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  <url><loc>https://www.quantrexacademy.com/q/104799/which-of-the-following-figure-represents-the-variation-of-ln-r-r-0-with-ln-a-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/104803/assertion-for-the-scattering-of-particles-at-a-large-angles-only-the-nucleus-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/104805/assertion-hydrogen-atom-consists-of-only-one-electron-but-its-emission-spectrum</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/104814/consider-the-following-statements-about-the-photoelectric-effect-1-the-photoelec</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/104815/match-the-following-array-c-c-c-c-and-list-i-and-and-list-ii-1-and-burning-candl</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/104818/match-the-column-i-with-column-ii-array-l-l-l-l-and-column-i-radiation-and-and-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/104820/what-is-the-distance-of-closest-approach-to-the-nucleus-of-a-7-7-mev-alpha-parti</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/117125/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>
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  <url><loc>https://www.quantrexacademy.com/q/117127/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/117128/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>
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  <url><loc>https://www.quantrexacademy.com/q/117130/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>
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  <url><loc>https://www.quantrexacademy.com/q/117132/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>
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  <url><loc>https://www.quantrexacademy.com/q/117140/in-acidic-medium-which-of-the-following-becomes-colourless</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/117148/assertion-k-cr-o-is-used-as-primary-standard-in-volumetric-analysis-reason-it-ha</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/117149/assertion-change-in-colour-of-acidic-solution-of-potassium-dichromate-by-breath</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/117155/when-calomel-is-treated-with-ammonium-hydroxide-a-black-substance-is-formed-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/117165/assertion-reduction-potential-of-mn-3-to-2-is-more-positive-than-fe-3-to-2-reaso</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/117170/assertion-the-degree-of-complex-formation-in-actinides-decreases-in-the-order-m</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/117173/assertion-magnetic-moment-of-dy-is-the-highest-among-the-lanthanoids-reason-orbi</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/117174/assertion-k-cr-o-is-used-as-primary-standard-in-volumetric-analysis-reason-it-ha</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/117176/assertion-change-in-colour-of-acidic-solution-of-potassium-dichromate-by-breath</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/117177/among-the-following-pairs-of-ions-the-lower-oxidation-state-in-aqueous-solution</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/117181/assertion-solution-of-na-cro-in-water-is-coloured-reason-oxidation-state-of-cr-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/117184/if-m-is-element-of-actinoids-series-the-degree-of-complex-formation-decreases-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/118296/the-correct-order-of-increasing-reactivity-of-c-x-bond-towards-nucleophile-in-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/118297/the-reaction-of-toluene-with-cl-in-presence-of-fecl-gives-x-and-reaction-in-pres</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/118303/propionic-acid-with-br-p-yields-a-dibromo-product-its-structure-would-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/118306/for-the-gas-phase-reaction-pcl-g-pcl-g-cl-g-which-of-the-following-conditions-ar</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/118307/in-a-s-n-2-substitution-reaction-of-the-type-r-br-cl-omf-r-cl-br-which-one-of-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/118308/which-of-the-following-undergoes-nucleophilic-substitution-exclusively-by-s-n-1</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/118310/correct-order-for-reaction-with-alcoholic-koh-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/118312/the-correct-order-of-reactivity-in-s-n-1-reaction-for-the-following-compounds-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/118314/the-decreasing-order-of-s-n-2-reaction-for-the-given-compounds-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/118315/decreasing-order-of-reactivity-in-williamson-synthesis-of-the-following-i-me-cch</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/118316/assertion-chlorobenzene-is-more-reactive-than-benzene-towards-the-electrophilic</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/118317/arrange-the-given-compounds-in-decreasing-order-of-boiling-points</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/118318/what-happens-when-chloroform-is-left-open-in-air-in-the-presence-of-sunlight</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/118319/which-one-of-the-following-forms-propanenitrile-as-the-major-product</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/118320/which-of-the-following-does-not-give-nitroalkane</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/118321/phch-cl-aq-nacn-catalytic-hydrogenation-the-final-product-u-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/118322/an-aromatic-compound-c-h-cl-a-gives-agcl-on-boiling-with-alcoholic-agno-solution</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/118323/assertion-rate-of-reaction-of-alkyl-halide-in-williamson-s-synthesis-reaction-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/118324/assertion-reason-it-follows-with-formation-of-more-stable-carbocation</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/118325/2-phenylethylbromide-when-heated-with-naoet-elimination-takes-place-no-deuterium</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/118326/assertion-c-h-br-reacts-with-alcoholic-solution-of-agno-to-form-nitroethane-as-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/118327/which-of-these-compounds-is-synthesised-by-chloral</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/118328/assertion-chloral-reacts-with-phenyl-chloride-to-form-ddt-reason-it-is-an-electr</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/118329/assertion-alkyl-iodide-can-be-prepared-by-treating-alkyl-chloride-bromide-with-n</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/118330/the-major-product-obtained-on-the-monobromination-with-br-febr-of-the-following</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/118332/the-correct-increasing-order-of-the-reactivity-of-halides-for-s-n-1-reaction-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/118333/the-major-product-formed-in-the-following-reaction-is-ch-ch-cl-ch-ch-oh-aq-koh</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/118334/assertion-the-presence-of-nitro-group-facilitates-nucleophilic-substitution-reac</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/118335/3-phenylpropene-on-reaction-with-hbr-gives-as-a-major-product</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/118336/assertion-rate-of-hydrolysis-of-methyl-chloride-to-methanol-is-higher-in-dmf-tha</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/118337/assertion-benzyl-bromide-when-kept-in-acetone-water-it-produces-benzyl-alcohol-r</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/118338/which-of-the-following-is-involved-in-sandmeyer-s-reaction</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/118339/ch-ch-ch-br-alc-koh-final-product-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/118340/which-of-the-following-is-not-correct</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/118342/the-reaction-c-h-oh-socl-pyridine-c-h-cl-so-hcl-is-known-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/118344/when-2-methyl-butyl-bromide-is-treated-with-sodium-ethoxide-in-ethanol-what-will</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/118346/r-ch-ch-oh-can-be-converted-into-r-ch-ch-cooh-by-the-following-sequence-of-steps</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/118348/which-one-of-the-following-does-not-undergo-iodoform-reaction</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/118349/the-above-reaction-is-known-as</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/118350/in-electrophilic-aromatic-substitution-reaction-the-nitro-group-is-meta-directin</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/118351/the-best-method-for-the-conversion-of-an-alcohol-into-an-alkyl-chloride-is-by-tr</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/118353/iodoform-gives-a-precipitate-with-agno-on-heating-but-chloroform-does-not-becaus</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/118355/which-rule-dictates-the-regioselectivity-of-the-addition-reaction-of-unsymmetric</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/118356/what-electrophile-reacts-with-the-phenoxide-ion-to-form-ortho-hydroxybenzoic-aci</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/118357/which-of-the-following-alcohols-is-most-likely-to-undergo-dehydrogenation-to-for</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/119309/choose-the-correct-sequence-of-reagents-in-the-conversion-of-4-nitrotoluene-to-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/119313/which-of-the-following-reactions-is-not-an-example-for-nucleophilic-addition-eli</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119314/match-list-i-with-list-ii-list-i-products-formed-list-ii-reaction-of-carbonyl-co</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119315/which-one-of-the-following-is-not-formed-when-acetone-reacts-with-2-pentanone-in</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119316/match-list-i-with-list-ii-list-i-list-ii-a-i-hell-volhard-zelinsky-reaction-b-ii</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