n-t-r-2-n-1-2-n-1-2-n-3-2-n-5-64-then-n-r-1-n-1-t-r-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37075/let-a-a-r-a-r-2-be-an-infinite-g-p-if-n-0-a-r-n-57-and-n-0-a-3-r-3-n-9747-then-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37076/if-1-1-1-2-1-1012-1-2-1-1-4-3-1-6-5-1-2024-2023-1-2024-then-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37077/if-the-sum-of-the-series-1-1-1-d-1-1-d-1-2-d-1-1-9-d-1-10-d-is-equal-to-5-then-5</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37078/in-an-increasing-geometric-progression-of-positive-terms-the-sum-of-the-second-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37079/an-arithmetic-progression-is-written-in-the-following-way-the-sum-of-all-the-ter</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37080/if-the-set-r-a-b-a-5-b-42-a-b-n-has-m-elements-and-n-1-m-1-i-n-x-i-y-where-i-1-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37081/let-the-positive-integers-be-written-in-the-form-if-the-k-th-row-contains-exactl</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37082/let-a-b-c-be-an-equilateral-triangle-a-new-triangle-is-formed-by-joining-the-mid</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37083/a-software-company-sets-up-m-number-of-computer-systems-to-finish-an-assignment</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37084/if-s-x-1-x-2-1-x-2-3-1-x-3-60-1-x-x-0-and-60-2-s-60-a-b-b-b-where-a-b-n-then-a-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37085/let-a-n-100-700-n-n-is-neither-a-multiple-of-3-nor-a-multiple-of-4-then-the-numb</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37086/let-the-first-term-of-a-series-be-t-6-and-its-r-th-term-t-r-3-t-r-1-6-r-r-2-3-if</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37087/for-x-0-the-least-value-of-k-for-which-4-1-x-4-1-x-k-2-16-x-16-x-are-three-conse</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37088/if-1-3-2-2-3-5-2-6-18-9-3-11-2-36-3-49-20-6-180-upto-2-b-a-1-e-a-b-where-a-and-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37089/if-1-1-2-1-2-3-1-99-100-m-and-1-1-2-1-2-3-1-99-100-n-then-the-point-m-n-lies-on</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37090/let-a-a-a-be-in-an-arithmetic-progression-of-positive-terms-let-a-k-a-2-a-2-a-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37091/the-value-of-1-2-2-2-3-2-100-101-2-1-2-2-2-2-3-100-2-101-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37092/let-three-real-numbers-a-b-c-be-in-arithmetic-progression-and-a-1-b-c-3-be-in-ge</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37093/let-the-first-three-terms-2-p-and-q-with-q-2-of-a-g-p-be-respectively-the-7-th-8</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37094/let-s-n-denote-the-sum-of-the-first-n-terms-of-an-arithmetic-progression-if-s-10</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37095/if-three-successive-terms-of-a-g-p-with-common-ratio-r-r-1-are-the-length-of-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37096/let-3-7-11-15-403-and-2-5-8-11-404-be-two-arithmetic-progressions-then-the-sum-o</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37097/let-3-a-b-c-be-in-a-p-and-3-a-1-b-1-c-9-be-in-g-p-then-the-arithmetic-mean-of-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37098/let-2-nd-8-th-and-44-th-terms-of-a-non-constant-a-p-be-respectively-the-1-st-2-n</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37099/the-sum-of-the-series-1-1-3-1-2-1-4-2-1-3-2-2-2-4-3-1-3-3-2-3-4-up-to-10-terms-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37100/let-a-and-b-be-two-distinct-positive-real-numbers-let-11-th-term-of-a-gp-whose-f</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37101/let-s-n-be-the-sum-to-n-terms-of-an-arithmetic-progression-3-7-11-if-40-6-n-n-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37102/let-s-a-denote-the-sum-of-first-n-terms-an-arithmetic-progression-if-s-20-790-an</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37103/let-1-2-4-2-8-2-13-2-19-2-26-2-upto-10-terms-and-n-1-10-n-4-if-4-55-k-40-then-k</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37104/if-log-e-a-log-e-b-log-e-c-are-in-an-a-p-and-log-e-a-log-e-2-b-log-e-2-b-log-e-3</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37105/if-each-term-of-a-geometric-progression-a-1-a-2-a-3-with-a-1-1-8-and-a-2-a-1-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37106/in-an-a-p-the-sixth-term-a-6-2-if-the-a-1-a-4-a-5-is-the-greatest-then-the-commo</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37107/if-in-a-g-p-of-64-terms-the-sum-of-all-the-terms-is-7-times-the-sum-of-the-odd-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37108/the-20-th-term-from-the-end-of-the-progression-20-19-1-4-18-1-2-17-3-4-129-1-4-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37109/the-number-of-common-terms-in-the-progressions-4-9-14-19-up-to-25-th-term-and-3</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37110/if-8-3-1-4-3-p-1-4-2-3-2-p-1-4-3-3-3-p-then-the-value-of-p-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37111/let-a-1-and-a-2-be-two-arithmetic-means-and-g-1-g-2-and-g-3-be-three-geometric-m</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37112/if-the-sum-of-the-series-1-2-1-3-1-2-2-1-2-and-183-3-1-3-2-1-2-3-1-2-2-and-183-3</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37113/let-a-1-a-2-a-3-and-8230-be-a-g-p-of-increasing-positive-numbers-let-the-sum-of</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37114/let-and-945-denote-the-greatest-integer-and-8804-and-945-then-1-2-3-120-is-equal</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37115/let-f-x-and-8721-k-1-10-k-and-183-x-k-x-and-8712-and-8477-if-2-f-2-f-and-39-2-11</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37116/let-s-1-s-2-s-3-s-10-respectively-be-the-sum-of-12-terms-of-10-a-ps-whose-first</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37117/the-sum-to-20-terms-of-the-series-2-and-183-2-2-3-2-2-and-183-4-2-5-2-2-and-183</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37118/let-and-60-a-n-and-62-be-a-sequence-such-that-a-1-a-2-a-n-n-2-3-n-n-1-n-2-if-28</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37119/let-a-b-c-and-d-be-positive-real-numbers-such-that-a-b-c-d-11-if-the-maximum-val</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37120/for-k-and-8712-and-8469-if-the-sum-of-the-series-1-4-k-8-k-2-13-k-3-19-k-4-is-10</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37121/let-x-1-x-2-and-8230-x-100-be-in-an-arithmetic-progression-with-x-1-2-and-their</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37122/let-s-109-108-5-107-5-2-and-8230-2-5-107-1-5-108-then-the-value-of-16-s-25-54-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37123/if-s-n-4-11-21-34-50-and-8230-to-n-terms-then-1-60-s-29-s-9-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37124/suppose-a-1-a-2-2-a-3-a-4-be-in-an-arithmetico-geometric-progression-if-the-comm</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37125/let-the-first-term-a-and-the-common-ratio-r-of-a-geometric-progression-be-positi</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37126/the-sum-of-all-those-terms-of-the-arithmetic-progression-3-8-13-373-which-are-no</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37127/let-a-n-be-n-th-term-of-the-series-5-8-14-23-35-50-and-s-n-and-8721-k-1-n-a-k-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37128/let-0-and-60-z-and-60-y-and-60-x-be-three-real-numbers-such-that-1-x-1-y-1-z-are</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37129/let-s-k-1-2-k-k-and-and-8721-j-1-n-s-2-j-n-a-b-n-2-c-n-d-where-a-b-c-d-and-8712</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37130/if-g-c-d-m-n-1-and-1-2-2-2-3-2-4-2-2021-2-2022-2-2023-2-1012-m-2-n-then-m-2-n-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37131/if-20-19-2-21-20-18-3-21-2-20-17-20-21-19-k-20-19-then-k-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37132/the-sum-of-the-first-20-terms-of-the-series-5-11-19-29-41-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37133/let-a-1-a-2-a-3-a-n-be-n-positive-consecutive-terms-of-an-arithmetic-progression</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37134/the-sum-and-8721-n-1-and-8734-2-n-2-3-n-4-2-n-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37135/the-sum-of-the-common-terms-of-the-following-three-arithmetic-progressions-3-7-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37136/the-sum-to-10-terms-of-the-series-1-1-1-2-1-4-2-1-2-2-2-4-3-1-3-2-3-4-and-8230-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37137/let-a-1-8-a-2-a-3-and-8230-a-n-be-an-a-p-if-the-sum-of-its-first-four-terms-is-5</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37138/the-number-of-3-digit-numbers-that-are-divisible-by-either-2-or-3-but-not-divisi</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37139/let-a-1-a-2-a-3-and-8230-and-8230-be-an-a-p-if-a-7-3-the-product-a-1-a-4-is-mini</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37140/the-sum-1-2-2-3-2-3-5-2-4-7-2-5-9-2-and-8230-15-29-2-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37141/if-the-sum-and-product-of-four-positive-consecutive-terms-of-a-g-p-are-126-and-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37142/let-a-1-a-2-and-8230-and-8230-a-n-be-in-a-p-if-a-5-2-a-7-and-a-11-18-then-12-1-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37143/number-of-4-digit-numbers-that-are-less-than-or-equal-to-2800-and-either-divisib</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37144/let-a-b-c-and-62-1-a-3-b-3-and-c-3-be-in-a-p-and-log-a-b-log-c-a-and-log-b-c-be</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37145/the-8-th-common-term-of-the-series-s-1-3-7-11-15-19-and-8230-s-2-1-6-11-16-21-an</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37146/if-a-n-2-4-n-2-16-n-15-then-a-1-a-2-and-8230-a-25-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37147/and-8721-n-0-and-8734-n-3-2-n-2-n-1-n-n-2-n-a-e-b-e-c-where-a-b-c-and-8712-and-8</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37148/let-a-1-b-1-1-and-a-n-a-n-1-n-1-b-n-b-n-1-a-n-1-and-8704-n-and-8805-2-if-s-and-8</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37149/let-a-k-and-b-k-k-n-be-two-g-p-s-with-common-ratio-r-and-r-respectively-such-tha</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37150/the-number-of-3-digit-numbers-that-are-divisible-by-either-3-or-4-but-not-divisi</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37151/let-a-1-a-2-a-3-and-8230-be-a-gp-of-increasing-positive-numbers-if-the-product-o</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37152/for-the-two-positive-numbers-a-b-if-a-b-and-1-18-are-in-a-geometric-progression</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37153/let-a-1-a-2-a-3-be-the-three-a-p-with-the-same-common-difference-d-and-having-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37154/if-1-3-2-3-3-3-upto-n-terms-1-and-183-3-2-and-183-5-3-and-183-7-upto-n-terms-9-5</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37155/for-three-positive-integers-p-q-r-x-p-q-2-y-q-r-z-p-2-r-and-r-p-q-1-such-that-3</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37156/the-4-th-term-of-gp-is-500-and-its-common-ratio-is-1-m-m-and-8712-n-let-s-n-deno</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37157/let-a-n-n-0-and-8734-be-a-sequence-such-that-a-0-a-1-0-and-a-n-2-3-a-n-1-2-a-n-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37158/and-8721-r-1-20-r-2-1-r-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37159/if-1-20-a-40-a-1-40-a-60-a-and-8230-and-8230-1-180-a-200-a-1-256-then-the-maximu</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37160/let-a-1-a-2-a-3-and-8230-be-an-a-p-if-and-8721-r-1-and-8734-a-r-2-r-4-then-4-a-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37161/if-1-2-and-215-3-and-215-4-1-3-and-215-4-and-215-5-1-4-and-215-5-and-215-6-and-8</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37162/if-6-3-12-10-3-11-20-3-10-40-3-9-and-8230-10240-3-2-n-and-183-m-where-m-is-odd-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37163/if-the-minimum-value-of-f-x-5-x-2-2-and-945-x-5-x-and-62-0-is-14-then-the-value</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37164/consider-the-sequence-a-1-a-2-a-3-and-8230-and-8230-such-that-a-1-1-a-2-2-and-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37165/for-p-q-and-8712-r-consider-the-real-valued-function-f-x-x-p-2-q-x-and-8712-r-an</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37166/let-x-1-x-2-x-3-and-8230-x-20-be-in-geometric-progression-with-x-1-3-and-the-com</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37167/let-the-sum-of-an-infinite-g-p-whose-first-term-is-a-and-the-common-ratio-is-r-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37168/2-3-1-3-1-and-215-7-4-3-3-3-2-3-1-3-2-and-215-11-6-3-5-3-4-3-3-3-2-3-1-3-3-and-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37169/suppose-a-1-a-2-and-8230-a-n-and-8230-be-an-arithmetic-progression-of-natural-nu</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37170/let-f-x-2-x-2-x-1-and-s-n-and-8712-and-8484-f-n-and-8804-800-then-the-value-of-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37171/if-and-8721-k-1-10-k-k-4-k-2-1-m-n-where-m-and-n-are-co-prime-then-m-n-is-equal</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37172/different-a-p-and-39-s-are-constructed-with-the-first-term-100-the-last-term-199</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37173/consider-two-g-ps-2-2-2-2-3-and-8230-and-4-4-2-4-3-and-8230-of-60-and-n-terms-re</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37174/the-series-of-positive-multiples-of-3-is-divided-into-sets-3-6-9-12-15-18-21-24</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37175/the-sum-and-8721-n-1-21-3-4-n-1-4-n-3-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37176/let-a-1-b-1-1-a-n-a-n-1-2-and-b-n-a-n-b-n-1-for-every-natural-number-n-and-8805</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37177/the-sum-of-the-infinite-series-1-5-6-12-6-2-22-6-3-35-6-4-51-6-5-70-6-6-and-8230</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37178/let-3-6-9-12-and-8230-upto-78-terms-and-5-9-13-17-and-8230-upto-59-terms-be-two</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37179/let-a-n-n-0-and-8734-be-a-sequence-such-that-a-0-a-1-0-and-a-n-2-2-a-n-1-a-n-1-f</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37180/if-n-arithmetic-means-are-inserted-between-a-and-100-such-that-the-ratio-of-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37181/let-for-n-1-2-and-8230-and-8230-50-s-n-be-the-sum-of-the-infinite-geometric-prog</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37182/let-a-1-a-2-a-3-and-8230-and-8230-be-an-increasing-geometric-progression-of-posi</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37183/let-s-2-6-7-12-7-2-20-7-3-30-7-4-and-8230-then-4-s-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37184/if-a-1-a-2-a-3-and-8230-and-b-1-b-2-b-3-and-8230-are-a-p-and-a-1-2-a-10-3-a-1-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37185/if-x-and-8721-n-0-and-8734-a-n-y-and-8721-n-0-and-8734-b-n-z-and-8721-n-0-and-87</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37186/if-the-sum-of-the-first-ten-terms-of-the-series-1-5-2-65-3-325-4-1025-5-2501-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37187/if-a-and-8721-n-1-and-8734-1-3-1-n-n-and-b-and-8721-n-1-and-8734-1-n-3-1-n-n-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37188/if-a-1-and-62-0-a-2-a-3-a-4-a-5-are-in-a-g-p-a-2-a-4-2-a-3-1-and-3-a-2-a-3-2-a-4</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37189/let-a-and-8721-i-1-10-and-8721-j-1-10-min-i-j-and-b-and-8721-i-1-10-and-8721-j-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37190/the-sum-1-2-and-183-3-3-and-183-3-2-and-8230-and-8230-10-and-183-3-9-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37191/the-greatest-integer-less-than-or-equal-to-the-sum-of-first-100-terms-of-the-seq</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37192/let-x-y-and-62-0-if-x-3-y-2-2-15-then-the-least-value-of-3-x-2-y-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37193/if-a-i-i-1-n-where-n-is-an-even-integer-is-an-arithmetic-progression-with-common</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37194/let-s-n-1-and-183-n-1-2-and-183-n-2-3-and-183-n-3-and-8230-n-1-and-183-1-n-and-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37195/let-a-1-a-2-and-8230-a-21-be-an-a-p-such-that-and-8721-n-1-20-1-a-n-a-n-1-4-9-if</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37196/let-a-1-a-2-a-3-and-8230-be-an-a-p-if-a-1-a-2-and-8230-a-10-a-1-a-2-and-8230-a-p</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37197/if-s-7-5-9-5-2-13-5-3-19-5-4-and-8230-then-160-s-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37198/the-sum-of-10-terms-of-the-series-3-1-2-and-215-2-2-5-2-2-and-215-3-2-7-3-2-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37199/three-numbers-are-in-an-increasing-geometric-progression-with-common-ratio-r-if</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37200/if-0-and-60-x-and-60-1-and-y-1-2-x-2-2-3-x-3-3-4-x-4-and-8230-and-8230-then-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37201/if-for-x-y-and-8712-r-x-and-62-0-y-log-10-x-log-10-x-1-3-log-10-x-1-9-and-8230-u</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37202/if-0-and-60-x-and-60-1-then-3-2-x-2-5-3-x-3-7-4-x-4-and-8230-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37203/let-a-1-a-2-and-8230-a-10-be-an-a-p-with-common-difference-3-and-b-1-b-2-and-823</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37204/the-sum-of-the-series-1-x-1-2-x-2-1-2-2-x-4-1-and-8230-2-100-x-2-100-1-when-x-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37205/if-the-sum-of-an-infinite-gp-a-a-r-a-r-2-a-r-3-and-8230-is-15-and-the-sum-of-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37206/if-p-1-1-2-and-183-p-2-2-3-and-183-p-3-3-and-8230-15-and-183-p-15-15-p-r-q-s-0-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37207/if-tan-and-960-9-x-tan-7-and-960-18-are-in-arithmetic-progression-and-tan-and-96</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37208/if-log-3-2-log-3-2-x-5-log-3-2-x-7-2-are-in-an-arithmetic-progression-then-the-v</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37209/let-s-n-be-the-sum-of-the-first-n-terms-of-an-arithmetic-progression-if-s-3-n-3</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37210/if-the-value-of-1-2-3-6-3-2-10-3-3-and-8230-upto-and-8734-log-0-25-1-3-1-3-2-1-3</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37211/let-s-n-denote-the-sum-of-first-n-terms-of-an-arithmetic-progression-if-s-10-530</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37212/if-sum-of-the-first-21-terms-of-the-series-log-9-1-2-x-log-9-1-3-x-log-9-1-4-x-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37213/let-a-n-n-1-and-8734-be-a-sequence-such-that-a-1-1-a-2-1-and-a-n-2-2-a-n-1-a-n-f</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37214/for-k-and-8712-n-let-1-and-945-and-945-1-and-945-2-and-8230-and-8230-and-945-20</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37215/let-s-1-be-the-sum-of-first-2-n-terms-of-an-arithmetic-progression-let-s-2-be-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37216/if-and-8721-r-1-10-r-r-3-6-r-2-2-r-5-and-945-11-then-the-value-of-and-945-is-equ</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37217/if-and-945-and-946-are-natural-numbers-such-that-100-and-945-199-and-946-100-100</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37218/1-3-2-1-1-5-2-1-1-7-2-1-and-8230-1-201-2-1-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37219/if-1-log-10-4-x-2-and-log-10-4-x-18-5-are-in-arithmetic-progression-for-a-real-n</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/37224/if-the-arithmetic-mean-and-the-geometric-mean-of-the-p-th-and-q-th-terms-of-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/37227/in-an-increasing-geometric-series-the-sum-of-the-second-and-the-sixth-term-is-25</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/37229/if-0-and-60-and-952-and-981-and-60-and-960-2-x-and-8721-n-0-and-8734-cos-2-n-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/37231/let-a-b-c-be-in-arithmetic-progression-let-the-centroid-of-the-triangle-with-ver</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37232/the-sum-of-first-four-terms-of-a-geometric-progression-g-p-is-65-12-and-the-sum</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/37234/a-man-is-walking-on-a-straight-line-the-arithmetic-mean-of-the-reciprocals-of-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37235/the-common-difference-of-the-a-p-b-1-b-2-b-m-is-2-more-than-common-difference-of</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/37237/if-the-sum-of-the-second-third-and-fourth-terms-of-a-positive-term-g-p-is-3-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/37239/if-2-10-2-9-and-183-3-1-2-8-and-183-3-2-and-8230-and-8230-2-and-183-3-9-3-10-s-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37240/if-3-2-sin-2-and-945-1-14-and-3-4-2-sin-2-and-945-are-the-first-three-terms-of-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37241/let-a-1-a-2-and-8230-a-n-be-a-given-a-p-whose-common-difference-is-an-integer-an</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/37244/if-m-arithmetic-means-a-ms-and-three-geometric-means-g-ms-are-inserted-between-3</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37245/if-the-first-term-of-an-a-p-is-3-and-the-sum-of-its-first-25-terms-is-equal-to-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37246/the-value-of-0-16-log-2-5-1-3-1-3-2-1-3-3-and-8230-and-8734-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37247/if-the-sum-of-first-11-terms-of-an-a-p-a-1-a-2-a-3-and-8230-and-8230-is-0-a-1-an</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/37249/the-sum-of-the-first-three-terms-of-g-p-is-s-and-their-products-is-27-then-all-s</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37250/if-x-and-60-1-y-and-60-1-and-x-and-8800-1-then-the-sum-to-infinity-of-the-follow</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37251/let-a-n-be-the-n-t-h-term-of-a-g-p-of-positive-terms-if-and-8721-n-1-100-a-2-n-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37252/if-x-and-8721-n-0-and-8734-1-n-tan-2-and-8289-and-952-and-y-and-8721-n-0-and-873</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37253/the-number-of-terms-common-to-the-two-a-p-andrsquo-s-3-7-11-and-8230-407-and-2-9</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37254/the-product-2-1-4-and-8729-4-1-16-and-8729-8-1-48-and-8729-16-1-128-and-8729-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37255/if-the-10-t-h-term-of-an-a-p-is-1-20-and-its-20-t-h-term-is-1-10-then-the-sum-of</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37256/the-sum-and-8721-n-1-7-n-n-1-2-n-1-4-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37257/the-sum-and-8721-k-1-20-1-2-3-and-8230-k-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37258/let-f-r-and-8594-r-be-such-that-for-all-x-and-8712-r-2-1-x-2-1-x-f-x-and-3-x-3-x</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/37261/five-numbers-are-in-a-p-whose-sum-is-25-and-product-is-2520-if-one-of-these-five</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37262/the-greatest-positive-integer-k-for-which-49-k-1-is-a-factor-of-the-sum-49-125-4</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/37275/the-sum-of-all-natural-numbers-n-such-that-100-and-60-n-and-60-200-and-h-c-f-91</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/37279/the-product-of-three-consecutive-terms-of-a-g-p-is-512-if-4-is-added-to-each-of</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37280/if-19-th-term-of-a-non-zero-a-p-is-zero-then-its-49th-term-29th-term-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37281/let-s-n-1-q-q-q-n-and-t-n-1-q-1-2-q-1-2-q-1-2-n-where-q-is-a-real-number-and-q-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37282/let-a-a-a-be-a-g-p-if-a-a-25-then-a-a-equals</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/37285/the-sum-of-all-two-digit-positive-numbers-which-when-divided-by-7-yield-2-or-5-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37286/the-sum-of-the-following-series-1-6-9-1-2-2-2-3-2-7-12-1-2-2-2-3-2-4-2-9-15-1-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/37289/let-a-1-a-2-and-8230-a-30-be-an-a-p-s-and-8721-i-1-30-a-i-and-t-and-8721-i-1-15</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37290/let-1-x-1-1-x-2-and-8230-1-x-n-x-i-and-8800-0-for-i-1-2-and-8230-n-be-in-a-p-suc</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37291/the-sum-of-the-first-20-terms-of-the-series-1-3-2-7-4-15-8-31-16-and-8230-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37292/let-a-n-3-4-3-4-2-3-4-3-1-n-1-3-4-n-and-b-n-1-a-n-then-the-least-odd-natural-num</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37293/if-a-b-c-are-in-a-p-and-a-2-b-2-c-2-are-in-g-p-such-that-a-b-c-and-a-b-c-3-4-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37294/if-b-is-the-first-term-of-an-infinite-g-p-whose-sum-is-five-then-b-lies-in-the-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/37297/if-x-1-x-2-and-8230-x-n-and-1-h-1-1-h-2-and-8230-1-h-n-are-two-a-p-s-such-that-x</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37298/let-a-be-the-sum-of-the-first-20-terms-and-b-be-the-sum-of-the-first-40-terms-of</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/37300/if-three-positive-numbers-a-b-and-c-are-in-a-p-such-that-a-b-c-8-then-the-minimu</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/37302/if-the-arithmetic-mean-of-two-numbers-a-and-b-a-and-62-b-and-62-0-is-five-times</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37303/if-the-sum-of-the-first-n-terms-of-the-series-3-75-243-507-and-8230-is-435-3-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/37306/let-x-y-z-be-positive-real-numbers-such-that-x-y-z-12-and-x-3-y-4-z-5-0-1-600-3</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/37310/if-and-8721-n-1-5-1-n-n-1-n-2-n-3-k-3-then-k-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/37316/the-number-of-terms-in-an-a-p-is-even-the-sum-of-the-odd-terms-in-it-is-24-and-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37317/let-g-be-the-geometric-mean-of-two-positive-numbers-a-and-b-and-m-be-the-arithme</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37318/the-least-positive-integer-n-such-that-1-2-3-2-3-2-2-3-n-1-1-100-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37319/if-1-x-4-x-5-i-0-5-a-i-1-x-i-for-all-x-in-r-then-a-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37320/in-a-geometric-progression-if-the-ratio-of-the-sum-of-first-5-terms-to-the-sum-o</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37321/the-sum-of-the-first-20-terms-common-between-the-series-3-7-11-15-and-1-6-11-16</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37322/given-an-a-p-whose-terms-are-all-positive-integers-the-sum-of-its-first-nine-ter</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/37324/if-10-9-2-11-1-10-8-3-11-2-10-7-10-11-9-k-10-9-then-k-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37325/three-positive-numbers-form-an-increasing-g-p-if-the-middle-term-in-this-g-p-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37326/given-a-sequence-of-4-numbers-first-three-of-which-are-in-g-p-and-the-last-three</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/37331/the-sum-3-1-2-5-1-2-2-2-7-1-2-2-2-3-2-upto-11-terms-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/37333/the-sum-of-the-series-1-1-1-2-1-1-2-3-upto-10-terms-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/37335/the-sum-of-first-20-terms-of-the-sequence-0-7-0-77-0-777-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/37458/define-a-relation-r-over-a-class-of-n-and-215-n-real-matrices-a-and-b-as-a-r-b-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/37460/let-a-2-3-4-5-and-8230-30-and-and-39-and-8771-and-39-be-an-equivalence-relation</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37461/let-r-p-q-p-and-q-are-at-the-same-distance-from-the-origin-be-a-relation-then-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37462/let-a-n-and-8712-n-n-is-a-3-digit-number-b-9-k-2-k-and-8712-n-and-c-9-k-l-k-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37463/set-a-has-m-elements-and-set-b-has-n-elements-if-the-total-number-of-subsets-of</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37464/a-survey-shows-that-73-of-the-persons-working-in-an-office-like-coffee-whereas-6</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/37466/a-survey-shows-that-63-of-the-people-in-a-city-read-newspaper-a-whereas-76-read</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37467/let-r-1-and-r-2-be-two-relations-defined-as-follows-r-1-a-b-and-8712-r-2-a-2-b-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37468/if-r-x-y-x-y-and-8712-z-x-2-3-y-2-and-8804-8-is-a-relation-on-the-set-of-integer</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37469/let-x-n-and-8712-n-1-and-8804-n-and-8804-50-if-a-n-and-8712-x-and-160-nand-160-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37470/let-a-b-and-c-be-sets-such-that-and-981-and-8800-a-and-8745-b-and-8838-c-then-wh</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37471/let-z-be-the-set-of-integers-if-a-x-and-8712-z-and-8201-2-x-2-x-2-5-x-6-1-and-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37472/in-a-class-of-140-students-numbered-1-to-140-all-even-numbered-students-opted-ma</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37473/let-n-denote-the-set-of-all-natural-numbers-define-two-binary-relations-on-n-as</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37474/consider-the-following-two-binary-relations-on-the-set-a-a-b-c-r-c-a-b-b-a-c-c-c</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37475/consider-the-following-two-binary-relations-on-the-set-a-a-b-c-r-1-c-a-b-b-a-c-c</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/37477/a-relation-on-the-set-a-x-x-3-x-z-where-z-is-the-set-of-integers-is-defined-by-r</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37478/let-p-be-the-relation-defined-on-the-set-of-all-real-numbers-such-that-p-a-b-sec</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37479/if-x-4-n-3-n-1-n-and-8712-n-and-y-9-n-1-n-and-8712-n-where-n-is-the-set-of-natur</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/37485/let-r-be-the-set-of-real-numbers-this-question-has-statement-1-and-statement-2-o</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/37624/the-mean-of-5-observations-is-5-and-their-variance-is-12-4-if-three-of-the-obser</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37625/if-the-mean-deviation-of-the-numbers-1-1-d-and-8230-1-100-d-from-their-mean-is-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/37628/the-mean-of-a-data-set-comprising-of-16-observations-is-16-if-one-of-the-observa</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37629/let-x-and-175-m-and-and-963-2-be-respectively-the-mean-mode-and-variance-of-n-ob</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37630/let-x-and-m-d-be-the-mean-and-the-mean-deviation-about-x-of-n-observations-x-i-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37631/in-a-set-of-2-n-distinct-observations-each-of-the-observation-below-the-median-o</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/37633/in-a-set-of-2-n-observations-half-of-them-are-equal-to-a-and-the-remaining-hall</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/37642/let-x-x-x-n-be-n-observations-and-let-x-be-their-arithematic-mean-and-2-be-their</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/37668/let-a-1-2-and-c-3-6-be-two-diagonally-opposite-vertices-of-a-rhombus-whose-sides</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37669/a-rectangle-is-formed-by-the-lines-x-0-y-0-x-3-and-y-4-let-the-line-l-be-perpend</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37670/among-the-statements-s-1-if-a-5-1-and-b-2-3-are-two-vertices-of-a-triangle-whose</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37671/let-a-point-a-lie-between-the-parallel-lines-l-and-l-such-that-its-distances-fro</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37672/a-line-passing-through-the-point-p-a-makes-an-acute-angle-with-the-positive-x-ax</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37673/let-a-be-the-length-of-a-side-of-a-square-oabc-with-o-being-the-origin-its-side</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/37675/let-abc-be-the-triangle-such-that-the-equations-of-lines-a-b-and-a-c-be-3-y-x-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/37683/let-a-b-c-be-a-triangle-formed-by-the-lines-7-x-6-y-3-0-x-2-y-31-0-and-9-x-2-y-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37684/two-equal-sides-of-an-isosceles-triangle-are-along-x-2-y-4-and-x-y-4-if-m-is-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37685/let-n-c-r-1-28-n-c-r-56-and-n-c-r-1-70-let-a-4-t-4-t-b-2-t-2-t-and-c-3-r-n-r-2-n</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37686/let-the-points-11-2-lie-on-or-inside-the-triangle-with-sides-x-y-11-x-2-y-16-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37687/let-the-lines-3-x-4-y-0-8-x-11-y-33-0-and-2-x-3-y-0-be-concurrent-if-the-image-o</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37688/a-rod-of-length-eight-units-moves-such-that-its-ends-a-and-b-always-lie-on-the-l</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37689/let-the-area-of-a-p-q-r-with-vertices-p-5-4-q-2-4-and-r-a-b-be-35-square-units-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37690/let-a-6-8-b-10-10-and-c-10-10-be-the-vertices-of-a-triangle-if-l-a-9-and-g-h-k-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37691/let-the-triangle-pqr-be-the-image-of-the-triangle-with-vertices-1-3-3-1-and-2-4</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37692/two-vertices-of-a-triangle-abc-are-a-3-1-and-b-2-3-and-its-orthocentre-is-p-1-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37693/a-ray-of-light-coming-from-the-point-p-1-2-gets-reflected-from-the-point-q-on-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37694/if-the-image-of-the-point-4-5-in-the-line-x-2-y-2-lies-on-the-circle-x-4-2-y-3-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37695/if-the-line-segment-joining-the-points-5-2-and-2-a-subtends-an-angle-4-at-the-or</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37696/let-a-ray-of-light-passing-through-the-point-3-10-reflects-on-the-line-2-x-y-6-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37697/the-equations-of-two-sides-ab-and-ac-of-a-triangle-abc-are-4-x-y-14-and-3-x-2-y</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37698/if-the-orthocentre-of-the-triangle-formed-by-the-lines-2-x-3-y-1-0-x-2-y-1-0-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37699/if-p-6-1-be-the-orthocentre-of-the-triangle-whose-vertices-are-a-5-2-b-8-3-and-c</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37700/if-the-locus-of-the-point-whose-distances-from-the-point-2-1-and-1-3-are-in-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37701/let-a-variable-line-of-slope-m-0-passing-through-the-point-4-9-intersect-the-coo</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37702/if-a-3-1-1-b-5-3-7-3-1-3-c-2-2-1-and-d-10-3-2-3-1-3-are-the-vertices-of-a-quadri</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37703/let-a-1-1-and-b-2-3-be-two-points-and-p-be-a-variable-point-above-the-line-a-b-s</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37704/let-two-straight-lines-drawn-from-the-origin-o-intersect-the-line-3-x-4-y-12-at</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37705/if-a-1-1-2-b-5-7-6-c-3-4-10-and-d-1-4-2-are-the-vertices-of-a-quadrilateral-a-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37706/consider-a-triangle-abc-having-the-vertices-a-1-2-b-and-c-and-angles-a-b-c-6-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37707/the-vertices-of-a-triangle-are-a-1-3-b-2-2-and-c-3-1-a-new-triangle-is-formed-by</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37708/let-a-b-c-be-an-isosceles-triangle-in-which-a-is-at-1-0-a-2-3-a-b-a-c-and-b-is-o</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37709/let-a-a-b-b-3-4-and-6-8-respectively-denote-the-centroid-circumcentre-and-orthoc</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37710/let-a-2-1-b-1-0-c-and-d-be-the-vertices-of-a-parallelogram-a-b-c-d-if-the-point</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37711/let-z-and-let-a-b-1-0-c-and-d-1-2-be-the-vertices-of-a-parallelogram-a-b-c-d-if</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37712/if-x-2-y-2-2-h-x-y-2-g-x-2-f-y-c-0-is-the-locus-of-a-point-which-moves-such-that</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37713/a-line-passing-through-the-point-a-9-0-makes-an-angle-of-30-with-the-positive-di</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37714/let-a-be-the-point-of-intersection-of-the-lines-3-x-2-y-14-5-x-y-6-and-b-be-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37715/the-distance-of-the-point-2-3-from-the-line-2-x-3-y-28-0-measured-parallel-to-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37716/let-5-a-4-be-the-circumcenter-of-a-triangle-with-vertices-a-a-2-b-a-6-and-c-a-4</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37717/in-a-abc-suppose-y-x-is-the-equation-of-the-bisector-of-the-angle-b-and-the-equa</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37718/let-a-and-b-be-two-finite-sets-with-m-and-n-elements-respectively-the-total-numb</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37719/if-the-sum-of-squares-of-all-real-values-of-for-which-the-lines-2-x-y-3-0-6-x-3</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37720/let-r-be-the-interior-region-between-the-lines-3-x-y-1-0-and-x-2-y-5-0-containin</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37721/the-portion-of-the-line-4-x-5-y-20-in-the-first-quadrant-is-trisected-by-the-lin</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37722/if-and-945-and-946-is-the-orthocenter-of-the-triangle-a-b-c-with-vertices-a-3-an</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37723/consider-the-triangles-with-vertices-a-2-1-b-0-0-and-c-t-4-t-0-4-if-the-maximum</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37724/let-and-945-and-946-be-the-centroid-of-the-triangle-formed-by-the-lines-15-x-y-8</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37725/if-the-point-and-945-7-3-3-lies-on-the-curve-traced-by-the-mid-points-of-the-lin</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37726/in-a-triangle-a-b-c-if-cos-a-2-cos-b-cos-c-2-and-the-lengths-of-the-sides-opposi</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37727/if-the-line-l-1-3-y-2-x-3-is-the-angular-bisector-of-the-lines-l-2-x-y-1-0-and-l</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37728/let-the-equations-of-two-adjacent-sides-of-a-parallelogram-a-b-c-d-be-2-x-3-y-23</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37729/let-a-0-1-b-1-1-and-c-1-0-be-the-mid-points-of-the-sides-of-a-triangle-with-ince</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37730/let-c-and-945-and-946-be-the-circumcentre-of-the-triangle-formed-by-the-lines-4</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37731/the-straight-lines-l-1-and-l-2-pass-through-the-origin-and-trisect-the-line-segm</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37732/the-combined-equation-of-the-two-lines-a-x-b-y-c-0-and-a-and-39-x-b-and-39-y-c-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37733/if-the-orthocentre-of-the-triangle-whose-vertices-are-1-2-2-3-and-3-1-is-and-945</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37734/a-straight-line-cuts-off-the-intercepts-oa-a-and-ob-b-on-the-positive-directions</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37735/a-light-ray-emits-from-the-origin-making-an-angle-30-and-176-with-the-positive-x</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37736/let-b-and-c-be-the-two-points-on-the-line-y-x-0-such-that-b-and-c-are-symmetric</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37737/a-triangle-is-formed-by-x-axis-y-axis-and-the-line-3-x-4-y-60-then-the-number-of</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37738/the-equations-of-the-sides-a-b-b-c-and-38-c-a-of-a-triangle-a-b-c-are-2-x-y-0-x</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37739/let-m-1-m-2-be-the-slopes-of-two-adjacent-sides-of-a-square-of-side-a-such-that</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37740/let-a-and-945-2-b-and-945-6-and-c-and-945-4-2-be-vertices-of-a-and-8710-a-b-c-if</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37741/let-the-circumcentre-of-a-triangle-with-vertices-a-a-3-b-b-5-and-c-a-b-a-b-and-6</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37742/for-t-and-8712-0-2-and-960-if-a-b-c-is-an-equilateral-triangle-with-vertices-a-s</