/119319/identify-compound-x-in-the-following-sequence-of-reactions</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119320/reaction-between-benzaldehyde-and-acetophenone-in-presence-of-dilute-naoh-is-kno</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119321/when-vapours-of-a-secondary-alcohol-is-passed-over-heated-copper-at-573-k-the-pr</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119322/the-compound-a-and-160-c-8-h-10-o-is-found-to-react-with-n-a-o-i-produced-by-rea</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119323/of-the-following-which-is-the-product-formed-when-cyclohexanone-undergoes-aldol</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119324/consider-the-reactions-identify-a-x-y-and-z</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119325/the-correct-structure-of-the-product-a-formed-in-the-reaction-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119326/the-product-formed-by-the-reaction-of-an-aldehyde-with-a-primary-amine-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119327/reaction-of-a-carbonyl-compound-with-one-of-the-following-reagents-involves-nucl</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119328/a-single-compound-of-the-structure-is-obtainable-from-ozonolysis-of-which-of-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119329/treatment-of-cyclopentanone-with-methyl-lithium-gives-which-of-the-following-spe</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119330/an-organic-compound-and-39-xand-39-having-molecular-formula-c-5-h-10-o-yields-ph</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119331/which-one-is-most-reactive-towards-nucleophilic-addition-reaction</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119332/on-hydrolysis-of-a-compound-two-compounds-are-obtained-one-of-which-on-treatment</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119333/number-of-isomeric-alcohols-of-molecular-formula-c-h-o-which-give-positive-iodof</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119334/reaction-by-which-benzaldehyde-cannot-be-prepared</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119335/predict-the-products-in-the-given-reaction</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119336/acetone-is-treated-with-excess-of-ethanol-in-the-presence-of-hydrochloric-acid-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119337/ch-cho-and-c-h-ch-cho-can-be-distinguished-chemically-by</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119338/consider-the-following-reaction-the-product-a-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119339/consider-the-reaction-r-cho-nh-nh-rch-n-nh-what-sort-of-reaction-is-it</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119340/which-of-the-following-compounds-will-give-a-yellow-precipitate-with-iodine-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119341/the-order-of-reactivity-of-phenyl-magnesium-bromide-phmgbr-with-the-following-co</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119342/match-the-compounds-given-in-list-i-with-list-ii-and-select-the-suitable-option</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119343/among-the-given-compounds-the-most-susceptible-to-nucleophilic-attack-at-the-car</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119344/which-of-the-following-reactions-will-not-result-in-the-formation-of-carbon-carb</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119345/following-compounds-are-given-a-ch-ch-oh-b-ch-coch-c-d-ch-oh-which-of-the-above</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119346/h-coh-ch-oh-on-heating-with-periodic-acid-gives</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119347/equal-volumes-of-three-acid-solutions-of-ph-3-4-and-5-are-mixed-in-a-vessel-what</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119348/in-a-reaction-of-aniline-a-coloured-product-c-was-obtained-ext-the-structure-of</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119349/a-strong-base-an-abstract-an-hydrogen-from</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119350/acetophenone-when-reacted-with-a-base-c-h-ona-yields-a-stable-compound-which-has</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119351/which-one-of-the-following-on-treatment-with-50-aqueous-sodium-hydroxide-yields</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119352/the-product-formed-in-aldol-condensation-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119353/nucleophilic-addition-reaction-will-be-most-favoured-in</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119354/a-carbonyl-compound-reacts-with-hydrogen-cyanide-to-form-cyanohydrine-which-on-h</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119355/which-one-of-the-following-can-be-oxidised-to-the-corresponding-carbonyl-compoun</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119356/which-one-of-the-following-will-not-form-a-yellow-precipitate-on-heating-with-an</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119357/a-and-b-in-the-following-reactions-are</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119358/when-m-chlorobenzaldehyde-is-treated-with-50-koh-solution-the-products-s-obtaine</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119359/in-the-following-reaction-product-p-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119360/for-the-following-compounds-2-c-h-cho-3-p-ch-c-h-cho-4-p-ch-o-c-h-cho-the-correc</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119362/c-h-o-a-reacts-with-ch-mgbr-to-give-a-compound-c-h-o-which-gives-the-iodoform-te</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119363/find-out-the-products-of-the-reaction</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119364/identify-structure-of-p-and-q</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119365/in-the-reaction-the-product-s-is-are</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119366/find-the-end-product-of-the-following-reaction</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119367/give-the-correct-sequence-of-reagents-used-for-the-following-conversion</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119368/number-of-stereoisomers-formed-in-the-given-reaction-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119369/final-product-of-the-given-reaction-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119370/the-final-product-of-the-given-reaction-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119371/what-is-the-name-of-the-following-reaction-phcho-ch-co-o-na-oac-phch-chco-h</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119372/benzaldehyde-can-be-prepared-from</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119373/ease-of-nucleophilic-addition-in-the-given-compounds-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119374/the-major-organic-product-formed-in-the-following-reaction</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119375/the-following-conversion-is-known-as</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119376/arrange-the-following-compounds-in-increasingorder-of-reactivity-towards-nucleop</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119377/assertion-mixture-of-benzaldehyde-and-acetaldehyde-in-hot-alkaline-medium-gives</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119378/compound-a-molecular-formula-c-h-o-is-treated-with-acidified-potassium-dichromat</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119379/assertion-aldol-condensation-can-be-catalysed-both-by-acids-and-bases-reason-hyd</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119380/in-oppenauer-s-oxidation</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119381/in-the-following-sequence-of-the-reactions-identify-the-final-product</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119382/assertion-p-n-n-dimethylaminobenzaldehyde-undergoes-benzoin-condensation-reason</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119383/toluene-on-treatment-with-cro-and-ch-co-o-followed-by-hydrolysis-with-dil-hcl-gi</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119384/identify-the-final-product</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119385/assertion-ch-ccoc-ch-and-acetone-can-be-distinguished-by-the-reaction-with-nahso</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119386/the-reagent-used-for-the-separation-of-acetaldehyde-from-acetophenone-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119387/the-most-suitable-reagent-for-the-conversion-of-r-ch-oh-r-cho-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119388/assertion-isobutanal-does-not-give-iodoform-test-reason-it-does-not-have-hydroge</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119389/at-higher-temperature-iodoform-reaction-is-given-by</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119390/assertion-hydroxyketones-are-not-directly-used-in-grignard-reaction-reason-grign</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119391/in-the-reaction-c-h-cho-c-h-nh-c-h-n-hcc-h-h-o-the-compound-c-h-n-hcc-h-is-known</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/119392/aligned-ch-ch-cho-ch-and-ch-and-ch-oh-aligned-suitable-reagent-for-conversion-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/119396/the-product-of-acid-hydrolysis-of-p-and-q-can-be-distinguished-by</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/128621/a-patient-presents-with-acute-weakness-fatigue-and-altered-carbohydrate-metaboli</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/128622/read-the-following-descriptions-of-two-hormones-and-identify-them-hormone-x-is-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/128623/assertion-type-i-diabetes-is-caused-by-destruction-of-cells-of-islets-of-langerh</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/128625/assertion-insulin-forms-hormone-receptor-complex-which-regulates-the-formation-o</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/128626/oxytocin-and-adh-are-produced-by-hypothalamus-and-released-from</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/128627/conn-s-disease-is-caused-by-the-oversecretion-of</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/128628/assertion-adrenocorticotropic-releasing-hormones-arh-excite-the-anterior-lobe-of</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/128629/assertion-pituitary-is-attached-to-hypothalamus-by-a-vein-reason-this-attachment</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/128630/a-patient-of-diabetes-mellitus-excretes-glucose-in-urine-even-when-he-is-kept-on</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/128631/according-to-the-accepted-concept-of-hormone-action-if-receptor-molecules-are-re</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/128632/assertion-adh-and-raas-work-in-response-to-low-blood-volume-and-blood-pressure-r</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/128633/gonadotropin-releasing-hormone-is-transferred-to-anterior-pituitary-by</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/128634/select-the-correct-statement-about-hormones-and-their-actions</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/128635/which-of-the-following-pairs-of-hormones-can-easily-pass-through-the-cell-membra</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/128636/assertion-adrenocorticotropic-releasing-hormones-arh-excite-the-anterior-lobe-of</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/128637/match-the-source-gland-with-its-respective-hormone-and-function-and-select-the-c</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/128638/catecholamine-in-a-normal-person-induces</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/128639/assertion-less-iodine-intake-causes-goitre-reason-less-iodine-in-body-decreases</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/128640/assertion-a-male-is-found-to-be-lacking-facial-hair-and-pubic-hair-reason-it-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/128641/assertion-oxytocin-is-also-known-as-antidiuretic-hormone-adh-reason-oxytocin-can</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/128643/assertion-adrenaline-is-called-an-emergency-hormone-reason-it-acts-on-the-cells</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/128644/assertion-insulin-is-antagonistic-to-glucagon-reason-it-is-an-anabolic-hormone</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/128645/assertion-hormone-calcitonin-has-antagonistic-effect-to-that-of-parathormone-rea</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/128646/assertion-mammary-glands-are-apocrine-glands-reason-the-distal-part-containing-s</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/128648/assertion-pituitary-is-attached-to-hypothalamus-by-a-vein-reason-this-attachment</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/128649/which-of-the-following-statements-regarding-glucagon-is-false</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/128650/assertion-aldosterone-is-a-steroid-hormone-and-is-important-in-the-control-of-so</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/128651/tadpoles-of-frog-can-be-made-to-grow-as-giant-sized-tadpoles-if-they-are</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/128652/assertion-our-body-secretes-adrenaline-in-intense-cold-reason-adrenaline-raises</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/128653/which-one-of-the-following-four-secretions-is-correctly-matched-with-its-source</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/128654/which-one-of-the-following-four-glands-is-correctly-matched-with-the-accompanyin</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/128655/assertion-diabetes-insipidus-is-marked-by-excessive-urination-and-too-much-thirs</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/128656/a-person-passes-much-urine-and-drinks-much-water-but-his-blood-glucose-level-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/128657/sella-turcica-is-found</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/128668/which-one-of-the-following-hormones-is-released-by-posterior-lobe-of-pituitary-g</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/128672/endemic-goitre-is-a-state-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/86282/the-three-thermodynamic-states-p-q-and-r-of-a-system-are-connected-by-the-paths</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86283/a-monoatomic-ideal-gas-kept-in-a-vessel-fitted-with-a-piston-is-expanded-irrever</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86284/consider-the-equations-y-x-3-x-2-3-x-4-and-y-x-2-x-4-r-the-number-of-values-of-f</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86285/let-g-r-r-be-a-differentiable-function-such-that-g-x-g-x-0-for-all-x-r-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86286/let-f-r-r-be-a-nonconstant-differentiable-function-such-that-x-f-x-1-and-x-f-x-f</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86287/a-continuous-function-f-r-r-is-said-to-be-good-if-given-a-b-r-a-b-the-line-segme</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86288/for-a-b-r-with-a-0-let-n-a-b-denote-the-number-of-elements-in-the-set-x-r-x-a-x</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86289/let-f-x-x-2023-x-2023-for-all-x-0-then-the-number-of-points-at-which-the-graph-o</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86290/let-f-0-3-6-9-r-be-a-differentiable-function-such-that-f-x-1-2-for-all-x-0-3-6-9</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86291/let-f-be-a-twice-differentiable-function-on-r-such-that-f-0-1-f-1-2-f-0-1-f-1-5</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86292/let-f-r-r-be-a-differentiable-function-such-that-x-f-x-x-0-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86293/let-positive-real-numbers-x-and-y-be-such-that-3-x-4-y-14-the-maximum-value-of-x</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86294/let-f-0-r-be-a-function-defined-as-f-x-x-e-x-1-x-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86295/the-number-of-real-solutions-of-e-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/86296/consider-a-function-f-x-x-1-x-defined-over-positive-real-numbers-which-of-the-fo</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86297/let-x-y-be-points-on-the-same-side-of-a-straight-line-in-a-plane-suppose-p-is-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86298/let-f-x-x-e-x-and-g-x-x-e-x-be-two-functions-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86299/let-f-be-the-function-on-r-defined-by-f-x-x-3-3-x-2-a-x-1-where-a-r-then-the-set</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86300/let-a-and-b-be-non-negative-real-numbers-satisfying-a-2-b-2-4-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/86301/let-p-be-a-polynomial-whose-coefficients-are-real-numbers-suppose-the-roots-of-p</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86302/the-number-of-solutions-of-e-x-x-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86303/for-a-given-positive-integer-n-let-f-0-r-be-defined-as-f-x-x-n-x-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86304/let-r-be-the-set-of-all-real-numbers-and-f-r-r-be-a-differentiable-function-sati</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86305/the-set-of-all-real-numbers-x-0-2-on-which-the-function-x-2-x-is-strictly-increa</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86306/a-right-circular-conical-glass-bottle-with-a-base-radius-r-and-height-h-contains</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86307/a-cylindrical-tank-of-height-3-units-and-diameter-2-units-resting-on-its-base-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86308/in-the-figure-pqrs-is-a-square-of-side-length-12-and-xpq-is-a-traingle-construct</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86309/let-a-b-c-be-an-equilateral-triangle-with-each-side-being-of-length-equal-to-2-w</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86310/let-a-b-c-d-be-a-square-with-sides-of-unit-length-let-p-and-q-be-the-points-in-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86311/let-abcd-be-a-square-inscribed-in-a-circle-of-unit-radius-let-e-be-the-point-on</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86312/let-c-x-y-x-y-1-c-x-y-x-2-y-2-1-and-c-x-y-x-y-1-be-three-regions-in-x-y-plane-if</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86313/let-r-be-the-equivalence-relation-on-n-1-n-n-n-2-defined-by-for-m-n-n-1-m-r-n-if</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86314/let-s-x-y-n-n-x-2-y-2-2022-then-the-number-of-elements-in-s-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86315/a-pair-of-positive-integers-m-n-is-said-to-be-a-happy-pair-if-gcd-m-n-is-a-perfe</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86317/let-a-b-c-be-real-numbers-each-greater-than-1-and-let-2-3-b-a-3-5-c-b-5-2-a-c-3</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86318/let-s-be-the-set-of-integers-n-such-that-1-n-1000-and-can-be-written-as-n-3-x-5</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86319/let-n-be-the-m-bius-function-defined-for-positive-integers-by-n-cases-1-and-if-n</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86320/the-number-of-pairs-x-y-of-rational-numbers-such-that-x-y-x-y-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86321/for-any-real-number-x-x-denotes-the-largest-integer-less-than-or-equal-to-x-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86322/for-three-arbitrary-real-numbers-r-s-t-the-mathematical-identity-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86323/for-any-real-number-x-let-x-denote-the-largest-integer-less-than-or-equal-to-x-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86324/the-greatest-common-divisor-of-n-2-4-n-3-and-2-n-6-where-n-is-any-natural-number</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86325/for-a-b-0-1-9-a-two-digit-number-a-b-is-defined-for-10-a-b-a-two-digit-number-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86326/if-x-y-are-positive-real-numbers-such-that-x-x-36-and-y-y-71-then-x-y-equals</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86327/the-number-of-two-digit-positive-integers-divisible-by-both-their-digits-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