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37743/the-equations-of-the-sides-a-b-b-c-and-c-a-of-a-triangle-a-b-c-are-2-x-y-0-x-p-y</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37744/let-a-1-1-b-4-3-c-2-5-be-vertices-of-a-triangle-a-b-c-p-be-a-point-on-side-b-c-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37745/the-equations-of-the-sides-a-b-b-c-and-c-a-of-a-triangle-a-b-c-are-2-x-y-0-x-p-y</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37746/let-the-point-p-and-945-and-946-be-at-a-unit-distance-from-each-of-the-two-lines</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37747/a-line-with-the-slope-greater-than-one-passes-through-the-point-a-4-3-and-inters</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37748/the-distance-of-the-origin-from-the-centroid-of-the-triangle-whose-two-sides-hav</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37749/the-distance-between-the-two-points-a-and-a-which-lie-on-y-2-such-that-both-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37750/let-a-triangle-be-bounded-by-the-lines-l-1-2-x-5-y-10-l-2-4-x-3-y-12-and-the-lin</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37751/a-ray-of-light-passing-through-the-point-p-2-3-reflects-on-the-x-axis-at-point-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37752/in-an-isosceles-triangle-a-b-c-the-vertex-a-is-6-1-and-the-equation-of-the-base</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37753/let-r-be-the-point-3-7-and-let-p-and-q-be-two-points-on-the-line-x-y-5-such-that</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37754/let-the-area-of-the-triangle-with-vertices-a-1-and-945-b-and-945-0-and-c-0-and-9</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37755/let-a-3-a-a-a-and-62-0-be-a-fixed-point-in-the-x-y-plane-the-image-of-a-in-y-axi</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37756/let-the-points-of-intersections-of-the-lines-x-y-1-0-x-2-y-3-0-and-2-x-5-y-11-0</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37757/a-man-starts-walking-from-the-point-p-3-4-touches-the-x-axis-at-r-and-then-turns</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37758/let-a-be-the-set-of-all-points-and-945-and-946-such-that-the-area-of-triangle-fo</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37759/if-p-and-q-are-the-lengths-of-the-perpendiculars-from-the-origin-on-the-lines-x</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37760/let-a-a-0-b-b-2-b-1-and-c-0-b-b-and-8800-0-b-and-8800-1-be-points-such-that-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37761/let-a-be-a-fixed-point-0-6-and-b-be-a-moving-point-2-t-0-let-m-be-the-mid-point</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37762/let-a-b-c-be-a-triangle-with-a-3-1-and-and-8736-a-c-b-and-952-0-and-60-and-952-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37763/the-point-p-a-b-undergoes-the-following-three-transformations-successively-a-ref</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37764/two-sides-of-a-parallelogram-are-along-the-lines-4-x-5-y-0-and-7-x-2-y-0-if-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37765/let-the-equation-of-the-pair-of-lines-y-p-x-and-y-q-x-can-be-written-as-y-p-x-y</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37766/consider-a-triangle-having-vertices-a-2-3-b-1-9-and-c-3-8-if-a-line-l-passing-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37767/let-the-centroid-of-an-equilateral-triangle-a-b-c-be-at-the-origin-let-one-of-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37768/the-number-of-integral-values-of-m-so-that-the-abscissa-of-point-of-intersection</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37769/the-equation-of-one-of-the-straight-lines-which-passes-through-the-point-1-3-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37770/let-tan-and-945-tan-and-946-and-tan-and-947-and-945-and-946-and-947-and-8800-2-n</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37771/in-a-triangle-p-q-r-the-co-ordinates-of-the-points-p-and-q-are-2-4-and-4-2-respe</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37772/let-a-1-1-b-3-4-and-c-2-0-be-given-three-points-a-line-y-m-x-m-and-62-0-intersec</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37773/the-intersection-of-three-lines-x-y-0-x-2-y-3-and-2-x-y-6-is-a-an</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37774/the-image-of-the-point-3-5-in-the-line-x-y-1-0-lies-on</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37775/let-a-point-p-be-such-that-its-distance-from-the-point-5-0-is-thrice-the-distanc</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37776/let-l-denote-the-line-in-the-x-y-plane-with-x-and-y-intercepts-as-3-and-1-respec</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37777/a-ray-of-light-coming-from-the-point-2-2-3-is-incident-at-an-angle-30-and-176-on</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37778/if-the-line-2-x-y-3-0-is-at-a-distance-1-5-and-2-5-from-the-lines-4-x-2-y-and-94</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37779/if-the-perpendicular-bisector-of-the-line-segment-joining-the-points-p-1-4-and-q</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37780/let-p-q-be-a-diameter-of-the-circle-x-2-y-2-9-if-and-945-and-and-946-are-the-len</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37781/a-triangle-a-b-c-lying-in-the-first-quadrant-has-two-vertices-as-a-1-2-and-b-3-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37782/if-a-and-8710-a-b-c-has-vertices-a-and-8211-1-7-b-and-8211-7-1-and-c-5-and-8211</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37783/the-set-of-all-possible-values-of-and-952-in-the-interval-0-and-960-for-which-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37784/let-two-points-be-a-1-1-and-b-0-2-if-a-point-p-x-y-be-such-that-the-area-of-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37785/the-locus-of-the-mid-points-of-the-perpendiculars-drawn-from-points-on-the-line</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37786/let-a-1-0-b-6-2-and-c-3-2-6-be-the-vertices-of-a-triangle-a-b-c-if-p-is-a-point</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37787/a-triangle-has-a-vertex-at-1-2-and-the-mid-points-of-the-two-sides-through-it-ar</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37788/a-straight-line-l-at-a-distance-of-4-units-from-the-origin-makes-positive-interc</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37789/lines-are-drawn-parallel-to-the-line-4-x-3-y-2-0-at-a-distance-3-5-units-from-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37790/if-the-two-lines-x-a-1-y-1-and-2-x-a-2-y-1-a-and-8712-r-0-1-are-perpendicular-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37791/slope-of-a-line-passing-through-p-2-3-and-intersecting-the-line-x-y-7-at-a-dista</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37792/suppose-that-the-points-h-and-8201-k-and-8201-1-and-8201-2-and-3-and-8201-4-lie</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37793/a-point-on-the-straight-line-3-x-5-y-15-which-is-equidistant-from-the-coordinate</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37794/if-a-straight-line-passing-through-the-point-p-3-4-is-such-that-its-intercepted</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37795/if-the-straight-line-2-x-3-y-17-0-is-perpendicular-to-the-line-passing-through-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37796/if-in-a-parallelogram-abdc-the-coordinates-of-a-b-and-c-are-respectively-1-2-3-4</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37797/in-a-triangle-the-sum-of-lengths-of-two-sides-is-x-and-the-product-of-the-length</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37798/two-vertices-of-a-triangle-are-0-2-and-4-3-if-its-orthocenter-is-at-the-origin-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37799/two-sides-of-a-parallelogram-are-along-the-lines-x-y-3-and-x-y-3-0-if-its-diagon</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37800/if-the-line-3-x-4-y-24-0-intersects-the-x-axis-is-at-the-point-a-and-the-y-axis</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37801/a-point-p-moves-on-the-line-2-x-3-y-4-0-if-q-1-4-and-r-3-2-are-fixed-points-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37802/let-s-be-the-set-of-all-triangles-in-the-x-y-plane-each-having-one-vertex-at-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37803/let-the-equations-of-two-sides-of-a-triangle-be-3-x-2-y-6-0-and-4-x-5-y-20-0-if</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37804/consider-the-set-of-all-lines-p-x-q-y-r-0-such-that-3-p-2-q-4-r-0-which-one-of-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37805/the-locus-of-the-point-of-intersection-of-the-lines-2-x-y-4-2-k-0-and-2-k-x-k-y</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37806/the-foot-of-the-perpendicular-drawn-from-the-origin-on-the-line-3-x-y-0-is-p-if</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37807/the-sides-of-a-rhombus-a-b-c-d-are-parallel-to-the-lines-x-y-2-0-and-7-x-y-3-0-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37808/in-a-triangle-a-b-c-coordianates-of-a-are-1-2-and-the-equations-of-the-medians-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37809/a-straight-line-through-a-fixed-point-2-3-intersects-the-coordinate-axes-at-dist</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37810/a-square-of-each-side-2-lies-above-the-x-axis-and-has-one-vertex-at-the-origin-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37811/the-locus-of-the-point-of-intersection-of-the-straight-lines-t-x-2-y-3-t-0-and-x</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37812/let-k-be-an-integer-such-that-the-triangle-with-vertices-k-3-k-5-k-and-k-2-has-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37813/a-straight-line-through-origin-o-meets-the-lines-3-y-10-4-x-and-8-x-6-y-5-0-at-p</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37814/a-ray-of-light-is-incident-along-a-line-which-meets-another-line-7-x-y-1-0-at-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37815/if-a-variable-line-drawn-through-the-intersection-of-the-lines-x-3-y-4-1-and-x-4</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37816/the-point-2-1-is-translated-parallel-to-the-line-l-x-y-4-by-2-3-units-if-the-new</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37817/two-sides-of-a-rhombus-are-along-the-lines-x-y-1-0-and-7-x-y-5-0-if-its-diagonal</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37818/a-straight-line-l-through-the-point-3-2-is-inclined-at-an-angle-of-60-and-176-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37819/let-l-be-the-line-passing-through-the-point-p-1-2-such-that-its-intercepted-segm</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37820/the-points-0-8-3-1-3-and-82-30</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37821/locus-of-the-image-of-the-point-2-3-in-the-line-2-x-3-y-4-k-x-2-y-3-0-k-and-8712</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37822/if-a-line-l-is-perpendicular-to-the-line-5-x-y-1-and-the-area-of-the-triangle-fo</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37823/the-circumcentre-of-a-triangle-lies-at-the-origin-and-its-centroid-is-the-midpoi</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37824/if-a-line-intercepted-between-the-coordinate-axes-is-trisected-at-a-point-a-4-3</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37825/if-the-three-distinct-lines-x-2-a-y-a-0-x-3-b-y-b-0-and-x-4-a-y-a-0-are-concurre</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37826/the-base-of-an-equilateral-triangle-is-along-the-line-given-by-3-x-4-y-9-if-a-ve</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37827/given-three-points-p-q-r-with-p-5-3-and-r-lies-on-the-x-axis-if-the-equation-of</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37828/let-a-and-b-be-any-two-numbers-satisfying-1-a-2-1-b-2-1-4-then-the-foot-of-perpe</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37829/let-p-s-be-the-median-of-the-triangle-with-vertices-p-2-2-q-6-1-and-r-7-3-the-eq</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37830/let-a-b-c-and-d-be-non-zero-numbers-if-the-point-of-intersection-of-the-lines-4</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37831/if-the-image-of-point-p-2-3-in-a-line-l-is-q-4-5-then-the-image-of-point-r-0-0-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37832/let-x-0-1-the-set-of-all-x-such-that-x-x-is-the-interval</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37833/if-two-lines-l-and-l-in-space-are-defined-by-aligned-and-l-x-y-1-and-z-1-y-and-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37834/let-be-the-angle-between-two-lines-2-x-3-y-c-0-and-x-5-y-c-0-and-be-the-angle-be</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37835/if-the-x-intercept-of-some-line-l-is-double-as-that-of-the-line-3-x-4-y-12-and-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37836/the-acute-angle-between-two-lines-such-that-the-direction-cosines-l-m-n-of-each</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37837/a-light-ray-emerging-from-the-point-source-placed-at-p-1-3-is-reflected-at-a-poi</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37838/if-the-three-lines-x-3-y-p-a-x-2-y-q-and-a-x-y-r-form-a-right-angled-triangle-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37839/a-ray-of-light-along-x-3-y-3-gets-reflected-upon-reaching-x-axis-the-equation-of</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37840/the-x-coordinate-of-the-incentre-of-the-triangle-that-has-the-coordinates-of-mid</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37841/the-line-parallel-to-x-axis-and-passing-through-the-point-of-intersection-of-lin</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37842/consider-the-straight-lines-aligned-and-l-x-y-1-and-l-x-y-1-and-l-2-x-2-y-5-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37843/let-l-be-the-line-y-2-x-in-the-two-dimensional-plane-statement-1-the-image-of-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37844/if-the-point-1-a-lies-between-the-straight-lines-x-y-1-and-2-x-y-3-then-a-lies-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37845/if-two-vertices-of-a-triangle-are-5-1-and-2-3-and-its-orthocentre-is-at-0-0-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37846/if-the-straight-lines-x-3-y-4-3-x-y-4-and-x-y-0-form-a-triangle-then-the-triangl</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37847/the-point-of-intersection-of-the-lines-a-3-3-x-a-y-a-3-0-and-a-5-2-x-a-2-y-2-a-3</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37848/if-the-line-2-x-y-k-passes-through-the-point-which-divides-the-line-segment-join</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37849/a-line-is-drawn-through-the-point-1-2-to-meet-the-coordinate-axes-at-p-and-q-suc</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37850/the-lines-l-y-x-0-and-l-2-x-y-0-intersect-the-line-l-y-2-0-at-p-and-q-respective</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37851/the-line-l-given-by-x-5-y-b-1-passes-through-the-point-13-32-the-line-k-is-paral</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37852/the-lines-p-p-2-1-x-y-q-0-and-p-2-1-2-x-p-2-1-y-2-q-0-are-perpendicular-to-a-com</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37853/three-distinct-points-a-b-and-c-are-given-in-the-2-dimensional-coordinate-plane</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37854/the-perpendicular-bisector-of-the-line-segment-joining-p-1-4-and-q-k-3-has-y-int</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37855/let-a-h-k-b-1-1-and-c-2-1-be-the-vertices-of-a-right-angled-triangle-with-a-c-as</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37856/let-p-1-0-q-0-0-and-r-3-3-3-be-three-points-the-equation-of-the-bisector-of-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37857/if-one-of-the-lines-of-m-y-2-1-m-2-x-y-m-x-2-0-is-a-bisector-of-the-angle-betwee</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37858/a-straight-line-through-the-point-a-3-4-is-such-that-its-intercept-between-the-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37859/the-two-lines-x-a-y-b-z-c-y-d-and-x-a-y-b-z-c-y-d-are-perpendicular-to-each-othe</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37860/if-a-a-2-falls-inside-the-angle-made-by-the-lines-y-x-2-x-0-and-y-3-x-x-0-then-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37861/if-a-vertex-of-a-triangle-is-1-1-and-the-mid-points-of-two-sides-through-this-ve</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37862/let-a-2-3-and-b-2-1-be-vertices-of-a-triangle-a-b-c-if-the-centroid-of-this-tria</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37863/the-equation-of-the-straight-line-passing-through-the-point-4-3-and-making-inter</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37864/if-one-of-the-lines-given-by-6-x-2-x-y-4-c-y-2-0-is-3-x-4-y-0-then-c-equals</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37865/a-line-makes-the-same-angle-with-each-of-the-x-and-z-axis-if-the-angle-which-it</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37866/a-square-of-side-a-lies-above-the-x-axis-and-has-one-vertex-at-the-origin-the-si</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37867/if-the-pair-of-straight-lines-x-2-2-p-x-y-y-2-0-and-x-2-2-p-x-y-y-2-0-be-such-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37868/locus-of-a-centriod-of-the-triangle-whose-vertices-are-a-t-a-t-b-t-b-t-and-1-0-w</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37869/the-vectors-ab-3-i-4-k-and-ac-5-i-2-j-4-k-are-the-sides-of-a-triangle-abc-the-le</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37870/if-the-equation-of-the-locus-of-a-point-equidistant-from-the-point-a-b-and-a-b-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37871/a-triangle-with-vertices-4-0-1-1-3-5-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37872/the-sides-of-a-triangle-are-3x-4y-4x-37-and-5x-57-where-x-y-0-then-the-triangle</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37873/if-the-pair-of-lines-a-x-2-2-h-x-y-b-y-2-2-g-x-2-f-y-c-0-intersect-on-the-y-axis</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37874/the-point-of-lines-represented-by-3-a-x-2-5-x-y-a-2-2-y-2-0-and-perpendicular-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37875/let-the-foot-of-perpendicular-from-the-point-2-3-on-the-line-x-4-1-y-9-2-z-5-1-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37876/let-a-line-l-pass-through-the-origin-and-be-perpendicular-to-the-lines-l-r-3-t-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37877/the-shortest-distance-between-the-lines-x-4-1-y-3-2-z-2-3-and-x-2-2-y-6-4-z-5-5</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37878/let-the-image-of-the-point-p-0-5-0-in-the-line-x-1-2-y-1-z-1-2-be-the-point-r-an</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37879/let-the-image-of-the-point-p-1-6-a-in-the-line-l-x-1-y-1-2-z-a-1-b-b-0-be-a-3-0</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37880/let-a-line-l-be-perpendicular-to-both-the-lines-l-x-1-3-y-3-5-z-5-7-and-l-x-2-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37881/let-a-triangle-pqr-be-such-that-p-and-q-lie-on-the-line-x-3-8-y-4-2-z-1-2-and-ar</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37882/if-the-distance-of-the-point-a-2-5-from-the-image-of-the-point-1-2-7-in-the-line</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37883/the-square-of-the-distance-of-the-point-p-5-6-7-from-the-line-x-2-2-y-5-3-z-2-4</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37884/the-square-of-the-distance-of-the-point-of-intersection-of-the-lines-r-i-j-k-a-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37885/the-shortest-distance-between-the-lines-r-1-3-i-2-j-8-3-k-2-i-5-j-6-k-and-r-2-3</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37886/if-2-1-2-3-1-2-is-the-image-of-2-1-in-the-line-x-2-3-y-1-2-z-1-then-the-possible</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37887/a-line-with-direction-ratios-1-1-2-intersects-the-lines-x-2-y-3-z-1-3-and-x-1-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37888/the-square-of-the-distance-of-the-point-2-8-6-from-the-line-x-1-1-y-1-2-z-1-alon</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37889/let-the-point-a-be-the-foot-of-perpendicular-drawn-from-the-point-p-a-b-0-on-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37890/if-the-point-of-intersection-of-the-lines-x-1-3-y-a-5-z-b-1-7-and-x-2-1-y-b-4-z</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37891/let-a-line-l-passing-through-the-point-1-1-1-be-perpendicular-to-both-the-vector</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37892/let-q-a-b-c-be-the-image-of-the-point-p-3-2-1-in-the-line-x-1-1-y-2-z-1-1-then-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37893/if-the-distance-of-the-point-p-43-0-from-the-line-r-4-i-k-2-i-3-k-r-along-a-line</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37894/if-the-distances-of-the-point-1-2-a-from-the-line-x-1-1-y-2-z-1-1-along-the-line</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37895/the-sum-of-all-values-of-for-which-the-shortest-distance-between-the-lines-x-1-y</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37896/let-the-lines-l-r-i-2-j-3-k-2-i-3-j-4-k-r-and-l-r-4-i-j-5-i-2-j-k-r-intersect-at</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37897/let-a-line-l-passing-through-the-point-p-1-1-1-be-perpendicular-to-the-lines-x-4</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37898/if-the-image-of-the-point-p-a-2-a-in-the-line-x-2-y-a-1-z-1-is-q-and-the-image-o</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37899/let-the-direction-cosines-of-two-lines-satisfy-the-equations-4-l-m-n-0-and-2-m-n</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37900/the-vertices-b-and-c-of-a-triangle-abc-lie-on-the-line-x-1-1-y-2-z-2-3-the-coord</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37901/let-l-be-the-line-x-1-2-y-1-3-z-3-6-and-let-s-be-the-set-of-all-points-a-b-c-on</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37902/if-the-image-of-the-point-p-1-2-a-in-the-line-x-6-3-y-7-2-7-z-2-is-q-5-b-c-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37903/let-p-be-the-point-on-the-line-x-1-2-y-1-3-z-at-a-distance-4-14-from-the-point-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37904/let-the-line-l-pass-through-the-point-3-5-2-and-make-equal-angles-with-the-posit</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37905/let-the-line-l-be-parallel-to-the-vector-3-i-2-j-4-k-and-pass-through-the-point</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37906/let-be-the-co-ordinates-of-the-foot-of-the-perpendicular-drawn-from-the-point-5</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37907/let-the-values-of-for-which-the-shortest-distance-between-the-lines-x-1-2-y-2-3</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37908/let-the-area-of-the-triangle-formed-by-the-lines-x-2-y-1-z-x-3-5-y-1-z-1-1-and-x</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37909/consider-the-lines-l-x-1-y-2-z-and-l-x-2-y-z-1-let-the-feet-of-the-perpendicular</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37910/if-the-equation-of-the-line-passing-through-the-point-0-1-2-0-and-perpendicular</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37911/if-the-shortest-distance-between-the-lines-x-1-2-y-2-3-z-3-4-and-x-1-y-z-5-1-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37912/let-the-line-l-pass-through-1-1-1-and-intersect-the-lines-x-1-2-y-1-3-z-1-4-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37913/let-the-values-of-p-for-which-the-shortest-distance-between-the-lines-x-1-3-y-4</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37914/let-a-be-the-point-of-intersection-of-the-lines-l-x-7-1-y-5-0-z-3-1-and-l-x-1-3</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37915/let-the-shortest-distance-between-the-lines-x-3-3-y-1-z-3-1-and-x-3-3-y-7-2-z-4</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37916/let-a-and-b-be-two-distinct-points-on-the-line-l-x-6-3-y-7-2-z-7-2-both-a-and-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37917/each-of-the-angles-and-that-a-given-line-makes-with-the-positive-y-and-z-axes-re</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37918/the-distance-of-the-point-7-10-11-from-the-line-x-4-1-y-4-0-z-2-3-along-the-line</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37919/let-a-line-passing-through-the-point-4-1-0-intersect-the-line-l-x-1-2-y-2-3-z-3</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37920/line-l-passes-through-the-point-1-2-3-and-is-parallel-to-z-axis-line-l-passes-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37921/the-line-l-is-parallel-to-the-vector-a-3-i-2-j-4-k-and-passes-through-the-point</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37922/if-the-image-of-the-point-p-1-0-3-in-the-line-joining-the-points-a-4-7-1-and-b-3</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37923/let-the-vertices-q-and-r-of-the-triangle-p-q-r-lie-on-the-line-x-3-5-y-1-2-z-4-3</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37924/let-p-be-the-foot-of-the-perpendicular-from-the-point-1-2-2-on-the-line-l-x-1-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37925/let-a-straight-line-l-pass-through-the-point-p-2-1-3-and-be-perpendicular-to-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37926/let-a-i-2-j-k-and-b-2-i-7-j-3-k-let-l-r-i-2-j-k-a-r-and-l-r-j-k-b-r-be-two-lines</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37927/let-l-x-1-1-y-2-1-z-1-2-and-l-x-1-1-y-2-2-z-1-be-two-lines-let-l-be-a-line-passi</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37928/the-square-of-the-distance-of-the-point-15-7-32-7-7-from-the-line-x-1-3-y-3-5-z</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37929/if-the-image-of-the-point-4-4-3-in-the-line-x-1-2-y-2-1-z-1-3-is-then-is-equal-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37930/let-a-x-y-z-be-a-point-in-x-y-plane-which-is-equidistant-from-three-points-0-3-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37931/let-p-be-the-image-of-the-point-q-7-2-5-in-the-line-l-x-1-2-y-1-3-z-4-and-r-5-p</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37932/let-in-a-a-b-c-the-length-of-the-side-a-c-be-6-the-vertex-b-be-1-2-3-and-the-ver</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37933/let-the-line-passing-through-the-points-1-2-1-and-parallel-to-the-line-x-1-2-y-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37934/the-distance-of-the-line-x-2-2-y-6-3-z-3-4-from-the-point-1-4-0-along-the-line-x</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37935/if-the-square-of-the-shortest-distance-between-the-lines-x-2-1-y-1-2-z-3-3-and-x</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37936/let-the-point-a-divide-the-line-segment-joining-the-points-p-1-1-2-and-q-5-5-10</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37937/let-p-be-the-foot-of-the-perpendicular-from-the-point-q-10-3-1-on-the-line-x-3-7</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37938/let-a-line-pass-through-two-distinct-points-p-2-1-3-and-q-and-be-parallel-to-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37939/the-perpendicular-distance-of-the-line-x-1-2-y-2-1-z-3-2-from-the-point-p-2-10-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37940/let-the-distance-between-two-parallel-lines-be-5-units-and-a-point-p-lie-between</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37941/let-l-x-1-2-y-2-3-z-3-4-and-l-x-2-3-y-4-4-z-5-5-be-two-lines-then-which-of-the-f</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37942/let-l-x-1-3-y-1-1-z-1-0-and-l-x-2-2-y-0-z-4-r-be-two-lines-which-intersect-at-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37943/consider-the-line-l-passing-through-the-points-1-2-3-and-2-3-5-the-distance-of-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37944/the-square-of-the-distance-of-the-image-of-the-point-6-1-5-in-the-line-x-1-3-y-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37945/let-the-line-l-intersect-the-lines-x-2-y-z-1-2-x-1-2-y-1-z-1-and-be-parallel-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37946/the-shortest-distance-between-the-lines-x-3-4-y-7-11-z-1-5-and-x-5-3-y-9-6-z-2-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37947/if-the-shortest-distance-between-the-lines-x-2-y-4-3-z-3-4-and-x-2-4-y-4-6-z-7-8</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37948/let-p-be-the-image-of-the-point-q-1-6-4-in-the-line-x-1-y-1-2-z-2-3-then-2-is-eq</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37949/if-the-shortest-distance-between-the-lines-array-ll-l-r-2-i-1-3-j-3-4-k-and-r-l</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37950/let-p-x-y-z-be-a-point-in-the-first-octant-whose-projection-in-the-x-y-plane-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37951/let-p-be-the-image-of-the-point-q-3-3-1-in-the-line-x-0-1-y-3-1-z-1-1-and-r-be-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37952/if-the-shortest-distance-between-the-lines-x-3-y-2-1-z-1-1-and-x-2-3-y-5-2-z-4-4</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37953/the-shortest-distance-between-the-lines-x-3-2-y-15-7-z-9-5-and-x-1-2-y-1-1-z-9-3</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37954/let-p-be-the-point-10-2-1-and-q-be-the-foot-of-the-perpendicular-drawn-from-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37955/let-be-the-image-of-the-point-8-5-7-in-the-line-x-1-2-y-1-3-z-2-5-then-is-equal</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37956/let-the-point-1-lie-on-the-line-of-the-shortest-distance-between-the-lines-x-2-3</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37957/if-the-line-2-x-3-3-y-2-4-1-4-z-makes-a-right-angle-with-the-line-x-3-3-1-2-y-6</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37958/let-d-be-the-distance-of-the-point-of-intersection-of-the-lines-x-6-3-y-2-z-1-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37959/let-p-be-the-point-of-intersection-of-the-lines-x-2-1-y-4-5-z-2-1-and-x-3-2-y-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37960/consider-a-line-l-passing-through-the-points-p-1-2-1-and-q-2-1-1-if-the-mirror-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37961/let-the-point-on-the-line-passing-through-the-points-p-1-2-3-and-q-5-4-7-farther</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37962/if-the-shortest-distance-between-the-lines-x-2-2-y-3-3-z-5-4-and-x-3-1-y-2-3-z-4</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37963/if-the-mirror-image-of-the-point-p-3-4-9-in-the-line-x-1-3-y-1-2-z-2-1-is-then-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37964/let-p-and-q-be-the-points-on-the-line-x-3-8-y-4-2-z-1-2-which-are-at-a-distance</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37965/if-the-shortest-distance-between-the-lines-x-2-y-2-1-z-1-1-and-x-3-1-y-1-2-z-2-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37966/let-the-line-of-the-shortest-distance-between-the-lines-l-1-r-i-2-j-3-k-i-j-k-an</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37967/let-be-mirror-image-of-the-point-2-3-5-in-the-line-x-1-2-y-2-3-z-3-4-then-2-3-4</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37968/the-shortest-distance-between-lines-l-1-and-l-2-where-l-1-x-1-2-y-1-3-z-4-2-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37969/a-line-passes-through-a-4-6-2-and-b-16-2-4-the-point-p-a-b-c-where-a-b-c-are-non</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37970/the-distance-of-the-point-q-0-2-2-form-the-line-passing-through-the-point-p-5-4</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37971/let-q-and-r-be-the-feet-of-perpendiculars-from-the-point-p-a-a-a-on-the-lines-x</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37972/let-l-1-r-i-j-2-k-i-j-2-k-r-l-2-r-j-k-3-i-j-p-k-r-and-l-3-r-l-i-m-j-n-k</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37973/let-a-line-passing-through-the-point-1-2-3-intersect-the-lines-l-1-x-1-3-y-2-2-z</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37974/let-be-the-foot-of-perpendicular-from-the-point-1-2-3-on-the-line-x-3-5-y-1-2-z</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37975/if-d-1-is-the-shortest-distance-between-the-lines-x-1-2-y-12-z-x-y-2-6-z-6-and-d</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37976/let-p-3-2-3-q-4-6-2-and-r-7-3-2-be-the-vertices-of-pqr-then-the-angle-qpr-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37977/let-o-be-the-origin-and-m-and-n-be-the-points-on-the-lines-x-5-4-y-4-1-z-5-3-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37978/let-o-be-the-origin-and-the-position-vector-of-a-and-b-be-2-i-2-j-k-and-2-i-4-j</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37979/let-p-q-r-be-a-triangle-with-r-1-4-2-suppose-m-2-1-2-is-the-mid-point-of-p-q-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37980/a-line-with-direction-ratio-2-1-2-meets-the-lines-x-y-2-z-and-x-2-2-y-2-z-respec</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37981/the-position-vectors-of-the-vertices-a-b-and-c-of-a-triangle-are-2-i-3-j-3-k-2-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37982/let-the-position-vectors-of-the-vertices-a-b-and-c-of-a-triangle-be-2-i-2-j-k-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37983/the-lines-x-2-2-y-2-z-7-16-and-x-3-4-y-2-3-z-2-1-intersect-at-the-point-p-if-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37984/let-the-image-of-the-point-1-0-7-in-the-line-x-1-y-1-2-z-2-3-be-the-point-then-w</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37985/the-distance-of-the-point-7-2-11-from-the-line-x-6-1-y-4-0-z-8-3-along-the-line</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37986/if-the-shortest-distance-between-the-lines-x-4-1-y-1-2-z-3-and-x-2-y-1-4-z-2-5-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37987/let-the-foot-of-perpendicular-of-the-point-p-3-and-8211-2-and-8211-9-on-the-plan</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37988/let-s-be-the-set-of-all-values-of-and-955-for-which-the-shortest-distance-betwee</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37989/if-the-line-x-y-z-intersects-the-line-x-sin-a-y-sin-b-z-sin-c-18-0-x-sin-2-a-y-s</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37990/let-the-plane-p-contain-the-line-2-x-y-z-3-0-5-x-3-y-4-z-9-and-be-parallel-to-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37991/the-plane-passing-through-the-points-0-and-8211-1-2-and-and-8211-1-2-1-and-paral</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37992/the-line-that-is-coplanar-to-the-line-x-3-3-y-1-1-z-5-5-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37993/let-n-be-the-foot-of-perpendicular-from-the-point-p-1-2-3-on-the-line-passing-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37994/let-the-equation-of-plane-passing-through-the-line-of-intersection-of-the-planes</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37995/the-distance-of-the-point-1-2-3-from-the-plane-r-and-8594-and-183-i-2-j-3-k-10-p</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37996/let-the-image-of-the-point-5-3-5-3-8-3-in-the-plane-x-2-y-z-and-8211-2-0-be-p-if</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37997/let-the-lines-l-1-x-5-3-y-4-1-z-and-945-2-and-l-2-3-x-2-y-z-2-0-x-3-y-2-z-13-be</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37998/let-the-plane-p-4-x-y-z-10-be-rotated-by-an-angle-and-960-2-about-its-line-of-in</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/37999/let-p-be-the-plane-passing-through-the-points-5-3-0-13-3-2-and-1-6-2-for-and-945</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38000/let-the-line-passing-through-the-points-p-2-1-2-and-q-5-3-4-meet-the-plane-x-y-z</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38001/let-the-line-l-x-1-y-2-z-3-and-955-and-955-and-8712-and-8477-meet-the-plane-p-x</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38002/let-and-945-and-946-and-947-be-the-image-of-point-p-2-3-5-in-the-plane-2-x-y-3-z</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38003/if-the-equation-of-the-plane-that-contains-the-point-2-3-5-and-is-perpendicular</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38004/let-a-line-l-pass-through-the-origin-and-be-perpendicular-to-the-lines-l-1-r-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38005/let-the-image-of-the-point-p-1-2-6-in-the-plane-passing-through-the-points-a-1-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38006/let-the-line-x-1-6-y-2-z-8-5-intersect-the-lines-x-5-4-y-7-3-z-2-1-and-x-3-6-3-y</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38007/let-the-foot-of-perpendicular-from-the-point-a-4-3-1-on-the-plane-p-x-y-2-z-3-0</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38008/let-two-vertices-of-a-triangle-a-b-c-be-2-4-6-and-0-2-5-and-its-centroid-be-2-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38009/the-shortest-distance-between-the-lines-x-2-1-y-2-z-5-2-and-x-4-1-y-1-2-z-3-0-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38010/let-p-be-the-point-of-intersection-of-the-line-x-3-3-y-2-1-1-z-2-and-the-plane-x</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38011/for-a-b-and-8712-z-and-a-b-and-8804-10-let-the-angle-between-the-plane-p-a-x-y-z</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38012/let-p-be-the-plane-passing-through-the-line-x-1-1-y-2-3-z-5-7-and-the-point-2-4</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38013/let-p-1-be-the-plane-3-x-y-7-z-11-and-p-2-be-the-plane-passing-through-the-point</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38014/the-shortest-distance-between-the-lines-x-4-4-y-2-5-z-3-3-and-x-1-3-y-3-4-z-4-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38015/if-the-equation-of-the-plane-containing-the-line-x-2-y-3-z-4-0-2-x-y-z-5-and-per</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38016/let-and-955-1-and-160-and-955-2-be-the-values-of-and-955-for-which-the-points-5</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38017/let-the-line-l-pass-through-the-point-0-1-2-intersect-the-line-x-1-2-y-2-3-z-3-4</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38018/a-plane-p-contains-the-line-of-intersection-of-the-plane-r-and-8594-and-183-i-j</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38019/if-the-lines-x-1-2-2-y-3-z-3-and-945-and-x-4-5-y-1-2-z-and-946-intersect-then-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38020/one-vertex-of-a-rectangular-parallelopiped-is-at-the-origin-o-and-the-lengths-of</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38021/if-the-equation-of-the-plane-passing-through-the-line-of-intersection-of-the-pla</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38022/let-the-image-of-the-point-p-1-and-160-2-and-160-3-in-the-plane-2-x-and-8211-y-z</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38023/let-the-plane-p-pass-through-the-intersection-of-the-planes-2-x-3-y-z-2-and-x-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38024/let-and-945-x-and-946-y-and-947-z-1-be-the-equation-of-a-plane-passing-through-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38025/the-point-of-intersection-c-of-the-plane-8-x-y-2-z-0-and-the-line-joining-the-po</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38026/let-the-image-of-the-point-p-2-1-3-in-the-plane-x-2-y-z-0-be-q-then-the-distance</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38027/the-shortest-distance-between-the-lines-x-5-1-y-2-2-z-4-3-and-x-3-1-y-5-4-z-1-5</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38028/let-the-plane-p-8-x-and-945-1-y-and-945-2-z-12-0-be-parallel-to-the-line-l-x-2-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38029/let-p-be-the-plane-passing-through-the-point-1-1-5-and-perpendicular-to-the-line</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38030/the-foot-of-perpendicular-from-the-origin-o-to-a-plane-p-which-meets-the-co-ordi</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38031/let-the-shortest-distance-between-the-lines-l-x-5-2-y-and-955-0-z-and-955-1-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38032/let-the-line-l-x-1-2-y-1-1-z-3-1-intersect-the-plane-2-x-y-3-z-16-at-the-point-p</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38033/let-and-952-be-the-angle-between-the-planes-p-1-r-and-8594-and-183-i-j-2-k-9-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38034/a-vector-v-and-8594-in-the-first-octant-is-inclined-to-the-x-axis-at-60-and-176</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38035/if-a-plane-passes-through-the-points-1-k-0-2-k-1-1-1-2-and-is-parallel-to-the-li</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38036/let-a-line-l-pass-through-the-point-p-2-3-1-and-be-parallel-to-the-line-x-3-y-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38037/the-line-l-1-passes-through-the-point-2-6-2-and-is-perpendicular-to-the-plane-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38038/let-a-unit-vector-o-p-and-8594-make-angle-and-945-and-946-and-947-with-the-posit</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38039/if-the-equation-