86328/for-a-positive-integer-m-let-m-denote-the-sum-of-positive-divisors-of-m-and-m-de</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86329/let-p-and-q-be-distinct-primes-then-the-number-of-positive-integer-solutions-of</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86330/let-a-2-b-22-and-c-20-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86331/the-number-of-terms-that-are-integers-in-the-binomial-expansion-of-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/86332/let-n-n-and-let-f-x-x-n-for-all-x-in-r-then-f-1-f-1-1-1-f-2-1-2-f-n-1-n-is-equal</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86333/suppose-the-coefficient-of-x-7-in-a-x-2-1-b-x-is-equal-to-the-coefficient-of-x-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86334/let-s-and-s-be-two-circles-drawn-inside-a-unit-square-abcd-touching-each-other-e</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86335/let-a-and-b-be-two-fixed-points-on-a-fixed-straight-line-two-circles-touch-this</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86336/let-a-b-c-d-be-a-square-with-each-side-of-length-1-let-c-c-c-be-circles-inside-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86337/let-c-and-c-be-two-circles-with-positive-radii-such-that-the-distance-between-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86338/the-ratio-of-the-perimeter-and-the-diameter-of-a-circle-is-always</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86339/for-a-positive-integer-k-let-p-k-be-the-parabola-given-by-y-x-2-k-5-and-let-c-be</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86340/let-p-and-q-be-the-points-of-intersection-of-the-circles-c-x-2-y-2-2-x-y-0-and-c</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86341/let-c-c-and-c-be-three-circles-having-the-same-radius-r-which-touch-each-other-e</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86342/let-p-be-an-interior-point-of-a-circle-c-different-from-its-center-the-locus-of</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86343/a-circle-s-with-centre-at-c-and-radius-r-touches-another-circle-s-with-centre-at</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86344/let-an-acute-angled-triangle-a-b-c-be-inscribed-in-a-circle-whose-centre-is-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86345/let-a-b-be-the-diameter-of-a-circle-with-radius-1-centred-at-the-point-o-let-c-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86346/let-c-be-the-set-of-all-complex-numbers-let-p-z-c-z-1-and-q-z-c-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/86347/the-real-and-imaginary-part-of-the-complex-number-1-i-where-i-1-are</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86348/let-z-a-i-b-and-z-c-i-d-be-complex-numbers-such-that-z-z-1-and-re-z-z-0-then-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86349/let-and-be-two-nonzero-complex-numbers-for-z-c-z-denotes-the-complex-conjugate-o</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86350/let-s-k-z-c-z-2-z-k-for-each-k-z-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86351/for-a-complex-number-z-x-iy-where-x-y-r-denote-z-y-ix-the-locus-of-z-satisfying</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86352/let-z-z-and-z-be-three-distinct-complex-numbers-if-z-2-z-2-z-2-z-z-z-z-z-z-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86353/for-n-n-a-complex-number-is-called-an-n-th-root-of-unity-if-n-1-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86354/let-x-z-z-z-1-1-be-a-subset-of-complex-numbers-then-in-the-complex-plane-x-repre</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86355/if-is-a-complex-cube-root-of-unity-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86356/let-c-be-the-set-of-all-complex-numbers-consider-the-function-h-c-c-defined-by-h</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86357/let-be-the-complex-cube-root-of-unity-consider-the-set-e-a-b-c-r-3-det-array-ccc</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86358/if-1-1-i-t-e-i-where-t-r-and-0-2-then-the-value-of-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86359/let-be-a-cube-root-of-1-which-is-different-from-1-then-the-value-of-1-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86360/let-w-be-a-complex-number-such-that-w-5-1-but-w-1-then-1-w-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/86361/let-s-x-c-x-1-1-if-z-is-an-element-of-s-with-argument-6-then-the-argument-of-z-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/89400/100-ml-of-o-2-g-effuse-from-a-porous-container-in-100-sec-75-ml-of-unknown-gas-e</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/89401/which-of-the-following-curve-is-correct-for-a-given-amount-of-an-ideal-gas-at-co</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/89402/at-what-temperature-would-n-2-molecules-have-same-average-speed-as-c-o-molecules</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/89405/an-air-column-closed-in-a-tube-sealed-at-one-end-by-a-h-g-column-having-height-h</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/89406/the-relative-humidity-of-air-is-80-at-27-o-c-if-the-aqueous-tension-at-the-same</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/89409/the-rms-speed-of-n-2-molecules-in-a-gas-is-u-if-the-temperature-is-doubled-and-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/89410/two-van-der-waal-s-gases-have-same-value-of-a-but-different-value-of-b-which-of</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/89411/c-o-2-gas-is-liquefied-at-27-o-c-gas-follows-the-following-graph-during-liquefac</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/89412/which-of-the-following-sketches-is-an-isobars-given-nr-p-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/89413/the-van-der-waals-equation-for-one-mole-of-a-real-gas-can-be-written-as-p-a-v-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/89414/if-density-of-vapours-of-a-substance-of-molar-mass-18-gm-mole-at-1-atm-pressure</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/89415/to-an-evacuated-vessel-with-movable-piston-under-external-pressure-of-1-atm-0-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/89416/for-one-mole-of-a-van-der-waals-gas-when-b-0-and-t-300-k-the-pv-vs-1-v-plot-is-s</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/89417/the-density-of-o-2-is-16-at-ntp-at-what-temperature-in-o-c-its-density-will-be-1</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/89419/at-what-temperature-in-kelvin-is-the-rms-speed-of-hydrogen-molecules-the-same-as</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/89420/the-diffusion-coefficient-of-an-ideal-gas-is-proportional-to-its-mean-free-path</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/89421/calculate-the-number-of-hours-of-service-that-can-be-derived-at-1-atm-300-k-from</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/89422/two-closed-bulbs-of-equal-volume-v-containing-an-ideal-gas-initially-at-pressure</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/89423/one-mole-of-a-monoatomic-real-gas-satisfies-the-equation-p-v-b-rt-where-b-is-a-c</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/89424/one-mole-of-n-2-o-4-g-at-300-k-is-kept-in-a-closed-container-under-one-atmospher</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/89425/the-volume-temperature-graphs-of-a-given-mass-of-an-ideal-gas-at-constant-pressu</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/89429/to-an-evacuated-vessel-with-movable-piston-under-external-pressure-of-1-atm-0-1</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/89459/the-root-mean-square-speed-of-n-2-molecules-in-sample-at-temperature-t-is-x-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/90042/consider-a-family-of-circles-passing-through-two-fixed-points-a-3-7-and-b-6-5-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/90044/the-foot-of-the-normal-from-the-point-4-3-to-a-circle-is-2-1-and-a-diameter-of-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90045/the-number-of-rational-point-s-a-point-a-b-is-rational-if-a-and-b-both-are-ratio</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90046/a-circle-touches-the-hypotenuse-of-a-right-angled-triangle-at-its-midpoint-and-p</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90047/a-circle-of-radius-2-units-is-touching-both-the-axes-and-a-circle-with-centre-at</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90048/the-locus-of-the-centre-of-a-circle-which-cuts-the-circle-x-2-20-x-y-2-4-0-ortho</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90049/let-c-1-x-2-y-2-5-and-c-2-x-2-y-2-9-the-tangent-at-1-2-to-c-1-meets-the-circle-c</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90050/the-tangents-to-x-2-y-2-a-2-having-inclinations-and-945-and-and-946-intersect-at</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90051/the-value-of-for-which-the-set-x-y-x-2-y-2-6-x-4-y-12-x-y-4-x-3-y-contains-only</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90052/total-number-of-lines-touching-atleast-two-circles-of-the-family-of-four-circles</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90053/lines-l-1-and-l-2-are-rotating-in-an-anticlockwise-direction-about-the-points-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90054/from-a-point-p-3-3-on-the-circle-x-2-y-2-18-two-chords-p-q-and-p-r-each-of-2-uni</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90055/let-a-0-3-and-b-0-12-be-two-vertices-of-a-a-b-c-where-c-x-0-if-the-circumcircle</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90056/equation-of-the-straight-line-which-meets-the-circle-x-2-y-2-8-at-two-points-whe</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90057/the-centre-of-the-circle-passing-through-the-points-of-intersection-of-the-curve</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90058/let-two-circles-having-radii-r-1-and-r-2-are-orthogonal-to-each-other-if-the-len</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90059/consider-circles-c-1-and-c-2-touching-both-the-axes-and-passing-through-4-4-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90060/in-the-figure-p-q-and-160-p-o-1-and-o-1-q-are-the-diameters-of-semicircles-c-1-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90061/let-p-and-q-be-the-length-of-two-chords-of-a-circle-which-subtend-angles-3-6-o-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90062/the-equation-of-the-chord-a-b-of-the-circle-x-2-y-2-2-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/90063/a-pair-of-tangents-are-drawn-from-a-point-p-to-the-circle-x-2-y-2-1-if-the-tange</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90064/tangents-are-drawn-to-the-circle-x-2-y-2-16-at-the-points-where-it-intersects-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90065/let-p-q-and-r-s-be-the-tangents-at-the-extremities-of-the-diameter-p-r-of-a-circ</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90066/let-c-1-and-c-2-be-two-circles-of-radius-r-1-and-r-2-respectively-r-1-r-2-touchi</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90067/if-the-radius-of-the-circle-passing-through-the-origin-and-touching-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/90068/the-radius-of-the-circle-touching-the-line-x-y-4-at-1-3-and-intersecting-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/90069/the-centres-of-two-circles-c-1-and-c-2-each-of-unit-radius-are-at-a-distance-of</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90070/if-the-length-of-direct-common-tangent-and-transverse-common-tangent-of-two-circ</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90071/line-l-1-3-x-4-y-1-0-touches-the-circles-c-1-and-c-2-centres-of-c-1-and-c-2-are</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90072/let-the-points-a-0-a-b-2-0-and-c-1-1-form-an-obtuse-angled-triangle-obtuse-angle</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90073/let-a-be-an-ordered-pair-of-real-numbers-satisfying-the-equation-x-2-4-x-4-y-2-3</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90074/the-perimeter-of-the-locus-of-the-point-at-which-the-two-circles-x-2-y-2-1-and-x</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90075/the-lengths-of-the-tangents-from-any-point-on-the-circle-x-2-y-2-8-x-1-0-to-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90076/the-angle-between-the-chords-of-the-circle-x-2-y-2-100-which-passes-through-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90077/which-of-the-following-equations-of-a-line-intercepts-on-the-circle-x-2-y-2-6-x</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90078/if-the-lengths-of-the-tangents-from-p-1-3-and-q-3-7-to-a-circle-are-2-units-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90079/the-possible-number-of-values-of-a-for-which-the-common-chord-of-the-circles-x-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90080/from-the-point-a-0-3-on-the-circle-x-2-9-x-y-3-2-0-a-chord-a-b-is-drawn-and-exte</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90081/let-a-be-the-centre-of-the-circle-x-2-y-2-2-x-4-y-20-0-if-the-tangents-at-the-po</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90082/if-4-x-3-y-12-0-touches-x-p-2-y-p-2-p-2-then-the-sum-of-all-the-possible-values</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90083/if-the-circles-x-2-y-2-10-x-16-y-89-r-2-0-and-x-2-y-2-6-x-14-y-42-0-have-common</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90084/the-locus-of-the-point-of-intersection-of-the-tangents-at-the-extremities-of-a-c</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90085/the-equation-of-the-circle-which-passes-through-the-points-a-0-5-and-b-6-1-and-w</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90086/let-four-circles-having-radii-r-1-5-units-r-2-5-units-r-3-8-units-and-r-4-units</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90087/let-the-vertices-of-a-triangle-are-a-3-2-sin-4-2-cos-b-3-2-cos-4-2-sin-and-c-3-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90088/the-point-at-which-the-line-segment-joining-a-1-1-and-b-5-5-subtends-an-obtuse-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90089/the-coordinates-of-a-point-p-on-the-line-x-y-13-0-nearest-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/90090/number-of-common-points-to-the-curves-c-1-1-2-cos-2-sin-and-c-2-4-3-sin-3-cos-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90091/the-tangent-to-the-circle-x-2-y-2-5-at-the-point-1-2-also-touches-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/90092/let-circles-c-1-c-2-and-c-3-with-centres-o-1-o-2-and-o-3-respectively-touch-each</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90093/let-the-lines-4-x-3-y-10-0-and-4-x-3-y-30-0-make-equal-intercepts-of-6-units-wit</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90094/the-lines-joining-the-origin-to-the-points-of-intersection-of-the-line-4-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/90095/the-equation-of-the-circle-whose-radius-is-5-units-and-which-touches-the-circle</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/90097/if-the-chord-of-contact-of-the-tangents-from-the-point-to-the-circle-x-2-y-2-r-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90098/the-number-of-common-tangents-to-the-circles-x-2-y-2-2-x-8-y-23-0-and-x-2-y-2-4</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90099/let-a-b-c-d-be-a-quadrilateral-in-which-a-b-is-parallel-to-c-d-a-b-is-perpendicu</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90100/the-line-2-x-y-1-0-touches-a-circle-at-the-point-2-5-and-the-centre-of-the-circl</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90101/a-point-p-moves-such-that-the-chord-of-contact-of-p-with-respect-to-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/90103/locus-of-the-mid-points-of-the-chords-of-contact-of-x-2-y-2-2-from-the-points-on</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90104/suppose-the-family-of-lines-a-x-b-y-c-0-where-a-b-c-are-in-arithmetic-progressio</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/90106/a-circle-is-drawn-whose-centre-is-on-the-x-a-x-i-s-and-it-touches-the-y-a-x-i-s</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90107/a-b-c-is-a-right-triangle-right-angled-at-the-vertex-a-a-circle-is-drawn-to-touc</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/90109/the-length-of-the-radius-of-the-circle-which-touches-the-x-axis-at-the-point-1-0</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90110/if-m-and-m-are-the-maximum-and-minimum-values-of-y-x-for-pair-of-real-numbers-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/90112/if-the-circles-x-3-2-y-4-4-16-and-x-7-2-y-7-2-9-intersect-at-points-a-and-b-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90113/a-straight-line-l-1-with-equation-x-2-y-10-0-meets-the-circle-with-equation-x-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90114/if-the-minimum-distance-of-the-point-sec-cosec-from-the-circle-x-2-y-2-3-can-be</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90115/from-a-point-p-3-3-on-the-circle-x-2-y-2-18-two-chords-p-q-and-p-r-each-of-lengt</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/90117/consider-circles-c-1-and-c-2-touching-both-the-axes-and-passing-through-4-4-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90118/the-sum-of-all-the-values-of-for-which-the-set-x-y-x-2-y-2-6-x-4-y-12-x-y-4-x-3</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90119/let-c-1-and-c-2-be-two-circles-of-radius-r-1-and-r-2-units-respectively-touching</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90120/the-sum-of-the-slopes-of-all-possible-chords-of-the-circle-x-2-y-2-100-which-pas</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90121/the-area-in-sq-units-of-the-circle-touching-the-line-x-y-4-at-1-3-and-intersecti</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90122/the-line-l-1-and-8801-3-x-4-y-1-0-touches-the-circles-c-1-and-c-2-centers-of-c-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90123/if-the-points-a-0-a-b-2-0-and-c-1-1-form-an-obtuse-angle-triangle-obtuse-angled</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90124/from-the-point-a-0-3-on-the-circle-x-2-4-x-y-3-2-0-a-chord-a-b-is-drawn-and-exte</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90125/tangents-are-drawn-to-a-unit-circle-with-centre-at-the-origin-from-each-point-on</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90126/two-circles-with-centers-at-a-and-b-touch-each-other-externally-at-t-let-bd-is-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90127/the-two-circles-x-2-y-2-a-x-and-x-2-y-2-c-2-c-0-touch-each-other-if-c-a-is-equal</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90128/let-the-lines-y-2-m-1-x-5-and-y-4-m-2-x-3-intersect-at-right-angles-at-p-where-m</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90129/let-p-and-q-be-2-circles-externally-touching-each-other-at-point-x-line-segment</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90130/if-the-circle-x-2-y-2-4-x-8-y-5-intersects-the-line-3-x-4-y-m-at-two-distinct-po</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90131/let-the-point-at-which-the-circle-passing-through-0-0-and-1-0-touches-the-circle</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90132/if-a-circle-passes-through-the-point-1-1-and-cuts-the-circle-x-2-y-2-1-orthogona</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90133/the-equation-of-a-circle-with-the-origin-as-the-centre-and-passing-through-the-v</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90134/two-circles-have-a-direct-common-tangent-with-length-36-and-160-c-m-the-shortest</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90135/a-circle-c-1-has-radius-2-units-and-a-circle-c-2-has-radius-3-units-the-distance</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90136/the-locus-of-the-centre-of-the-circle-which-makes-equal-intercepts-on-the-lines</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90137/the-equation-of-incircle-of-the-triangle-formed-by-common-tangents-to-the-circle</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90138/let-triangle-a-b-c-is-right-angled-at-a-the-circle-with-centre-a-and-radius-a-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90139/a-circle-of-unit-radius-touches-the-positive-x-and-y-axes-two-parallel-tangents</