of-the-plane-passing-through-the-point-1-1-2-and-perpendicular-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38040/if-and-955-1-and-60-and-955-2-are-two-values-of-and-955-such-that-the-angle-betw</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38041/shortest-distance-between-the-lines-x-1-2-y-8-7-z-4-5-and-x-1-2-y-2-1-z-6-3-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38042/the-plane-2-x-y-z-4-intersects-the-line-segment-joining-the-points-a-a-2-4-and-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38043/if-the-lines-x-1-1-y-2-2-z-3-1-and-x-a-2-y-2-3-z-3-1-intersects-at-the-point-p-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38044/let-the-equation-of-the-plane-p-containing-the-line-x-10-8-y-2-z-be-a-x-b-y-3-z</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38045/let-the-co-ordinates-of-one-vertex-of-and-8710-a-b-c-be-a-0-2-and-945-and-the-ot</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38046/the-shortest-distance-between-the-lines-x-1-2-y-12-z-and-x-y-2-6-z-6-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38047/the-foot-of-perpendicular-of-the-point-2-0-5-on-the-line-x-1-2-y-1-5-z-1-1-is-an</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38048/if-the-shortest-distance-between-the-line-joining-the-points-1-2-3-and-2-3-4-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/38050/consider-the-lines-l-1-and-l-2-given-by-l-1-x-1-2-y-3-1-z-2-2-l-2-x-2-1-y-2-2-z</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38051/let-the-equation-of-the-plane-passing-through-the-line-x-2-y-z-5-0-x-y-3-z-5-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38052/let-the-plane-containing-the-line-of-intersection-of-the-planes-p-1-x-and-955-4</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38053/if-the-foot-of-the-perpendicular-drawn-from-1-9-7-to-the-line-passing-through-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/38055/the-distance-of-the-point-7-3-4-from-the-plane-containing-the-points-2-3-1-1-1-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38056/the-distance-of-the-point-1-9-16-from-the-plane-2-x-3-y-z-5-measure-parallel-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/38058/let-q-be-the-foot-of-perpendicular-drawn-from-the-point-p-1-2-3-to-the-plane-x-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/38062/a-plane-p-is-parallel-to-two-lines-whose-direction-ratios-are-2-1-3-and-1-2-2-an</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38063/the-foot-of-the-perpendicular-from-a-point-on-the-circle-x-2-y-2-1-z-0-to-the-pl</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/38065/if-the-length-of-the-perpendicular-drawn-from-the-point-p-a-4-2-a-and-62-0-on-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/38069/a-vector-a-and-8594-is-parallel-to-the-line-of-intersection-of-the-plane-determi</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/38071/the-plane-passing-through-the-line-l-l-x-y-3-1-l-z-1-x-2-y-z-2-and-perpendicular</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38072/the-length-of-the-perpendicular-from-the-point-1-2-5-on-the-line-passing-through</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38073/let-q-and-r-be-two-points-on-the-line-x-1-2-y-2-3-z-1-2-at-a-distance-26-from-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38074/a-plane-e-is-perpendicular-to-the-two-planes-2-x-2-y-z-0-and-x-y-2-z-4-and-passe</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38075/the-shortest-distance-between-the-lines-x-7-6-y-6-7-z-and-7-x-2-y-2-z-6-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38076/let-p-be-the-plane-containing-the-straight-line-x-3-9-y-4-1-z-7-5-and-perpendicu</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38077/the-line-of-shortest-distance-between-the-lines-x-2-0-y-1-1-z-1-and-x-3-2-y-5-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38078/let-x-2-3-y-1-2-z-3-1-lie-on-the-plane-p-x-q-y-z-5-for-some-p-q-and-8712-r-the-s</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38079/let-q-be-the-mirror-image-of-the-point-p-1-2-1-with-respect-to-the-plane-x-2-y-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38080/if-the-mirror-image-of-the-point-2-4-7-in-the-plane-3-x-y-4-z-2-is-a-b-c-the-2-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38081/let-d-be-the-distance-between-the-foot-of-perpendiculars-of-the-points-p-1-2-1-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38082/let-p-1-r-and-8594-and-183-2-i-j-3-k-4-be-a-plane-let-p-2-be-another-plane-which</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38083/let-the-plane-a-x-b-y-c-z-d-pass-through-2-3-5-and-is-perpendicular-to-the-plane</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38084/let-the-image-of-the-point-p-1-2-3-in-the-line-l-x-6-3-y-1-2-z-2-3-be-q-let-r-an</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38085/if-two-distinct-point-q-r-lie-on-the-line-of-intersection-of-the-planes-x-2-y-z</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38086/the-acute-angle-between-the-planes-p-1-and-p-2-when-p-1-and-p-2-are-the-planes-p</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38087/let-the-plane-p-r-and-8594-and-183-a-and-8594-d-contain-the-line-of-intersection</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38088/let-the-foot-of-the-perpendicular-from-the-point-1-2-4-on-the-line-x-2-4-y-1-2-z</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38089/the-shortest-distance-between-the-lines-x-3-2-y-2-3-z-1-1-and-x-3-2-y-6-1-z-5-3</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38090/if-two-straight-lines-whose-direction-cosines-are-given-by-the-relations-l-m-n-0</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38091/let-the-mirror-image-of-the-point-a-b-c-with-respect-to-the-plane-3-x-4-y-12-z-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38092/if-the-plane-2-x-y-5-z-0-is-rotated-about-its-line-of-intersection-with-the-plan</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38093/if-the-lines-r-and-8594-i-j-k-and-955-3-j-k-and-r-and-8594-and-945-i-j-and-956-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38094/if-the-two-lines-l-1-x-2-3-y-1-2-z-2-and-l-2-x-1-1-2-y-3-and-945-z-5-2-are-perpe</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38095/let-the-plane-2-x-3-y-z-20-0-be-rotated-through-a-right-angle-about-its-line-of</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38096/let-p-be-the-plane-passing-through-the-intersection-of-the-planes-r-and-8594-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38097/let-l-1-be-the-line-in-x-y-plane-with-x-and-y-intercepts-1-8-and-1-4-2-respectiv</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38098/let-q-be-the-mirror-image-of-the-point-p-1-0-1-with-respect-to-the-plane-s-x-y-z</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38099/let-the-lines-l-1-r-and-8594-and-955-i-2-j-3-k-and-955-and-8712-r-and-l-2-r-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38100/if-the-shortest-distance-between-the-lines-x-1-2-y-2-3-z-3-and-955-and-x-2-1-y-4</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38101/let-the-points-on-the-plane-p-be-equidistant-from-the-points-4-2-1-and-2-2-3-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/38103/if-the-shortest-distance-between-the-lines-r-and-8594-i-3-k-and-955-i-a-j-and-r</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38104/the-distance-of-line-3-y-2-z-1-0-3-x-z-4-from-the-point-2-1-6-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/38109/the-square-of-the-distance-of-the-point-of-intersection-of-the-line-x-1-2-y-2-3</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/38113/the-distance-of-the-point-1-2-3-from-the-plane-x-y-z-5-measured-parallel-to-a-li</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/38115/let-p-be-the-plane-passing-through-the-point-1-2-3-and-the-line-of-intersection</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38116/let-q-be-the-foot-of-the-perpendicular-from-the-point-p-7-2-13-on-the-plane-cont</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/38131/let-the-mirror-image-of-the-point-1-3-a-with-respect-to-the-plane-r-and-8594-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38132/let-p-be-a-plane-containing-the-line-x-1-3-y-6-4-z-5-2-and-parallel-to-the-line</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/38140/if-the-foot-of-the-perpendicular-from-point-4-3-8-on-the-line-l-1-x-a-l-y-2-3-z</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38141/if-the-distance-of-the-point-1-2-3-from-the-plane-x-2-y-3-z-10-0-measured-parall</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38142/if-for-a-and-62-0-the-feet-of-perpendiculars-from-the-points-a-a-2-a-3-and-b-0-4</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38143/let-the-position-vectors-of-two-points-p-and-q-be-3-i-j-2-k-and-i-2-j-4-k-respec</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38144/let-p-be-a-plane-l-x-m-y-n-z-0-containing-the-line-1-x-1-y-4-2-z-2-3-if-plane-p</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/38147/consider-the-three-planes-p-1-3-x-15-y-21-z-9-p-2-x-3-y-z-5-and-p-3-2-x-10-y-14</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38148/let-and-955-2-1-be-a-point-on-the-plane-which-passes-through-the-point-4-2-2-if</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/38150/a-line-l-passing-through-origin-is-perpendicular-to-the-lines-l-1-r-and-8594-3-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38151/let-and-945-be-the-angle-between-the-lines-whose-direction-cosines-satisfy-the-e</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38152/the-equation-of-the-line-through-the-point-0-1-2-and-perpendicular-to-the-line-x</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38153/the-vector-equation-of-the-plane-passing-through-the-intersection-of-the-planes</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/38155/let-and-955-be-an-integer-if-the-shortest-distance-between-the-lines-x-and-955-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38156/the-distance-of-the-point-1-1-9-from-the-point-of-intersection-of-the-line-x-3-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38157/the-equation-of-the-plane-passing-through-the-point-1-2-3-and-perpendicular-to-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38158/a-plane-p-meets-the-coordinate-axes-at-a-b-and-c-respectively-the-centroid-of-an</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38159/the-shortest-distance-between-the-lines-x-1-0-y-1-1-z-1-and-x-y-z-1-0-2-x-y-z-3</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38160/if-for-some-and-945-and-8712-r-the-lines-l-1-x-1-2-y-2-1-z-1-1-and-l-2-x-2-and-9</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38161/if-a-b-c-is-the-image-of-the-point-1-2-3-in-the-line-x-1-2-y-3-2-z-1-then-a-b-c</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38162/the-distance-of-the-point-1-2-3-from-the-plane-x-y-z-5-measured-parallel-to-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38163/if-the-equation-of-a-plane-p-passing-through-the-intersection-of-the-planes-x-4</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38164/the-plane-which-bisects-the-line-joining-the-points-4-2-3-and-2-4-1-at-right-ang</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/38166/the-foot-of-the-perpendicular-drawn-from-the-point-4-2-3-to-the-line-joining-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38167/the-lines-r-and-8594-i-j-l-2-i-k-and-r-and-8594-2-i-j-m-i-j-k</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38168/a-plane-passing-through-the-point-3-1-1-contains-two-lines-whose-direction-ratio</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38169/the-plane-passing-through-the-points-1-2-1-2-1-2-and-parallel-to-the-line-2-x-3</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/38172/the-projection-of-the-line-segment-joining-the-point-1-1-3-and-2-4-11-on-the-lin</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/38175/if-the-foot-of-the-perpendicular-drawn-from-the-point-1-0-3-on-a-line-passing-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/38177/a-plane-which-bisects-the-angle-between-the-two-given-planes-2-x-y-2-z-4-0-and-x</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38178/the-length-of-the-perpendicular-drawn-from-the-point-2-1-4-to-the-plane-containi</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38179/if-the-line-x-2-3-y-1-2-z-1-1-intersects-the-plane-2-x-3-y-z-13-0-at-a-point-p-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38180/if-the-plane-2-x-y-2-z-3-0-has-the-distances-1-3-and-2-3-units-from-the-planes-4</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38181/a-perpendicular-is-drawn-from-a-point-on-the-line-x-1-2-y-1-1-z-1-to-the-plane-x</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38182/if-the-length-of-the-perpendicular-from-the-point-and-946-0-and-946-and-946-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/38185/let-p-be-the-plane-which-contains-the-line-of-intersection-of-the-planes-x-y-z-6</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/38190/the-length-of-the-perpendicular-from-the-point-2-1-4-on-the-straight-line-x-3-10</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/38386/if-2-x-3-4-then-12-13-x-5-13-x-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38387/let-60-60-1-8-0-2-then-the-sum-of-all-0-2-where-3-attains-its-maximum-value-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/38389/if-x-3-5-where-x-3-2-then-80-2-x-x-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38390/if-tan-a-1-x-x-2-x-1-tan-b-x-x-2-x-1-and-tan-c-x-3-x-2-x-1-1-2-0-a-b-c-2-then-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38391/for-0-2-let-3-sin-2-sin-and-a-real-number-k-be-such-that-tan-tan-then-the-value</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38392/96-cos-and-960-33-cos-2-and-960-33-cos-4-and-960-33-cos-8-and-960-33-cos-16-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/38394/the-value-of-tan-9-o-tan-27-o-tan-63-o-tan-81-o-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38395/if-tan-15-and-176-1-tan-75-and-176-1-tan-105-and-176-tan-195-and-176-2-a-then-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38396/let-s-and-952-and-8712-0-and-960-2-and-8721-m-1-9-sec-and-952-m-1-and-960-6-sec</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38397/the-value-of-2-sin-and-960-22-sin-3-and-960-22-sin-5-and-960-22-sin-7-and-960-22</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38398/if-cot-and-945-1-and-sec-and-946-5-3-where-and-960-and-60-and-945-and-60-3-and-9</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38399/and-945-sin-36-and-176-is-a-root-of-which-of-the-following-equation</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38400/the-value-of-cos-2-and-960-7-cos-4-and-960-7-cos-6-and-960-7-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38401/16-sin-20-and-176-sin-40-and-176-sin-80-and-176-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38402/if-sin-2-10-and-176-sin-20-and-176-sin-40-and-176-sin-50-and-176-sin-70-and-176</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38403/the-value-of-2-sin-12-and-176-sin-72-and-176-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38404/cosec-18-and-176-is-a-root-of-the-equation</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38405/a-10-inches-long-pencil-a-b-with-mid-point-c-and-a-small-eraser-p-are-placed-on</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38406/the-value-of-2-sin-and-960-8-sin-2-and-960-8-sin-3-and-960-8-sin-5-and-960-8-sin</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38407/if-sin-and-952-cos-and-952-1-2-then-16-sin-2-and-952-cos-4-and-952-sin-6-and-952</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38408/the-value-of-cot-and-960-24-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38409/if-15-sin-4-and-945-10-cos-4-and-945-6-for-some-and-945-and-8712-r-then-the-valu</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38410/the-number-of-integral-values-of-k-for-which-the-equation-3-sin-x-4-cos-x-k-1-ha</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38411/if-l-sin-2-and-960-16-sin-2-and-960-8-and-m-cos-2-and-960-16-sin-2-and-960-8</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38412/if-the-equation-cos-4-and-952-sin-4-and-952-and-955-0-has-real-solutions-for-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38413/the-value-of-cos-3-and-960-8-cos-3-and-960-8-sin-3-and-960-8-sin-3-and-960-8-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38414/if-2-s-i-n-and-945-1-c-o-s-2-and-945-1-7-and-1-c-o-s-2-and-946-2-1-10-and-945-an</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38415/the-equation-y-s-i-n-x-sin-and-8289-x-2-sin-2-and-8289-x-1-represents-a-straight</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38416/the-value-of-s-i-n-10-and-176-s-i-n-30-and-176-s-i-n-50-and-176-s-i-n-70-and-176</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38417/the-value-of-cos-2-10-and-176-and-8211-cos-10-and-176-cos-50-and-176-c-o-s-2-50</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38418/if-c-o-s-and-945-and-946-3-5-sin-and-8289-and-945-and-946-5-13-and-0-and-60-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38419/the-maximum-value-of-3-cos-and-8289-and-952-5-sin-and-8289-and-952-and-960-6-for</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38420/let-f-k-x-1-k-k-x-k-x-for-k-1-2-3-then-for-all-x-r-the-value-of-f-x-f-x-is-equal</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38421/the-value-of-cos-and-8289-and-960-2-2-and-8901-cos-and-8289-and-960-2-3-and-8901</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38422/for-any-and-952-and-8712-and-960-4-and-960-2-the-expression-3-sin-and-952-cos-an</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38423/the-lengths-of-two-adjacent-sides-of-a-cyclic-quadrilateral-are-2-units-and-5-un</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38424/if-5-tan-2-and-8289-x-cos-2-and-8289-x-2-cos-and-8289-2-x-9-then-the-value-of-co</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38425/if-a-and-62-0-b-and-62-0-and-a-b-and-960-6-then-the-minimum-positive-value-of-ta</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38426/if-m-and-m-are-the-minimum-and-the-maximum-values-of-4-1-2-sin-2-and-8289-2-x-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38427/the-number-of-x-and-8712-0-2-and-960-for-which-2-sin-4-x-18-cos-2-x-2-cos-4-x-18</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38428/in-a-and-916-a-b-c-a-b-2-3-and-and-8736-c-60-and-176-then-the-ordered-pair-and-8</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38429/if-cosec-and-952-p-q-p-q-p-and-8800-q-p-and-8800-0-then-cot-and-960-4-and-952-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38430/let-f-k-x-1-k-sin-k-x-cos-k-x-where-x-and-8712-r-and-k-and-8805-1-then-f-4-x-f-6</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38431/the-expression-tana-1-cota-cota-1-tana-can-be-written-as</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/38433/suppose-and-0-are-such-that-sec-and-are-in-a-p-if-k-2-for-some-k-then-k-is-equal</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/38435/let-be-such-that-3-if-21-65-and-27-65-then-the-value-of-2-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/38437/let-a-4-i-j-3-k-b-10-i-2-j-k-and-a-vector-c-be-such-that-2-a-b-3-b-c-0-if-a-c-15</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38438/let-a-2-i-3-j-3-k-and-b-6-i-3-j-3-k-then-the-square-of-the-area-of-the-triangle</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38439/if-a-i-j-k-b-j-k-and-c-be-three-vectors-such-that-a-c-b-and-a-c-3-then-c-a-2-b-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38440/let-o-be-the-origin-op-a-and-oq-b-if-r-is-the-point-on-op-such-that-op-5-or-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38441/let-a-7-i-j-k-and-b-j-2-k-if-r-is-a-vector-such-that-r-a-a-b-0-and-r-a-0-then-3</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38442/let-u-and-v-be-unit-vectors-inclined-at-an-acute-angle-such-that-u-v-3-2-if-a-u</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38443/let-a-k-k-i-j-and-b-k-i-k-j-where-k-2-k-1-2-n-1-for-some-n-n-n-5-then-the-value</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38444/let-the-vectors-a-i-j-3-k-and-b-i-3-j-k-for-some-r-let-c-a-b-if-c-3-i-6-j-2-k-10</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38445/two-adjacent-sides-of-a-parallelogram-pqrs-are-given-by-pq-j-k-and-ps-i-j-if-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38446/if-a-and-b-are-two-vectors-such-that-a-2-and-b-3-then-the-maximum-value-of-3-3-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38447/let-p-be-a-point-in-the-plane-of-the-vectors-a-b-3-i-j-k-and-a-c-i-j-3-k-such-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38448/for-three-unit-vectors-a-b-c-satisfying-a-b-b-c-c-a-9-and-2-a-k-b-k-c-3-the-posi</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38449/let-p-q-r-be-a-triangle-such-that-p-q-2-i-j-2-k-and-pr-a-i-b-j-4-k-a-b-z-let-s-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38450/let-a-2-i-5-j-5-k-and-b-i-j-3-k-if-c-is-a-vector-such-that-2-a-c-3-b-c-0-and-a-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38451/let-a-2-i-j-k-b-i-3-j-k-and-c-2-i-j-3-k-let-v-be-the-vector-in-the-plane-of-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38452/let-a-2-i-j-2-k-b-i-j-and-c-a-b-let-d-be-a-vector-such-that-d-a-11-c-d-3-and-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38453/let-a-i-2-j-3-k-b-2-i-j-k-c-i-j-k-and-v-a-b-if-v-c-11-and-the-length-of-the-proj</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38454/let-a-b-c-be-three-vectors-such-that-a-b-2-a-c-if-a-1-b-4-c-2-and-the-angle-betw</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38455/let-a-i-j-2-k-b-i-j-3-k-c-a-b-and-d-c-a-then-a-b-d-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38456/let-a-2-i-j-k-and-b-j-2-k-z-be-two-vectors-let-c-a-b-and-d-be-a-vector-of-magnit</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38457/let-a-vector-a-2-i-j-k-0-make-an-obtuse-angle-with-the-vector-b-i-4-2-j-4-2-k-an</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38458/let-ab-2-i-4-j-5-k-and-ad-i-2-j-k-r-let-the-projection-of-the-vector-v-i-j-k-on</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38459/for-a-triangle-abc-let-p-bc-q-ca-and-r-ba-if-p-2-3-q-2-and-1-3-where-is-the-angl</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38460/let-a-i-2-j-2-k-b-8-i-7-j-3-k-and-c-be-vector-such-that-a-c-b-if-c-i-j-k-4-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38461/let-a-i-2-j-k-and-b-2-i-j-k-let-c-be-a-unit-vector-in-the-plane-of-the-vectors-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38462/let-a-and-b-be-the-vectors-of-the-same-magnitude-such-that-a-b-a-b-a-b-a-b-2-1-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38463/let-the-angle-0-2-between-two-unit-vectors-a-and-b-be-65-9-if-the-vector-c-3-a-6</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38464/let-the-three-sides-of-a-triangle-a-b-c-be-given-by-the-vectors-2-i-j-k-i-3-j-5</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38465/consider-two-vectors-u-3-i-j-and-v-2-i-j-k-0-the-angle-between-them-is-given-by</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38466/let-a-i-2-j-k-b-3-i-3-j-3-k-c-2-i-j-2-k-and-d-be-a-vector-such-that-b-d-c-d-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38467/let-a-i-j-k-b-3-i-2-j-k-c-j-k-and-d-be-a-unit-vector-such-that-a-d-b-d-and-c-d-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38468/let-a-2-i-3-j-k-b-3-i-2-j-5-k-and-a-vector-c-be-such-that-a-c-b-18-i-3-j-12-k-an</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38469/let-a-b-c-d-be-a-tetrahedron-such-that-the-edges-ab-ac-and-ad-are-mutually-perpe</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38470/if-a-is-nonzero-vector-such-that-its-projections-on-the-vectors-2-i-j-2-k-i-2-j</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38471/let-a-be-a-unit-vector-perpendicular-to-the-vectors-b-i-2-j-3-k-and-c-2-i-3-j-k</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38472/let-a-2-i-j-3-k-b-3-i-5-j-k-and-c-be-a-vector-such-that-a-c-c-b-and-a-c-b-c-168</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38473/if-the-components-of-a-i-j-k-along-and-perpendicular-to-b-3-i-j-k-respectively-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38474/let-a-b-c-be-three-points-in-x-y-plane-whose-position-vector-are-given-by-3-i-j</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38475/let-a-i-j-k-b-2-i-2-j-k-and-d-a-b-if-c-is-a-vector-such-that-a-c-c-c-2-a-2-8-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38476/let-the-position-vectors-of-three-vertices-of-a-triangle-be-4-p-q-3-r-5-p-q-2-r</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38477/let-a-3-i-j-2-k-b-a-i-2-k-and-c-b-k-then-the-projection-of-c-2-j-on-a-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38478/let-a-i-2-j-3-k-b-3-i-j-k-and-c-be-three-vectors-such-that-c-is-coplanar-with-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38479/let-the-position-vectors-of-the-vertices-a-b-and-c-of-a-tetrahedron-a-b-c-d-be-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38480/let-a-and-b-be-two-unit-vectors-such-that-the-angle-between-them-is-3-if-a-2-b-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38481/let-c-be-the-projection-vector-of-b-i-4-k-0-on-the-vector-a-i-2-j-2-k-if-a-c-7-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38482/between-the-following-two-statements-statement-i-let-a-i-2-j-3-k-and-b-2-i-j-k-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38483/let-a-2-i-j-k-b-i-k-c-j-k-where-and-are-integers-and-6-let-the-values-of-the-ord</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38484/let-three-vectors-a-i-4-j-2-k-b-5-i-3-j-4-k-c-x-i-y-j-z-k-form-a-triangle-such-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38485/let-o-a-2-a-o-b-6-a-5-b-and-o-c-3-b-where-o-is-the-origin-if-the-area-of-the-par</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38486/let-a-4-i-j-k-b-11-i-j-k-and-c-be-a-vector-such-that-a-b-c-c-2-a-3-b-if-2-a-3-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38487/let-a-i-2-j-3-k-b-2-i-3-j-5-k-and-c-3-i-j-k-be-three-vectors-let-r-be-anit-vecto</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38488/the-set-of-all-for-which-the-vectors-a-t-i-6-j-3-k-and-b-t-i-2-j-2-t-k-are-incli</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38489/let-a-9-i-13-j-25-k-b-3-i-7-j-13-k-and-c-17-i-2-j-k-be-three-given-vectors-if-r</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38490/let-a-2-i-j-k-b-a-i-j-i-i-then-the-square-of-the-projection-of-a-on-b-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38491/let-a-6-i-j-k-and-b-i-j-if-c-is-a-is-vector-such-that-c-6-a-c-6-c-c-a-2-2-and-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38492/let-a-2-i-3-j-4-k-b-3-i-4-j-5-k-and-a-vector-c-be-such-that-a-b-c-b-c-i-8-j-13-k</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38493/consider-three-vectors-a-b-c-let-a-2-b-3-and-a-b-c-if-0-3-is-the-angle-between-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38494/let-a-2-i-5-j-k-b-2-i-2-j-2-k-and-c-be-three-vectors-such-that-c-i-a-b-i-a-c-i-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38495/let-a-i-3-j-7-k-b-2-i-j-k-and-c-be-a-vector-such-that-a-2-b-c-3-c-a-if-a-c-130-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38496/let-a-i-j-k-b-2-i-4-j-5-k-and-c-x-i-2-j-3-k-x-r-if-d-is-the-unit-vector-in-the-d</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38497/for-0-let-be-the-angle-between-the-vectors-a-i-j-3-k-and-b-3-i-j-2-k-if-the-vect</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38498/let-a-unit-vector-which-makes-an-angle-of-60-with-2-i-2-j-k-and-angle-45-with-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38499/let-abc-be-a-triangle-of-area-15-2-and-the-vectors-ab-i-2-j-7-k-bc-a-i-b-j-ck-an</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38500/consider-a-a-b-c-where-a-1-3-2-b-2-8-0-and-c-3-6-7-if-the-angle-bisector-of-b-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38501/let-a-i-j-k-b-i-8-j-2-k-and-c-4-i-c-2-j-c-3-k-be-three-vectors-such-that-b-a-c-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38502/let-a-5-i-j-3-k-b-i-2-j-4-k-and-c-a-b-i-i-i-then-c-i-j-k-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38503/let-a-3-i-2-j-k-b-2-i-j-3-k-and-c-be-a-vector-such-that-a-b-c-2-a-b-24-j-6-k-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38504/let-a-3-i-j-2-k-b-4-i-j-7-k-and-c-i-3-j-4-k-be-three-vectors-if-a-vectors-p-sati</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38505/let-a-and-b-be-two-vectors-such-that-a-1-b-4-and-a-b-2-if-c-2-a-b-3-b-and-the-an</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38506/let-a-i-j-k-r-let-a-vector-b-be-such-that-the-angle-between-a-and-b-is-4-and-b-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38507/let-a-and-b-be-two-vectors-such-that-b-1-and-b-a-2-then-b-a-b-2-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38508/let-a-2-3-5-and-c-3-4-2-be-opposite-vertices-of-a-parallelogram-a-b-c-d-if-the-d</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38509/let-a-a-i-i-a-2-j-a-3-k-and-b-b-1-i-b-2-j-b-3-k-be-two-vectors-such-that-a-1-a-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38510/let-oa-a-ob-12-a-4-b-and-oc-b-where-o-is-the-origin-if-s-is-the-parallelogram-wi</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38511/let-a-unit-vector-u-x-i-y-j-z-k-make-angles-2-3-and-2-3-with-the-vectors-1-2-i-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38512/let-a-b-and-c-be-three-non-zero-vectors-such-that-b-and-c-are-non-collinear-if-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38513/if-a-i-2-j-k-b-3-i-j-k-and-c-be-the-vector-such-that-a-c-b-and-a-c-3-then-a-c-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38514/the-least-positive-integral-value-of-for-which-the-angle-between-the-vectors-i-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38515/let-s-be-the-set-of-all-and-955-and-956-for-which-the-vectors-and-955-i-j-k-j-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38516/let-a-b-c-d-be-a-quadrilateral-if-e-and-f-are-the-mid-points-of-the-diagonals-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38517/let-a-and-8594-2-b-and-8594-3-and-the-angle-between-the-vectors-a-and-8594-and-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38518/let-for-a-triangle-a-b-c-a-b-and-8594-2-i-j-3-k-c-b-and-8594-and-945-i-and-946-j</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38519/let-a-and-8594-i-4-j-2-k-b-and-8594-3-i-2-j-7-k-and-c-and-8594-2-i-j-4-k-if-a-ve</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38520/let-a-and-8594-3-i-j-k-and-c-and-8594-2-i-3-j-3-k-if-b-and-8594-is-a-vector-such</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38521/let-a-b-c-be-three-distinct-real-numbers-none-equal-to-one-if-the-vectors-a-i-j</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38522/let-and-955-and-8712-and-8484-a-and-8594-and-955-i-j-k-and-b-and-8594-3-i-j-2-k</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38523/let-the-plane-x-3-y-2-z-6-0-meet-the-co-ordinate-axes-at-the-points-a-b-c-if-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38524/if-four-distinct-points-with-position-vectors-a-and-8594-b-and-8594-c-and-8594-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38525/let-a-and-8594-i-2-j-3-k-and-b-and-8594-i-j-k-if-c-and-8594-is-a-vector-such-tha</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38526/for-any-vector-a-and-8594-a-1-i-a-2-j-a-3-k-with-10-a-i-and-60-1-i-1-2-3-conside</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38527/let-a-and-8594-be-a-non-zero-vector-parallel-to-the-line-of-intersection-of-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38528/let-a-and-8594-2-i-7-j-k-b-3-i-5-k-and-c-and-8594-i-j-2-k-let-d-and-8594-be-a-ve</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38529/if-the-points-p-and-q-are-respectively-the-circumcenter-and-the-orthocentre-of-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38530/an-arc-p-q-of-a-circle-subtends-a-right-angle-at-its-centre-o-the-mid-point-of-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38531/let-o-be-the-origin-and-the-position-vector-of-the-point-p-be-i-2-j-3-k-if-the-p</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38532/let-the-vectors-u-1-and-8594-i-j-a-k-u-2-and-8594-i-b-j-k-and-u-3-and-8594-c-i-j</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38533/the-area-of-the-quadrilateral-a-b-c-d-with-vertices-a-2-1-1-b-1-2-5-c-2-3-5-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38534/if-the-points-with-position-vectors-and-945-i-10-j-13-k-6-i-11-j-11-k-9-2-i-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38535/let-a-and-8594-6-i-9-j-12-k-b-and-8594-and-945-i-11-j-2-k-and-c-and-8594-be-vect</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38536/let-the-vectors-a-and-8594-b-and-8594-c-and-8594-represent-three-coterminous-edg</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38537/the-sum-of-all-values-of-and-945-for-which-the-points-whose-position-vectors-are</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38538/let-the-position-vectors-of-the-points-a-b-c-and-d-be-5-i-5-j-2-and-955-k-i-2-j</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38539/let-a-and-8594-2-i-3-j-4-k-b-and-8594-i-2-j-2-k-and-c-and-8594-i-4-j-3-k-if-d-an</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38540/let-a-and-8594-5-i-j-3-k-and-b-and-8594-i-3-j-5-k-be-two-vectors-then-which-one</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38541/let-a-and-8594-2-i-7-j-5-k-b-and-8594-i-k-and-c-and-8594-i-2-j-3-k-be-three-give</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38542/let-v-and-8594-and-945-i-2-j-3-k-w-and-8594-2-and-945-i-j-k-and-u-and-8594-be-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38543/a-2-6-2-b-4-0-and-955-c-2-3-1-and-d-4-5-0-and-955-and-8804-5-are-the-vertices-of</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38544/let-a-and-8594-i-2-j-3-k-b-and-8594-i-j-2-k-and-c-and-8594-5-i-3-j-3-k-be-there</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38545/let-a-and-8594-b-and-8594-c-and-8594-be-three-vectors-such-that-a-and-8594-31-4</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38546/let-a-and-8594-2-i-j-k-and-b-and-8594-and-c-and-8594-be-two-nonzero-vectors-such</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38547/let-a-and-8594-and-b-and-8594-be-two-vector-such-that-a-and-8594-14-b-and-8594-6</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38548/let-and-955-and-8712-and-8477-a-and-8594-and-955-i-2-j-3-k-b-and-8594-i-and-955</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38549/let-a-and-8594-and-b-and-8594-be-two-vectors-let-a-and-8594-1-b-and-8594-4-and-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38550/if-a-and-8594-b-and-8594-c-and-8594-are-three-non-zero-vectors-and-n-is-a-unit-v</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38551/if-a-and-8594-i-2-k-b-and-8594-i-j-k-c-and-8594-7-i-3-j-4-k-r-and-8594-and-215-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38552/let-a-and-8594-4-i-3-j-and-b-and-8594-3-i-4-j-5-k-and-c-and-8594-is-a-vector-suc</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38553/if-the-vectors-a-and-8594-and-955-i-and-956-j-4-k-b-and-8594-2-i-4-j-2-k-and-c-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38554/let-a-and-8594-b-and-8594-and-c-and-8594-be-three-non-zero-non-coplanar-vectors</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38555/if-the-four-points-whose-position-vectors-are-3-i-4-j-2-k-i-2-j-k-2-i-j-3-k-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38556/let-a-and-8594-i-j-k-a-and-8594-and-183-b-and-8594-1-and-a-and-8594-and-215-b-an</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38557/let-a-and-8594-b-and-8594-and-c-and-8594-be-three-non-zero-vectors-such-that-b-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38558/the-vector-a-and-8594-i-2-j-k-is-rotated-through-a-right-angle-passing-through-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38559/let-and-945-and-8594-4-i-3-j-5-k-and-and-946-and-8594-i-2-j-4-k-let-and-946-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38560/let-a-and-8594-i-2-j-and-955-k-b-and-8594-3-i-5-j-and-955-k-a-and-8594-and-183-c</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38561/let-u-and-8594-i-j-2-k-v-and-8594-2-i-j-k-v-and-8594-and-183-w-and-8594-2-and-v</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38562/let-p-q-r-be-a-triangle-the-points-a-b-and-c-are-on-the-sides-q-r-r-p-and-p-q-re</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38563/if-2-3-9-5-2-1-1-and-955-8-and-and-955-2-3-are-coplanar-then-the-product-of-all</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38564/let-a-and-8594-b-and-8594-c-and-8594-be-three-coplanar-concurrent-vectors-such-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38565/let-a-and-8594-and-b-and-8594-be-two-vectors-such-that-a-and-8594-b-and-8594-2-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38566/let-a-and-8594-3-i-j-and-b-and-8594-i-2-j-k-let-c-and-8594-be-a-vector-satisfyin</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38567/let-a-and-b-be-two-unit-vectors-such-that-the-angle-between-them-is-and-960-4-if</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38568/let-s-be-the-set-of-all-a-and-8712-r-for-which-the-angle-between-the-vectors-u-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38569/let-the-vectors-a-and-8594-1-t-i-1-t-j-k-b-and-8594-1-t-i-1-t-j-2-k-and-c-and-85</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38570/let-a-vector-a-and-8594-has-a-magnitude-9-let-a-vector-b-and-8594-be-such-that-f</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38571/let-a-and-8594-b-and-8594-c-and-8594-be-three-non-coplanar-vectors-such-that-a-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38572/let-a-and-8594-and-945-i-j-and-946-k-and-b-and-8594-3-i-5-j-4-k-be-two-vectors-s</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38573/let-a-and-8594-2-i-j-5-k-and-b-and-8594-and-945-i-and-946-j-2-k-if-a-and-8594-an</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38574/let-a-and-8594-and-945-i-j-k-and-b-and-8594-2-i-j-and-945-k-and-945-and-62-0-if</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38575/let-a-and-8594-i-j-2-k-and-let-b-and-8594-be-a-vector-such-that-a-and-8594-and-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38576/let-a-b-c-be-a-triangle-such-that-b-c-and-8594-a-and-8594-c-a-and-8594-b-and-859</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38577/let-a-b-c-be-three-points-whose-position-vectors-respectively-are-a-and-8594-i-4</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38578/let-a-and-8594-i-2-j-3-k-b-and-8594-i-j-k-and-c-and-8594-be-a-vector-such-that-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38579/let-a-and-8594-and-945-i-3-j-k-b-and-8594-3-i-and-946-j-4-k-and-c-and-8594-i-2-j</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38580/let-a-and-8594-and-945-i-2-j-k-and-b-and-8594-2-i-and-945-j-k-where-and-945-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38581/let-a-and-8594-be-a-vector-which-is-perpendicular-to-the-vector-3-i-1-2-j-2-k-if</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38582/if-a-and-8594-2-i-j-3-k-b-and-8594-3-i-3-j-k-and-c-and-8594-c-1-i-c-2-j-c-3-k-ar</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38583/let-a-and-8594-and-b-and-8594-be-the-vectors-along-the-diagonal-of-a-parallelogr</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38584/let-a-and-8594-i-j-k-and-c-and-8594-2-i-3-j-2-k-then-the-number-of-vectors-b-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38585/let-a-and-8594-i-j-2-k-b-and-8594-2-i-3-j-k-and-c-and-8594-i-j-k-be-the-three-gi</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38586/if-a-and-8594-and-183-b-and-8594-1-b-and-8594-and-183-c-and-8594-2-and-c-and-859</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38587/let-b-and-8594-i-j-and-955-k-and-955-and-8712-and-8477-if-a-and-8594-is-a-vector</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38588/let-a-and-8594-a-1-i-a-2-j-a-3-k-a-i-and-62-0-i-1-2-3-be-a-vector-which-makes-eq</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38589/let-and-952-be-the-angle-between-the-vectors-a-and-8594-and-b-and-8594-where-a-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38590/let-a-and-b-be-two-unit-vectors-such-that-a-b-2-a-and-215-b-2-if-and-952-and-871</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38591/let-a-b-be-unit-vectors-if-c-and-8594-be-a-vector-such-that-the-angle-between-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38592/let-a-and-8594-2-i-j-2-k-and-b-and-8594-i-2-j-k-let-a-vector-v-and-8594-be-in-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38593/let-a-and-8594-b-and-8594-c-and-8594-be-three-vectors-mutually-perpendicular-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38594/let-a-and-8594-and-b-and-8594-be-two-vectors-such-that-2-a-and-8594-3-b-and-8594</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38595/let-a-and-8