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90140/the-line-2-x-y-1-0-is-tangent-to-the-circle-at-the-point-2-5-and-the-centre-of-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90141/the-equation-of-the-circumcircle-of-the-square-formed-by-the-lines-x-2-8-x-12-0</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90142/the-radius-of-the-circle-with-centre-at-3-2-and-whose-common-chord-with-the-circ</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90143/the-equation-of-an-ex-circle-of-a-triangle-formed-by-the-common-tangents-to-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90144/z-c-satisfies-the-condition-z-3-then-the-least-value-of-z-1-z-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90145/let-z-1-and-z-2-be-the-n-t-h-roots-of-unity-which-are-ends-of-a-line-segment-tha</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90146/the-real-values-of-x-and-y-satisfying-the-equation-1-i-x-2-i-3-i-2-3-i-y-i-3-i-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90147/if-z-1-2-3-i-and-the-least-positive-integral-value-of-n-such-that-z-101-i-109-10</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90148/if-z-is-a-non-real-complex-number-then-the-minimum-value-of-i-m-z-5-i-m-z-5-is-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90149/if-z-1-z-2-and-z-3-are-three-complex-numbers-such-that-z-1-z-2-z-3-1-z-1-1-z-2-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90150/if-z-1-z-1-0-then-z-2003-1-z-2003-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90151/if-iz-3-z-2-z-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/90152/if-z-i-be-any-complex-number-such-that-z-i-z-i-is-a-purely-imaginary-number-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90153/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/90154/the-value-of-k-1-10-sin-2-k-11-i-cos-2-k-11-is-where-i-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90155/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/90156/let-and-be-the-roots-of-the-equation-x-2-2-x-2-0-then-15-15-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90157/if-a-complex-number-z-lie-on-a-circle-of-radius-1-2-units-then-the-complex-numbe</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90158/if-z-be-a-complex-number-satisfying-z-4-8-i-4-then-the-least-and-the-greatest-va</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90159/if-z-is-a-complex-number-satisfying-z-2-3-z-2-4-then-the-sum-of-the-absolute-val</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90160/if-z-3-4-i-then-the-value-of-expression-z-4-3-z-3-3-z-2-99-z-95-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90161/let-z-r-e-i-r-0-and-3-is-a-root-of-the-equation-z-8-z-7-z-6-z-5-z-4-z-3-z-2-z-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90162/if-p-1-1-w-2-w-2-4-w-3-8-and-p-2-1-w-2-2-where-w-is-non-real-root-of-the-equatio</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90163/if-equation-z-1-n-z-n-1-n-n-has-solutions-then-n-can-be</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90164/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/90165/if-the-arguments-of-1-i-3-i-1-3-i-and-z-2-z-1-are-equal-then-the-locus-of-z-is-p</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90166/if-p-z-is-a-variable-point-in-the-complex-plane-such-that-m-1-z-1-4-then-the-val</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90167/if-a-and-b-are-two-real-numbers-lying-between-0-and-1-such-that-z-1-a-i-z-2-1-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90168/let-n-be-a-positive-integer-and-a-complex-number-with-unit-modulus-is-a-solution</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90169/the-solution-of-the-equation-z-z-1-2-i-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90170/the-minimum-value-of-the-expression-3-z-3-2-z-4-is-equal-to-where-z-is-a-complex</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90171/if-x-1-x-1-and-955-x-4-0-0-0-1-x-4-0-0-0-and-and-956-be-the-digit-at-the-unit-pl</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90172/the-number-of-solutions-of-the-equation-z-3-3-z-2-z-0-where-z-is-a-complex-numbe</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90173/let-o-0-0-a-3-0-b-0-1-and-c-3-2-then-the-minimum-value-of-z-z-3-z-i-z-3-2-i-occu</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90174/if-r-such-that-the-origin-and-the-non-real-roots-of-the-equation-2-z-2-2-z-0-for</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90175/if-im-i-z-2-z-i-1-where-z-c-z-i-represents-part-of-a-circle-then-the-radius-in-u</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90176/the-locus-of-a-point-z-represented-by-the-equation-z-1-z-i-on-the-argand-plane-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90177/if-z-1-z-2-and-z-3-are-3-distinct-complex-numbers-such-that-3-z-1-z-2-5-z-2-z-3</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90178/let-z-1-1-and-160-z-2-2-and-160-z-3-3-and-z-1-z-2-z-3-3-5-i-then-the-value-of-re</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90179/let-z-and-w-be-non-zero-complex-numbers-such-that-z-w-z-2-and-z-z-w-w-4-if-w-var</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90180/if-z-and-w-are-two-non-zero-complex-numbers-such-that-z-w-1-and-a-r-g-z-a-r-g-w</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90181/the-value-of-and-8721-k-1-4-s-i-n-2-and-960-k-5-i-c-o-s-2-and-960-k-5-4-is-where</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90182/if-arg-z-10-6-i-z-4-2-i-4-where-z-is-a-complex-number-then-the-perimeter-of-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90183/for-a-complex-number-z-if-all-the-roots-of-the-equation-z-3-a-z-2-b-z-c-0-are-un</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90184/for-a-complex-number-z-if-one-root-of-the-equation-z-2-a-z-a-0-is-1-i-and-its-ot</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90185/if-z-2-2-z-1-then-the-value-of-r-e-z-z-2-is-where-z-is-a-complex-number-and-re-z</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90186/for-a-complex-number-z-if-z-1-i-z-i-1-then-the-range-of-the-principle-argument-o</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90187/if-a-2-3-i-and-b-3-4-i-are-two-vertices-of-a-square-a-b-c-d-taken-in-anticlockwi</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90188/let-the-complex-numbers-z-1-z-2-and-z-3-are-the-vertices-a-b-and-c-respectively</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90189/if-a-and-b-are-positive-integers-such-that-n-a-i-b-3-107-i-where-n-is-a-natural</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90190/for-a-complex-number-z-if-z-4-1-i-4-1-i-i-i-1-i-then-the-value-of-z-amp-z-is-equ</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90191/for-a-complex-number-z-if-arg-and-8289-z-and-960-4-and-z-1-z-4-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/90192/for-the-equation-1-i-x-1-i-x-s-i-n-7-i-c-o-s-7-if-x-c-o-t-k-28-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/90193/for-a-complex-number-z-if-the-argument-of-z-a-z-b-is-4-or-3-4-where-a-b-are-two</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90194/if-4-i-3-i-2-i-1-2-r-cos-and-8289-and-952-i-sin-and-8289-and-952-then-cos-and-82</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90195/if-the-complex-numbers-sin-x-i-cos-2-x-and-cos-x-i-sin-2-x-are-conjugate-of-each</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90196/for-a-complex-number-z-the-equation-of-the-line-of-common-chord-of-the-circles-z</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90197/if-x-4-2-x-i-3-x-2-y-i-3-5-i-1-2-y-i-then-the-number-of-ordered-pairs-x-y-is-are</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90198/for-a-complex-number-z-z-1-and-arg-z-if-z-z-2-z-3-z-n-1-then-the-value-of-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90199/if-z-cos-i-sin-3-then-the-value-of-arg-z-2-z-is-equal-to-where-arg-z-represents</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90200/let-z-x-i-y-is-a-complex-number-such-that-x-2-y-2-1-in-which-of-the-following-ca</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90201/for-a-complex-number-z-the-equation-z-2-p-i-q-z-r-i-s-0-has-a-real-root-where-p</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90202/let-the-points-a-b-c-and-d-are-represented-by-complex-numbers-z-1-z-2-z-3-and-z</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90203/for-the-complex-number-z-the-sum-of-all-the-solutions-of-z-2-z-z-and-175-2-is-eq</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90204/let-z-x-i-y-and-w-u-i-v-be-two-complex-numbers-such-that-z-w-1-and-z-2-w-2-1-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90205/if-z-1-a-b-i-c-and-a-2-b-2-c-2-1-then-1-i-z-1-and-8722-i-z-where-a-b-c-and-8712</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90206/if-z-is-a-complex-number-then-the-area-of-the-triangle-in-sq-units-whose-vertice</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90207/let-and-be-the-roots-of-x-2-x-1-0-then-the-equation-whose-roots-are-2020-and-202</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90208/if-z-1-2-3-i-z-2-3-2-i-and-z-3-1-2-3-i-then-which-of-the-following-is-true-where</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90209/the-real-values-of-x-and-y-for-which-the-equation-x-4-2-x-i-3-x-2-y-i-3-5-i-1-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90210/the-minimum-value-of-the-expression-e-z-2-z-3-2-z-6-i-2-where-z-is-a-complex-num</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90211/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/90212/let-the-locus-of-any-point-p-z-in-the-argand-plane-is-a-r-g-z-5-i-z-5-i-4-if-o-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90213/two-points-p-and-q-in-the-argand-plane-represent-the-complex-numbers-z-and-3-z-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90214/the-number-of-distinct-complex-number-s-z-such-that-z-1-and-z-3-is-purely-imagin</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90215/if-z-1-z-2-and-z-3-are-the-vertices-of-a-triangle-in-the-argand-plane-such-that</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90216/the-value-of-and-8721-k-1-99-i-k-and-969-k-is-where-i-1-and-and-969-is-non-real</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90217/if-is-the-non-real-cube-root-of-unity-then-the-number-of-ordered-pairs-of-intege</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90218/the-complex-number-z-satisfying-the-equation-z-3-z-and-arg-and-8289-z-1-and-960</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90219/if-z-is-a-complex-number-satisfying-the-equation-z-1-i-2-2-and-2-z-z-0-then-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90220/for-a-complex-number-z-the-product-of-the-real-parts-of-the-roots-of-the-equatio</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90221/for-a-complex-number-z-if-z-i-2-and-z-1-5-3-i-then-the-maximum-value-of-i-z-z-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90222/the-minimum-value-of-8-z-8-2-z-4-exists-when-z-is-equal-to-where-z-is-a-complex</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90223/for-the-complex-number-z-satisfying-the-condition-z-2-z-2-the-maximum-value-of-z</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90224/for-a-complex-number-z-if-the-argument-of-3-3-i-and-z-2-z-1-are-equal-then-the-m</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90225/let-and-969-and-160-and-969-and-8800-1-is-a-cube-root-of-unity-such-that-1-and-9</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90226/if-i-2-1-then-for-a-complex-number-z-the-minimum-value-of-z-z-3-z-i-z-3-2-i-occu</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90227/if-the-origin-and-the-non-real-roots-of-the-equation-3-z-2-3-z-0-r-are-the-verti</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90228/if-im-i-z-2-z-i-1-represents-part-of-a-circle-with-radius-r-units-then-the-value</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90229/let-z-1-3-z-2-2-and-z-1-z-2-z-3-3-4-i-if-the-real-part-of-z-1-z-2-z-2-z-3-z-3-z</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90230/if-z-1-z-2-z-3-are-3-distinct-complex-such-that-3-z-1-z-2-5-z-2-z-3-7-z-3-z-1-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90231/let-z-be-a-complex-number-satisfying-the-relation-z-3-4-z-and-175-2-z-0-if-the-l</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90232/if-z-i-where-i-1-2-and-8230-and-8230-and-8230-6-be-the-roots-of-the-equation-z-6</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90233/if-the-cubic-equation-z-3-a-z-2-b-z-c-0-and-160-and-8704-a-b-c-and-8712-r-and-16</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90234/the-real-part-of-the-complex-number-z-satisfying-z-1-2-i-1-and-having-the-least</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90235/if-z-and-w-are-complex-numbers-satisfying-z-i-w-0-and-amp-z-w-then-amp-w-is-equa</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90236/if-m-and-m-denotes-the-minimum-and-maximum-value-of-2-z-1-where-z-2-i-and-8804-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90237/an-insect-starts-from-the-origin-in-the-argand-plane-and-goes-4-and-160-k-m-n-an</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90238/if-the-locus-of-the-complex-number-z-given-by-ar-g-z-i-a-r-g-z-i-2-and-960-3-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90239/let-p-h-k-be-a-point-on-an-argand-plane-equidistant-from-the-roots-of-the-equati</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90240/if-z-is-a-complex-number-such-that-z-2-then-the-area-in-sq-units-of-the-triangle</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90241/if-z-1-and-z-2-are-two-distinct-complex-numbers-satisfying-the-relation-z-1-2-z</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90242/for-a-complex-number-z-if-z-2-z-z-4-i-and-z-does-not-lie-in-the-first-quadrant-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90243/for-two-non-zero-complex-numbers-a-and-b-if-a-1-b-a-and-175-and-1-a-b-b-and-175</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90244/if-z-x-i-y-x-y-r-i-2-1-x-y-0-and-z-2-then-the-imaginary-part-of-z-2-z-2-cannot-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90245/for-a-complex-number-z-if-arg-z-then-arg-1-cos-6-5-i-sin-6-5-is-here-i-2-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90246/if-the-complex-number-and-969-x-i-y-and-8704-x-y-and-8712-r-and-i-2-1-satisfy-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90247/let-z-1-z-2-and-z-3-are-the-points-on-the-argand-plane-which-lie-on-the-circle-w</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90248/let-a-z-1-b-z-2-and-c-z-3-be-complex-numbers-satisfying-the-equation-z-1-and-als</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90249/if-i-2-1-and-and-8721-r-1-n-i-r-and-160-and-8704-n-and-8712-n-is-a-non-zero-real</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90250/if-i-2-1-and-1-i-2-n-1-i-2-m-1-and-160-and-8704-n-m-and-8712-n-then-the-minimum</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90251/for-a-complex-number-z-if-arg-z-and-8712-and-960-and-960-then-arg-1-cos-and-8289</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90252/the-number-of-discontinuity-of-the-greatest-integer-function-f-x-x-x-7-2-100-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90253/in-0-2-the-total-number-of-points-where-f-x-m-a-x-sin-x-cos-x-1-cos-x-is-not-dif</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90254/the-value-of-f-0-so-that-the-function-f-x-1-cos-1-cos-x-x-4-is-continuous-everyw</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90255/the-function-f-x-1-sin-x-cos-x-1-sin-x-cos-x-is-not-defined-at-x-and-960-the-val</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90256/if-f-x-4-a-x-4-a-x-x-1-x-0-3-x-2-x-8-0-x-1-is-continuous-in-1-1-then-the-value-o</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90257/given-f-x-x-2-e-2-x-1-0-x-1-a-sgn-x-1-cos-2-x-2-b-x-2-1-x-2-if-f-x-is-differenti</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90258/for-x-r-f-x-log-2-sin-x-and-g-x-f-f-x-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90259/let-f-g-and-h-are-differentiable-functions-if-f-0-1-g-0-2-h-0-3-and-the-derivati</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90260/if-f-x-x-p-cos-and-8289-1-x-x-and-8800-0-0-x-0-is-differentiable-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/90261/the-function-f-x-x-sin-x-where-denotes-the-greatest-integer-function-and-is-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90262/on-differentiating-tan-1-1-x-2-1-x-with-respect-to-x-the-result-would-be</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90263/let-f-1-1-r-be-a-function-defined-by-f-x-max-x-1-x-2-if-k-be-the-set-of-all-poin</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90264/if-f-x-max-x-n-sin-x-n-n-has-maximum-points-of-non-differentiability-for-x-0-4-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90265/the-value-of-f-0-such-that-f-x-1-x-2-1-c-o-s-s-i-n-x-can-be-made-continuous-at-x</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90266/the-number-of-points-at-which-the-function-f-x-x-0-5-x-1-tan-and-8289-x-is-not-d</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90267/if-f-x-2-sin-x-and-960-and-8804-x-and-8804-3-and-960-2-p-cos-x-q-3-and-960-2-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90268/if-f-x-2-x-3-0-x-3-x-12-3-x-9-is-differentiable-at-x-3-then-the-value-of-is-equa</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90269/if-f-x-s-i-n-2-x-c-x-x-4-x-a-2-a-x-0-a-0-c-0-b-x-0-b-0-and-f-x-is-continuous-at</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90270/if-f-x-1-5-x-a-x-4-0-and-8804-x-and-60-4-b-x-and-8805-4-is-continuous-at-x-4-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/90719/if-f-x-2-sin-and-8289-x-1-2-cot-and-8289-x-then-the-value-of-f-and-960-3-is-equa</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90720/if-f-r-and-8594-r-is-a-function-defined-as-f-x-3-x-5-and-160-and-8704-x-and-8712</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90721/if-y-2-sin-x-2-sin-x-2-sin-x-then-the-value-of-d-y-d-x-at-x-0-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90722/let-f-x-is-a-differentiable-function-on-x-and-8712-r-such-that-f-x-y-f-x-f-y-for</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90723/if-f-x-x-4-x-4-t-a-n-1-1-2-x-2-x-and-160-and-8704-4-and-60-x-and-60-8-then-the-v</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90724/if-f-x-x-and-8211-1-x-and-8211-2-x-and-8211-3-x-and-8211-4-x-and-8211-5-then-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90725/consider-the-function-f-x-t-a-n-1-3-x-2-3-2-x-x-0-if-g-x-is-the-inverse-function</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90726/let-f-x-t-a-n-1-x-3-1-x-2-x-then-the-value-of-17-f-and-8242-2-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90727/if-i-n-d-n-d-x-n-x-n-ln-and-8289-x-then-the-value-of-1-50-i-7-7-i-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/90728/let-y-x-l-o-g-e-x-if-the-value-of-d-y-d-x-at-x-e-4-is-k-then-the-value-of-4-e-3</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90729/if-x-y-y-x-16-then-the-value-of-d-y-d-x-at-2-2-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90730/let-f-x-be-a-differentiable-function-on-x-r-such-that-f-x-y-f-x-f-y-for-all-x-y</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90731/if-y-s-i-n-1-2-x-1-x-2-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/90732/if-the-function-f-x-cos-1-x-3-2-1-x-x-2-x-3-where-0-x-1-then-the-value-of-3-f-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90733/consider-a-function-f-x-x-x-x-1-if-g-x-is-the-inverse-function-of-f-x-then-the-v</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90734/if-x-log-8-log-3-x-then-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/90735/if-f-x-s-i-n-1-2-and-215-3-x-1-9-x-then-f-1-2-is-equal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90736/the-angle-between-the-pair-of-tangents-drawn-to-the-ellipse-3-x-2-2-y-2-5-from-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90737/if-the-line-x-2-y-12-is-a-tangent-to-the-ellipse-x-2-a-2-y-2-b-2-1-at-the-point</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90738/the-point-which-is-at-the-shortest-distance-from-the-line-x-y-7-and-lying-on-an</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90739/if-the-locus-of-the-foot-of-the-perpendicular