594-i-5-j-and-945-k-b-and-8594-i-3-j-and-946-k-and-c-and-8594-i-2-j-3</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38596/a-hall-has-a-square-floor-of-dimension-10-m-and-215-10-m-see-the-figure-and-vert</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38597/if-the-projection-of-the-vector-i-2-j-k-on-the-sum-of-the-two-vectors-2-i-4-j-5</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38598/let-a-and-8594-i-j-k-and-b-and-8594-j-k-if-c-and-8594-is-a-vector-such-that-a-an</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38599/let-a-and-8594-b-and-8594-and-c-and-8594-be-three-vectors-such-that-a-and-8594-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38600/let-a-and-8594-i-and-945-j-and-946-k-b-and-8594-3-i-and-946-j-and-945-k-and-c-an</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38601/let-a-and-8594-i-j-2-k-and-b-and-8594-i-2-j-3-k-then-the-vector-product-a-and-85</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38602/let-a-and-8594-i-j-k-b-and-8594-and-c-and-8594-j-k-be-three-vectors-such-that-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38603/let-a-b-and-c-be-distinct-positive-numbers-if-the-vectors-a-i-a-j-c-k-i-k-and-c</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38604/if-a-and-8594-2-b-and-8594-5-and-a-and-8594-and-215-b-and-8594-8-then-a-and-8594</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38605/if-a-and-8594-and-b-and-8594-are-unit-vectors-and-a-and-8594-3-b-and-8594-is-per</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38606/let-the-vectors-2-a-b-i-a-2-b-c-j-b-c-k-1-b-i-2-b-j-b-k-and-2-b-i-2-b-j-1-b-k-an</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38607/let-p-and-8594-2-i-3-j-k-and-q-and-8594-i-2-j-k-be-two-vectors-if-a-vector-r-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38608/let-a-vector-a-and-8594-be-coplanar-with-vectors-b-and-8594-2-i-j-k-and-c-and-85</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38609/let-three-vectors-a-and-8594-b-and-8594-and-c-and-8594-be-such-that-a-and-8594-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38610/in-a-triangle-a-b-c-if-b-c-and-8594-3-c-a-and-8594-5-and-b-a-and-8594-7-then-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38611/for-p-and-62-0-a-vector-v-and-8594-2-2-i-p-1-j-is-obtained-by-rotating-the-vecto</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38612/let-a-and-8594-2-i-j-2-k-and-b-and-8594-i-j-if-c-and-8594-is-a-vector-such-that</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38613/let-a-and-8594-b-and-8594-c-and-8594-be-three-mutually-perpendicular-vectors-of</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38614/in-a-triangle-a-b-c-if-b-c-and-8594-8-c-a-and-8594-7-a-b-and-8594-10-then-the-pr</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38615/let-a-and-8594-and-b-and-8594-be-two-non-zero-vectors-perpendicular-to-each-othe</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38616/a-vector-a-and-8594-has-components-3-p-and-1-with-respect-to-a-rectangular-carte</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38617/let-x-and-8594-be-a-vector-in-the-plane-containing-vectors-a-and-8594-2-i-j-k-an</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38618/let-o-be-the-origin-let-o-p-and-8594-x-i-y-j-k-and-o-q-and-8594-i-2-j-3-x-k-x-y</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38619/let-a-and-8594-2-i-3-j-4-k-and-b-and-8594-7-i-j-6-k-if-r-and-8594-and-215-a-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38620/if-a-and-8594-and-945-i-and-946-j-3-k-b-and-8594-and-946-i-and-945-j-k-and-c-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38621/let-a-and-8594-i-2-j-3-k-and-b-and-8594-2-i-3-j-5-k-if-r-and-8594-and-215-a-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38622/let-c-and-8594-be-a-vector-perpendicular-to-the-vectors-a-and-8594-i-j-k-and-b-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38623/let-a-vector-and-945-i-and-946-j-be-obtained-by-rotating-the-vector-3-i-j-by-an</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38624/if-vectors-a-1-and-8594-x-i-j-k-and-a-2-and-8594-i-y-j-z-k-are-collinear-then-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38625/if-a-and-8594-and-b-and-8594-are-perpendicular-then-a-and-8594-and-215-a-and-859</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38626/if-1-5-35-7-5-5-1-and-955-7-and-2-and-955-1-2-are-coplanar-then-the-sum-of-all-p</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38627/let-a-and-8594-i-and-945-j-3-k-and-b-and-8594-3-i-and-945-j-k-if-the-area-of-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38628/let-a-and-8594-i-2-j-k-b-and-8594-i-j-and-c-and-8594-i-j-k-be-three-given-vector</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38629/let-three-vectors-a-and-8594-b-and-8594-and-c-and-8594-be-such-that-c-and-8594-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38630/if-x-and-8594-and-y-and-8594-be-two-non-zero-vectors-such-that-x-and-8594-y-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38631/if-a-and-8594-and-b-and-8594-are-unit-vectors-then-the-greatest-value-of-3-a-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38632/let-the-vectors-a-and-8594-b-and-8594-c-and-8594-be-such-that-a-and-8594-2-b-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38633/if-the-volume-of-a-parallelopiped-whose-coterminous-edges-are-given-by-the-vecto</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38634/if-a-and-8594-2-i-j-2-k-then-the-value-of-i-and-215-a-and-8594-and-215-i-2-j-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38635/let-x-0-be-the-point-of-local-maxima-of-f-x-a-and-8594-and-183-b-and-8594-and-21</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38636/let-a-b-c-and-8712-r-be-such-that-a-2-b-2-c-2-1-if-a-cos-and-952-b-cos-and-952-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38637/let-the-position-vectors-of-points-and-39-a-and-39-and-and-39-b-and-39-be-i-j-k</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38638/let-a-and-8594-b-and-8594-and-c-and-8594-be-three-unit-vectors-such-that-a-and-8</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38639/let-a-and-8594-b-and-8594-and-c-and-8594-be-three-vectors-such-that-a-and-8594-3</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38640/if-the-vectors-p-and-8594-a-1-i-a-j-a-k-q-and-8594-a-i-a-1-j-a-k-and-r-and-8594</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38641/let-a-and-8594-i-2-j-k-and-b-and-8594-i-j-k-be-two-vectors-if-c-and-8594-is-a-ve</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38642/let-the-volume-of-a-parallelepiped-whose-coterminous-edges-are-given-by-u-and-85</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38643/let-a-and-8594-b-and-8594-and-c-and-8594-be-three-unit-vectors-such-that-a-and-8</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38644/a-vector-a-and-8594-and-945-i-2-j-and-946-k-and-945-and-946-and-8712-r-lies-in-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38645/let-and-945-and-8201-and-8712-r-and-the-three-vectors-a-and-8594-and-945-i-j-3-k</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38646/if-the-volume-of-parallelepiped-formed-by-the-vectors-i-and-955-j-k-j-and-955-k</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38647/let-a-and-8594-3-i-2-j-2-k-and-b-and-8594-i-2-j-2-k-be-two-vectors-if-a-vector-p</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38648/the-distance-of-the-point-having-position-vector-i-2-j-6-k-from-the-straight-lin</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38649/let-a-3-0-1-b-2-10-6-and-c-1-2-1-be-the-vertices-of-a-triangle-and-m-be-the-mid</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38650/if-a-unit-vector-a-and-8594-makes-angles-and-960-3-with-i-and-960-4-with-j-and-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38651/let-and-945-and-8594-3-i-j-and-and-946-and-8594-2-i-j-3-k-if-and-946-and-8594-an</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38652/let-a-and-8594-3-i-2-j-x-k-and-b-and-8594-i-j-k-for-some-real-x-then-the-conditi</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38653/the-magnitude-of-the-projection-of-the-vector-2-i-3-j-k-on-the-vector-perpendicu</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38654/let-a-and-8594-and-8201-b-and-8594-and-c-and-8594-be-three-unit-vectors-out-of-w</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38655/the-sum-of-the-distinct-real-values-of-and-956-for-which-the-vectors-and-956-i-j</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38656/let-3-i-j-i-3-j-and-i-1-j-respectively-be-the-position-vectors-of-the-points-a-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38657/let-a-i-2-j-4-k-b-i-j-4-k-and-c-2-i-4-j-1-k-be-coplanar-vectors-then-the-non-zer</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38658/let-and-945-and-8594-and-955-2-a-and-8594-b-and-8594-and-and-946-and-8594-4-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38659/let-a-and-8594-2-i-and-955-1-j-3-k-b-and-8594-4-i-3-and-955-2-j-6-k-and-c-and-85</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38660/let-a-be-a-point-on-the-line-r-and-8594-1-3-and-956-i-and-956-1-j-2-5-and-956-k</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38661/let-a-and-8594-i-j-2-k-b-and-8594-b-1-i-b-2-j-2-k-and-c-and-8594-5-i-j-2-k-be-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38662/let-a-and-8594-i-j-b-and-8594-i-j-k-and-c-and-8594-be-a-vector-such-that-a-and-8</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38663/let-a-and-8594-i-j-k-c-and-8594-j-k-and-a-vector-b-and-8594-be-such-that-a-and-8</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38664/if-the-position-vectors-of-the-vertices-a-b-and-c-of-a-abc-are-respectively-4-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38665/an-angle-between-the-lines-whose-direction-cosines-are-given-by-the-equations-l</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38666/if-a-b-and-c-are-unit-vectors-such-that-a-2-b-2-c-0-then-a-c-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38667/if-a-and-8594-b-and-8594-c-and-8594-are-unit-vectors-such-that-a-and-8594-2-b-an</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38668/let-u-and-8594-be-a-vector-coplanar-with-the-vectors-a-and-8594-2-i-3-j-k-and-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38669/if-the-vector-b-and-8594-3-j-4-k-is-written-as-the-sum-of-a-vector-b-1-and-8594</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38670/the-area-in-sq-units-of-the-parallelogram-whose-diagonals-are-along-the-vectors</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38671/given-a-and-8594-2-i-j-2-k-and-b-and-8594-i-j-let-c-and-8594-be-a-vector-such-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38672/the-number-of-distinct-real-values-of-and-955-for-which-the-lines-x-1-1-y-2-2-z</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38673/in-a-triangle-a-b-c-right-angle-at-vertex-a-if-the-position-vectors-of-a-b-and-c</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38674/let-a-and-8594-b-and-8594-and-c-and-8594-be-three-unit-vectors-such-that-a-and-8</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38675/in-a-parallelogram-a-b-c-d-a-b-and-8594-a-a-d-and-8594-b-and-38-a-c-and-8594-c-d</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38676/let-a-and-8594-and-b-and-8594-be-two-unit-vectors-such-that-a-and-8594-b-and-859</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38677/let-a-and-8594-b-and-8594-and-c-and-8594-be-three-non-zero-vectors-such-that-no</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38678/if-x-and-8594-3-i-6-j-k-y-and-8594-i-4-j-3-k-and-z-and-8594-3-i-4-j-1-2-k-then-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38679/if-x-y-and-z-are-three-unit-vectors-in-threedimensional-space-then-the-minimum-v</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38680/if-c-2-60-and-c-i-2-j-5-k-0-then-a-value-of-c-7-i-2-j-3-k-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38681/if-a-and-8594-2-b-and-8594-3-and-2-a-and-8594-b-and-8594-5-then-2-a-and-8594-b-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38682/if-a-and-8594-and-215-b-and-8594-b-and-8594-and-215-c-and-8594-c-and-8594-and-21</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38683/let-a-2-i-j-2-k-b-i-j-if-c-is-a-vector-such-that-a-c-c-c-a-2-2-and-the-angle-bet</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38684/if-a-and-b-are-non-collinear-vectors-then-the-value-of-for-which-the-vectors-u-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38685/if-a-b-and-c-are-unit-vectors-satisfying-a-3-b-c-0-then-the-angle-between-the-ve</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38686/let-a-2-i-j-k-b-i-2-j-k-and-c-i-j-2-k-be-three-vectors-a-vector-of-the-type-b-c</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38687/the-vector-i-a-b-i-j-a-b-j-k-a-b-k-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38688/a-vector-n-is-inclined-to-x-axis-at-45-to-y-axis-at-60-and-at-an-acute-angle-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38689/if-the-vectors-ab-and-8594-3-i-4-k-and-ac-and-8594-5-i-2-j-4-k-are-the-sides-of</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38690/statement-1-the-vectors-a-b-and-c-lie-in-the-same-plane-if-and-only-if-a-b-c-0-s</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38691/if-a-b-c-0-a-3-b-5-and-c-7-then-the-angle-between-a-and-b-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38692/if-u-j-4-k-v-i-3-k-and-w-i-j-are-vectors-in-3-dimensional-space-then-the-maximum</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38693/statement-1-if-the-points-1-2-2-2-1-2-and-2-2-z-and-1-1-1-are-coplanar-then-z-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38694/a-b-c-d-is-parallelogram-the-position-vectors-of-a-and-c-are-respectively-3-i-3</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38695/if-a-i-2-j-3-k-b-2-i-3-j-k-and-c-i-j-2-1-k-are-coplanar-vectors-then-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38696/let-a-and-b-be-two-unit-vectors-if-the-vectors-c-a-2-b-and-d-5-a-4-b-are-perpend</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38697/let-a-b-c-d-be-a-parallelogram-such-that-a-b-q-a-d-p-and-b-a-d-be-an-acute-angle</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38698/if-a-1-10-3-i-k-and-b-1-7-2-i-3-j-6-k-then-the-value-of-2-a-b-a-b-a-2-b-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38699/the-vector-a-and-b-are-not-perpendicular-and-c-and-d-are-two-vectors-satisfying</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38700/let-a-j-k-and-c-i-j-k-then-vector-b-satisfying-a-b-c-0-and-a-b-3-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38701/if-the-vectors-a-i-j-2-k-b-2-i-4-j-k-and-c-i-j-k-are-mutually-orthogonal-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38702/if-u-v-w-are-non-coplanar-vectors-and-p-q-are-real-numbers-then-the-equality-arr</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38703/the-non-zero-verctors-a-b-and-c-are-related-by-a-8-b-and-c-7-b-then-the-angle-be</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38704/the-resultant-of-two-forces-p-n-and-3-n-is-a-force-of-7-n-if-the-direction-of-3</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38705/if-u-and-v-are-unit-vectors-and-is-the-acute-angle-between-them-then-2-u-3-v-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38706/let-a-i-j-k-b-i-j-2-k-and-c-x-i-x-2-j-k-if-the-vector-c-lies-in-the-plane-of-a-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38707/a-b-c-is-a-triangle-right-angled-at-a-the-resultant-of-the-forces-acting-along-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38708/if-a-b-c-a-b-c-where-a-b-and-c-are-any-three-vectors-such-that-a-b-0-b-c-0-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38709/a-particle-has-two-velocities-of-equal-magnitude-inclined-to-each-other-at-an-an</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38710/the-values-of-a-for-which-the-points-a-b-c-with-position-vectors-2-i-j-k-i-3-j-5</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38711/if-c-is-the-mid-point-of-a-b-and-p-is-any-point-outside-a-b-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38712/for-any-vectora-a-the-value-of-a-i-2-a-j-2-a-k-2-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38713/if-a-b-c-are-non-coplanar-vectors-and-is-a-real-number-then-a-b-2-b-c-a-b-c-b-fo</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38714/let-a-i-k-b-x-i-j-1-x-k-and-c-y-i-x-j-1-x-y-k-then-a-b-c-depends-on</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38715/the-resultant-r-of-two-forces-acting-on-a-particle-is-at-right-angles-to-one-of</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38716/if-the-straight-lines-x-1-s-y-3-s-z-1-s-and-x-t-2-y-1-t-z-2-t-with-parameters-s</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38717/let-a-b-and-c-be-three-non-zero-vectors-such-that-no-two-of-these-are-collinear</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38718/a-particle-is-acted-upon-by-constant-forces-4-i-j-3-k-and-3-i-j-k-which-displace</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38719/if-a-b-c-are-non-coplanar-vectors-and-is-a-real-number-then-the-vectors-a-2-b-3</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38720/let-a-b-and-c-be-non-zero-vectors-such-that-a-b-c-1-3-b-c-a-if-is-the-acute-angl</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38721/with-two-forces-acting-at-a-point-the-maximum-effect-is-obtained-when-their-resu</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38722/in-a-right-angle-abc-a-90-and-sides-a-b-c-are-respectively-5-cm-4-cm-and-3-cm-if</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38723/three-forces-p-q-and-r-acting-along-ia-ib-and-ic-where-i-is-the-incentre-of-a-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38724/a-velocity-1-4-m-s-is-resolved-into-two-components-along-oa-and-ob-making-angles</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38725/a-couple-is-of-moment-g-and-the-force-forming-the-couple-is-p-if-p-is-turned-thr</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38726/the-resultant-of-forces-p-and-q-is-r-if-q-is-doubled-then-r-is-doubled-if-the-di</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38727/let-u-i-j-v-i-j-and-w-i-2-j-3-k-if-n-is-a-unit-vector-such-that-u-n-0-and-v-n-0</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38728/a-particle-acted-on-by-constant-forces-4-i-j-3-k-and-3-i-j-k-to-the-point-5-i-4</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38729/the-lines-x-2-1-y-3-1-z-4-k-and-x-1-k-y-4-1-z-5-1-are-coplanar-if</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38730/a-b-c-are-3-vectors-such-that-a-b-c-0-a-1-b-2-a-then-a-b-b-c-c-a-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38731/a-tetrahedron-has-vertices-at-o-0-0-0-a-1-2-1-b-2-1-3-and-c-1-1-2-then-the-angle</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38732/if-array-lll-a-and-a-2-and-1-a-3-b-and-b-2-and-1-b-3-c-and-c-2-and-1-c-3-array-0</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38733/consider-points-a-b-c-and-d-with-position-vectors-7-i-4-j-7-k-i-6-j-10-k-i-3-j-4</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38734/if-u-v-and-w-are-three-non-coplanar-vectors-then-u-v-w-u-v-v-w-equals</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38735/if-a-4-b-2-and-the-angle-between-a-and-b-is-6-then-a-b-2-2-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38736/if-a-b-c-are-vectors-such-that-a-b-c-4-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38737/if-a-b-c-are-vectors-such-that-a-b-c-0-and-a-7-b-5-c-3-then-angle-between-vector</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38738/if-a-5-b-4-c-3-thus-what-will-be-the-value-of-a-b-b-c-c-a-given-that-a-b-c-0</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38739/3-c-2-a-b-0-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38740/a-3-i-5-j-and-b-6-i-3-j-are-two-vectors-and-c-is-a-vector-such-that-c-a-b-then-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38741/if-a-b-b-c-c-a-then-a-b-c</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38742/the-sum-of-two-forces-is-18-n-and-resultant-whose-direction-is-at-right-angles-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38743/a-lcr-series-circuit-driven-with-e-rms-90-v-at-frequency-f-d-30-hz-has-resistanc</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38744/a-series-lcr-circuit-with-r-20-l-1-6-h-and-c-40-f-is-connected-to-a-variable-fre</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38745/an-a-c-source-of-angular-frequency-is-connected-across-a-resistor-r-and-a-capaci</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38746/an-inductor-of-10-mh-capacitor-of-0-1-f-and-a-resistor-of-100-are-connected-in-s</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38747/the-figure-given-below-shows-an-lcr-series-circuit-with-two-switches-s-and-s-whe</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38748/an-inductor-stores-16-j-of-magnetic-field-energy-and-dissipates-32-w-of-thermal</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38749/the-electric-current-in-the-circuit-is-given-as-i-i-o-t-t-the-r-m-s-current-for</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38750/for-the-series-l-c-r-circuit-connected-with-220-v-50-hz-a-c-source-as-shown-in-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/38838/in-an-ac-circuit-an-inductor-a-capacitor-and-a-resistor-are-connected-in-series</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/38844/a-100-and-937-resistance-a-0-1-and-956-f-capacitor-and-an-inductor-are-connected</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38845/a-0-07-h-inductor-and-a-12-and-937-resistor-are-connected-in-series-to-a-220-v-5</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38846/a-10-and-937-resistance-is-connected-across-220-v-50-hz-ac-supply-the-time-taken</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38847/two-circuits-are-shown-in-figure-a-and-b-at-a-frequency-of-rad-s-1-the-average-p</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38848/an-inductor-of-10-mh-is-connected-to-a-20-v-battery-through-a-resistor-of-10-kan</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38849/in-a-circuit-consisting-of-a-capacitance-and-a-generator-with-alternating-emf-e</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38850/match-list-i-with-list-ii-list-i-list-ii-a-and-969-l-and-62-1-and-969-c-i-curren</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38851/for-a-series-lcr-circuit-with-r-100-and-937-l-0-5-mh-and-c-0-1-pf-connected-acro</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38852/a-series-lcr-circuit-of-r-5-and-937-l-20-mh-and-c-0-5-and-956-f-is-connected-acr</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38853/a-c-voltage-v-t-20-sin-and-969-t-of-frequency-50-hz-is-applied-to-a-parallel-pla</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38854/in-an-l-c-r-series-circuit-an-inductor-30-mh-and-a-resistor-1-and-937-are-connec</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38855/in-a-series-lcr-circuit-the-inductive-reactance-x-l-is-10-and-937-and-the-capaci</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/38857/in-a-scries-l-c-r-resonance-circuit-if-we-change-the-resistance-only-from-a-lowe</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38858/an-a-c-source-rated-220-v-50-hz-is-connected-to-a-resistor-the-time-taken-by-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38859/match-list-i-with-list-ii-list-i-list-ii-a-phase-difference-between-current-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38860/what-happens-to-the-inductive-reactance-and-the-current-in-a-purely-inductive-ci</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38861/an-a-c-current-is-given-by-i-i-1-s-i-n-and-969-t-i-2-c-o-s-and-969-t-a-hot-wire</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38862/for-the-given-circuit-comment-on-the-type-of-transformer-used</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38863/an-r-c-circuit-as-shown-in-the-figure-is-driven-by-a-a-c-source-generating-a-squ</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38864/a-sinusoidal-voltage-of-peak-value-250-v-is-applied-to-a-series-l-c-r-circuit-in</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38865/find-the-peak-current-and-resonant-frequency-of-the-following-circuit-as-shown-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38866/an-alternating-current-is-given-by-the-equation-i-i-1-sin-and-969-t-i-2-cos-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38867/in-a-series-lcr-resonant-circuit-the-quality-factor-is-measured-as-100-if-the-in</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38868/match-list-i-with-list-ii-list-i-list-ii-a-rectifier-i-used-either-for-stepping</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38869/an-l-c-r-circuit-contains-resistance-of-110-and-937-and-a-supply-of-220-v-at-300</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38870/the-current-i-at-time-t-0-and-t-and-8734-respectively-for-the-given-circuit-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38871/the-angular-frequency-of-alternating-current-in-a-l-c-r-circuit-is-100-rad-s-1-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38872/a-transmitting-station-releases-waves-of-wavelength-960-and-160-m-a-capacitor-of</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38873/the-figure-shows-a-circuit-that-contains-four-identical-resistors-with-resistanc</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38874/a-series-lcr-circuit-is-designed-to-resonate-at-an-angular-frequency-and-969-0-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38875/a-common-transistor-radio-set-requires-12-and-160-v-d-c-for-its-operation-the-d</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38876/a-resonance-circuit-having-inductance-and-resistance-2-and-215-10-4-h-and-6-28-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38877/in-a-series-lr-circuit-power-of-400-w-is-dissipated-from-a-source-of-250-v-50-hz</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38878/an-ac-circuit-has-r-100-and-937-c-2-and-956-f-and-l-80-mh-connected-in-series-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38879/a-part-of-a-complete-circuit-is-shown-in-the-figure-at-some-instant-the-value-of</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38880/a-series-l-r-circuit-is-connected-to-a-battery-of-emf-v-if-the-circuit-is-switch</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38881/a-750-hz-20-v-rms-source-is-connected-to-a-resistance-of-100-and-937-an-inductan</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38882/magnetic-materials-used-for-making-permanent-magnets-p-and-magnets-in-a-transfor</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38883/in-l-c-circuit-the-inductance-l-40-mh-and-capacitance-c-100-and-956-f-if-a-volta</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/38885/as-shown-in-the-figure-a-battery-of-emf-and-8712-is-connected-to-an-inductor-l-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38886/an-emf-of-20-v-is-applied-at-time-t-0-to-a-circuit-containing-in-series-10-m-h-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38887/a-l-c-r-circuit-behaves-like-a-clamped-harmonic-oscillator-comparing-it-with-a-p</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38888/consider-the-lr-circuit-shown-in-the-figure-if-the-switch-s-is-closed-at-t-0-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38889/a-transformer-consisting-of-300-turns-in-the-primary-and-150-turns-in-the-second</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38890/a-circuit-connected-to-an-ac-source-of-emf-e-e-0-sin-and-8289-100-t-with-t-in-se</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38891/a-20-h-inductor-coil-is-connected-to-a-10-and-937-resistance-in-series-as-shown</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38892/an-alternating-voltage-v-t-220-sin-100-and-960-t-volt-is-applied-to-a-purely-res</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/38895/in-the-circuit-shown-the-switch-s-is-closed-at-time-t-0-and-the-switch-s-is-kept</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/38897/a-series-a-c-circuit-containing-an-inductor-20-mh-a-capacitor-120-and-956-f-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/38899/an-ideal-capacitor-of-capacitance-0-2-and-956-f-is-charged-to-a-potential-differ</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/38903/a-series-l-r-circuit-is-connected-to-a-voltage-source-with-v-t-v-0-sin-and-969-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/38906/for-the-lcr-circuit-shown-here-the-current-is-observed-to-lead-the-applied-volta</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38907/an-lcr-circuit-is-equivalent-to-a-damped-pendulum-in-an-lcr-circuit-the-capacito</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/38916/in-a-series-l-c-r-circuit-c-10-farad-l-10-5-henry-and-r-100-ohm-when-a-constant</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/38918/the-amplitude-of-a-damped-oscillator-decreases-to-0-9-times-its-original-magnitu</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38919/a-resistance-r-and-a-capacitance-c-are-connected-in-series-to-a-battery-of-negli</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38920/in-an-l-c-r-circuit-shown-in-the-following-figure-what-will-be-the-readings-of-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38921/a-fully-charged-capacitor-c-with-initial-charge-q-is-connected-to-a-coil-of-self</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38922/in-a-series-lcr-circuit-r-200-and-the-voltage-and-the-frequency-of-the-main-supp</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38923/in-an-a-c-circuit-the-voltage-applied-is-e-e-t-the-resulting-current-in-the-circ</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38924/in-a-series-resonant-lcr-circuit-the-voltage-across-r-is-100-volts-and-r-1-k-wit</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38925/an-inductor-l-100-mh-a-resistor-r-100-and-a-battery-e-100-v-are-initially-connec</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38926/a-circuit-has-a-resistance-of-12-and-an-impedance-of-15-the-power-factor-of-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38927/the-phase-difference-between-the-alternating-current-and-emf-is-2-which-of-the-f</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38928/alternating-current-can-not-be-measured-by-d-c-ammeter-because</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38929/in-an-lcr-series-a-c-circuit-the-voltage-across-each-of-the-components-l-c-and-r</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38930/in-a-lcr-circuit-capacitance-is-changed-from-c-to-2-c-for-the-resonant-frequency</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38931/in-an-oscillating-lc-circuit-the-maximum-charge-on-the-capacitor-is-q-the-charge</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38932/the-core-of-any-transformer-is-laminated-so-as-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38933/a-metal-wire-of-linear-mass-density-of-9-8-g-m-is-stretched-with-a-tension-of-10</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38934/the-power-factor-of-an-a-c-circuit-having-resistance-r-and-inductance-l-connecte</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38935/in-a-transformer-number-of-turns-in-the-primary-coil-are-140-and-that-in-the-sec</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38936/the-ratio-of-momentum-of-the-photons-of-the-1-st-and-2-nd-line-of-balmer-series</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38937/in-the-hydrogen-atom-the-electron-makes-a-transition-from-the-higher-orbit-i-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38938/in-rutherford-s-alpha-particle-scattering-experiment-only-a-few-alpha-particles</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38939/using-bohr-s-model-calculate-the-ratio-of-the-magnetic-fields-generated-due-to-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38940/angular-momentum-of-an-electron-in-a-hydrogen-atom-is-3h-then-the-energy-of-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38941/two-electrons-are-moving-in-orbits-of-two-hydrogen-like-atoms-with-speeds-3-10-m</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38942/in-hydrogen-atom-spectrum-r-rydberg-s-constant-a-the-maximum-wavelength-of-the-r</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38943/the-smallest-wavelength-of-lyman-series-is-91-nm-the-difference-between-the-larg</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38944/the-energy-of-an-electron-in-an-orbit-of-the-bohr-s-atom-is-0-04-e-ev-where-e-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38945/if-an-alpha-particle-with-energy-7-7-mev-is-bombarded-on-a-thin-gold-foil-the-cl</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38946/in-a-hydrogen-like-ion-the-energy-difference-between-the-2-nd-excitation-energy</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38947/for-a-hydrogen-atom-the-ratio-of-the-largest-wavelength-of-lyman-series-to-that</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38948/considering-the-bohr-model-of-hydrogen-like-atoms-the-ratio-of-the-ratio-of-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38949/given-below-are-two-statements-one-is-labelled-as-assertion-a-and-the-other-is-l</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38950/an-electron-in-the-hydrogen-atom-initially-in-the-fourth-excited-state-makes-a-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38951/assuming-the-validity-of-bohr-s-atomic-model-for-hydrogen-like-ions-the-radius-o</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38952/considering-bohr-s-atomic-model-for-hydrogen-atom-a-the-energy-of-h-atom-in-grou</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38953/the-number-of-spectral-lines-emitted-by-atomic-hydrogen-that-is-in-the-4-th-ener</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38954/given-below-are-two-statements-one-is-labelled-as-assertion-a-and-the-other-is-l</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38955/the-frequency-of-revolution-of-the-electron-in-bohr-s-orbit-varies-with-n-the-pr</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38956/arrange-the-following-in-the-ascending-order-of-wavelength-a-microwaves-b-ultrav</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38957/during-the-transition-of-electron-from-state-a-to-state-c-of-a-bohr-atom-the-wav</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38958/a-hydrogen-atom-in-ground-state-is-given-an-energy-of-10-2-ev-how-many-spectral</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38959/in-an-alpha-particle-scattering-experiment-distance-of-closest-approach-for-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38960/the-longest-wavelength-associated-with-paschen-series-is-given-r-h-1-097-10-7-si</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38961/in-franck-hertz-experiment-the-first-dip-in-the-current-voltage-graph-for-hydrog</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38962/the-ratio-of-the-shortest-wavelength-of-balmer-series-to-the-shortest-wavelength</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38963/radius-of-a-certain-orbit-of-hydrogen-atom-is-8-48-if-energy-of-electron-in-this</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38964/the-angular-momentum-of-an-electron-in-a-hydrogen-atom-is-proportional-to-where</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38965/the-shortest-wavelength-of-the-spectral-lines-in-the-lyman-series-of-hydrogen-sp</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38966/an-electron-rotates-in-a-circle-around-a-nucleus-having-positive-charge-ze-corre</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38967/according-to-bohr-s-theory-the-moment-of-momentum-of-an-electron-revolving-in-4</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38968/a-hydrogen-atom-changes-its-state-from-n-3-to-n-2-due-to-recoil-the-percentage-c</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38969/a-particular-hydrogen-like-ion-emits-the-radiation-of-frequency-3-10-15-hz-when</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38970/the-minimum-energy-required-by-a-hydrogen-atom-in-ground-state-to-emit-radiation</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38971/the-mass-defect-in-a-particular-reaction-is-0-4-g-the-amount-of-energy-liberated</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38972/if-the-wavelength-of-the-first-member-of-lyman-series-of-hydrogen-is-the-wavelen</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38973/an-electron-revolving-in-n-th-bohr-orbit-has-magnetic-moment-n-if-n-n-x-the-valu</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38974/the-ratio-of-the-magnitude-of-the-kinetic-energy-to-the-potential-energy-of-an-e</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38975/an-electron-of-hydrogen-atom-on-an-excited-state-is-having-energy-e-n-0-85-ev-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38976/given-below-are-two-statements-statement-i-most-of-the-mass-of-the-atom-and-all</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38977/hydrogen-atom-is-bombarded-with-electrons-accelerated-through-a-potential-differ</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38978/when-a-hydrogen-atom-going-from-n-2-to-n-1-emits-a-photon-its-recoil-speed-is-x</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38979/if-rydberg-s-constant-is-r-the-longest-wavelength-of-radiation-in-paschen-series</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38980/the-radius-of-third-stationary-orbit-of-electron-for-bohr-s-atom-is-r-the-radius</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38981/as-per-given-figure-a-b-and-c-are-the-first-second-and-third-excited-energy-leve</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38982/an-atom-absorbs-a-photon-of-wavelength-500-nm-and-emits-another-photon-of-wavele</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38983/the-radius-of-2-nd-orbit-of-he-of-bohrand-39-s-model-is-r-1-and-that-of-fourth-o</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38984/a-12-5-ev-electron-beam-is-used-to-bombard-gaseous-hydrogen-at-room-temperature</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/38989/the-ratio-of-wavelength-of-spectral-lines-h-and-945-and-h-and-946-in-the-balmer</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/38991/the-radius-of-fifth-orbit-of-li-is-and-215-10-12-m-take-radius-of-hydrogen-atom</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38992/an-electron-of-a-hydrogen-like-atom-having-z-4-jumps-from-4-t-h-energy-state-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38993/nucleus-a-having-z-17-and-equal-number-of-protons-and-neutrons-has-1-2-mev-bindi</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38994/the-mass-of-proton-neutron-and-helium-nucleus-are-respectively-1-0073-u-1-0087-u</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38995/a-light-of-energy-12-75-and-160-ev-is-incident-on-a-hydrogen-atom-in-its-ground</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/38996/the-radius-of-electronand-39-s-second-stationary-orbit-in-bohrand-39-s-atom-is-r</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/38998/speed-of-an-electron-in-bohrandrsquo-s-7-th-orbit-for-hydrogen-atom-is-3-6-and-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/40624/a-two-point-charges-4-q-and-and-8211-q-are-fixed-on-the-x-axis-at-x-and-8722-d-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/40625/concentric-metallic-hollow-spheres-of-radii-r-and-4r-hold-charges-q-1-and-q-2-re</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/40626/two-isolated-conducting-spheres-s-1-and-s-2-of-radius-2-3-r-and-1-3-r-have-12-an</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/40627/a-charge-q-is-distributed-over-two-concentric-conducting-thin-spherical-shells-r</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/40628/an-electric-field-e-and-8594-4-x-i-y-2-1-j-n-c-passes-through-the-box-shown-in-f</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/40629/consider-a-sphere-of-radius-r-which-carries-a-uniform-charge-density-and-961-if</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/40630/an-electric-dipole-of-moment-p-and-8594-i-3-j-2-k-and-215-10-29-c-m-at-the-origi</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/40631/consider-two-charged-metallic-spheres-s-1-and-s-2-of-radii-r-1-and-r-2-respectiv</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/40633/in-finding-the-electric-field-using-gauss-law-the-formula-e-and-8594-q-e-n-c-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/40640/in-free-space-a-particle-a-of-charge-1-and-956-c-is-held-fixed-at-point-p-anothe</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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  <url><loc>https://www.quantrexacademy.com/q/40740/in-an-experiment-a-set-of-reading-are-obtained-as-follows-1-24-mm-1-25-mm-1-23-m</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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