-drawn-from-centre-upon-any-tangent</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90740/if-common-tangents-of-x-2-y-2-r-2-and-x-2-16-y-2-9-1-forms-a-square-then-the-len</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90741/if-a-tangent-of-slope-2-of-the-ellipse-x-2-a-2-y-2-1-1-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/90742/let-from-a-point-a-h-k-chord-of-contacts-are-drawn-to-the-ellipse-x-2-2-y-2-6-su</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90743/if-any-tangent-to-the-ellipse-25-x-2-9-y-2-225-meets-the-coordinate-axes-at-a-an</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90744/if-the-normal-to-the-ellipse-x-2-25-y-2-1-1-is-at-a-distance-p-from-the-origin-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90745/suppose-s-and-s-are-foci-of-the-ellipse-x-2-25-y-2-16-1-if-p-is-a-variable-point</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90746/the-line-2-x-y-3-cuts-the-ellipse-4-x-2-y-2-5-at-points-p-and-q-if-is-the-acute</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90747/a-tangent-having-slope-4-3-to-the-ellipse-x-2-18-y-2-32-1-intersects-the-major-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90748/an-ellipse-has-foci-4-2-and-160-2-2-and-it-passes-through-the-point-p-2-4-the-ec</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90749/the-line-2-x-y-3-interesects-the-ellipse-4-x-2-y-2-5-at-two-points-the-point-of</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90750/let-the-line-y-m-x-and-the-ellipse-2-x-2-y-2-1-intersect-at-a-point-p-in-the-fir</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90751/the-length-of-the-latus-rectum-of-the-curve-represented-by-x-3-cos-t-sin-t-and-y</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90752/if-m-1-and-m-2-are-the-slopes-of-the-tangents-to-the-ellipse-x-2-16-y-2-9-1-whic</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90753/if-p-and-q-are-points-with-eccentric-angles-and-6-on-the-ellipse-x-2-16-y-2-4-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90754/if-y-x-c-touches-the-ellipse-3-x-2-4-y-2-12-at-the-point-p-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/90755/if-is-the-angle-between-the-pair-of-tangents-drawn-to-the-ellipse-3-x-2-2-y-2-5</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90756/the-focus-and-corresponding-directrix-of-an-ellipse-are-3-4-and-x-y-1-0-respecti</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90757/if-0-3-5-is-a-point-on-the-ellipse-whose-foci-are-2-3-and-2-3-then-the-length-of</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90758/let-s-and-s-are-the-focii-of-the-ellipse-x-3-5-cos-y-2-4-sin-if-b-is-one-of-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90759/the-length-of-the-portion-of-the-common-tangent-to-x-2-y-2-16-and-9-x-2-25-y-2-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90760/let-there-are-exactly-two-points-on-the-ellipse-x-2-a-2-y-2-b-2-1-whose-distance</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90761/the-point-on-the-ellipse-x-2-6-y-2-3-1-which-is-nearest-to-the-line-x-y-7-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90762/p-1-and-p-2-are-corresponding-points-on-the-ellipse-x-2-16-y-2-9-1-and-its-auxil</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90763/if-two-points-are-taken-on-the-minor-axis-of-the-ellipse-x-2-25-y-2-9-1-at-the-s</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90764/the-length-of-the-minor-axis-of-the-ellipse-5-x-10-2-5-y-15-2-3-x-4-y-7-2-4-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90765/if-a-tangent-having-slope-2-of-the-ellipse-x-2-a-2-y-2-b-2-1-is-normal-to-the-ci</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90766/variable-ellipses-are-drawn-with-x-4-as-directrix-and-the-origin-as-the-correspo</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90767/the-tangents-at-the-extremities-of-the-latus-rectum-of-the-ellipse-3-x-2-4-y-2-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90768/the-ellipse-e-1-x-2-9-y-2-4-1-is-inscribed-in-a-rectangle-r-whose-sides-are-para</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90769/an-equilateral-triangle-is-inscribed-in-the-ellipse-whose-equation-is-x-2-4-y-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90770/if-the-tangent-to-the-ellipse-x-2-4-y-2-16-at-p-4-cos-2-sin-is-also-a-normal-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90771/if-the-circle-whose-diameter-is-the-major-axis-of-the-ellipse-x-2-a-2-y-2-b-2-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90772/the-product-of-the-slopes-of-the-common-tangents-of-the-ellipse-x-2-4-y-2-16-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90773/if-x-2-y-2-a-2-and-x-2-16-y-2-9-1-intersect-at-4-points-p-q-r-and-s-which-form-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90774/a-tangent-of-slope-2-of-the-ellipse-x-2-a-2-y-2-1-1-passes-through-2-0-then-thre</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90775/let-from-a-point-a-h-k-chords-of-contact-are-drawn-to-the-ellipse-x-2-2-y-2-6-wh</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90776/if-the-tangents-p-q-and-p-r-are-drawn-from-a-variable-point-p-to-the-ellipse-x-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90777/the-line-2-x-y-3-cuts-the-ellipse-4-x-2-y-2-5-at-p-and-q-if-is-the-acute-angle-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90778/if-the-common-tangents-of-x-2-y-2-r-2-and-x-2-16-y-2-9-1-form-a-square-then-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90779/if-eccentricity-of-the-ellipse-x-2-a-2-1-y-2-a-2-2-1-is-1-6-then-the-ratio-of-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90780/if-a-b-r-satisfy-the-equation-a-2-4-b-2-4-0-then-the-minimum-value-of-2-a-3-b-wi</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90781/two-lines-l-1-and-l-2-of-slope-1-are-tangent-to-y-2-4-x-and-x-2-2-y-2-4-respecti</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90782/the-focal-chord-of-the-parabola-y-2-32-x-touches-the-ellipse-x-2-4-2-y-2-2-2-1-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90783/a-trapezium-is-formed-by-the-pair-of-tangents-of-parabola-p-y-x-2-4-1-drawn-from</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90784/from-the-point-p-3-4-pair-of-tangents-p-a-and-p-b-are-drawn-to-the-ellipse-x-2-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90785/the-tangent-to-the-ellipse-x-2-25-y-2-16-1-at-point-p-lying-in-the-first-quadran</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90786/the-vertices-of-the-triangle-a-b-c-are-a-0-0-and-160-b-3-0-and-c-3-4-where-a-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90787/if-a-number-of-ellipses-whose-major-axis-is-x-axis-and-the-minor-axis-is-y-axis</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90788/a-normal-is-drawn-to-the-ellipse-x-2-9-y-2-1-at-the-point-3-cos-and-8289-and-952</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90789/the-domain-of-definition-of-the-function-y-3-e-x-2-1-log-x-1-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90790/let-f-r-r-be-a-periodic-function-such-that-f-t-x-1-1-3-f-x-3-f-x-2-f-x-3-1-3-whe</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/90791/if-f-x-cos-ln-x-then-f-x-f-y-1-2-f-x-y-f-x-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/90792/if-f-x-y-x-y-xy-then-the-arithmetic-mean-of-f-x-y-and-f-y-x-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/92043/the-lengths-of-the-perpendiculars-from-the-points-m-2-2-m-m-n-m-n-and-n-2-2-n-to</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92044/the-perimeter-of-a-parallelogram-whose-sides-are-represented-by-the-lines-x-2-y</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92045/let-the-lengths-of-the-altitudes-from-the-vertices-a-1-1-b-5-2-c-3-1-of-a-b-c-ar</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92046/point-p-1-7-lies-on-the-line-4-x-3-y-17-then-the-coordinates-of-the-points-farth</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92047/the-equation-of-the-external-bisector-of-and-8736-b-a-c-of-and-916-a-b-c-with-ve</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92048/let-a-variable-line-passing-through-a-fixed-point-p-in-the-first-quadrant-cuts-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92049/the-midpoint-of-a-0-0-and-b-1024-2048-is-a-1-midpoint-of-a-1-and-b-is-a-2-midpoi</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92050/let-the-equations-of-the-sides-p-q-q-r-r-s-and-s-p-of-a-quadrilateral-p-q-r-s-ar</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92051/if-the-equation-of-the-hypotenuse-of-a-right-angled-isosceles-triangle-is-3-x-4</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92052/the-vertices-of-a-triangle-are-the-points-p-26-17-q-30-17-and-r-10-2-if-g-and-be</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92053/let-the-images-of-the-point-a-2-3-about-the-lines-y-x-and-y-m-x-are-p-and-q-resp</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92054/let-p-be-the-image-of-the-point-3-1-7-with-respect-to-the-plane-x-y-z-3-the-equa</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92055/a-variable-line-through-the-point-6-5-6-5-cuts-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/92056/the-sum-of-the-intercepts-on-the-coordinate-axes-made-by-a-line-passing-through</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92057/if-the-lines-x-1-y-2-z-3-x-k-3-y-3-1-z-4-h-and-2-x-1-3-y-1-1-z-2-1-are-concurren</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92058/the-points-2-1-1-0-4-3-and-1-2-are</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92059/the-coordinate-axes-is-rotated-and-shifted-in-such-a-way-that-the-iv-th-quadrant</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92060/let-p-1-0-and-q-1-0-are-two-fixed-points-and-r-is-a-variable-point-on-one-side-o</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92061/the-point-a-2-a-1-lies-in-the-angle-between-the-lines-3-x-y-1-0-and-x-2-y-5-0-co</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92062/if-the-straight-lines-x-2-y-3-2-x-3-y-5-and-k-2-x-ky-1-represent-a-triangle-whic</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92063/the-coordinates-of-the-points-on-the-line-3-x-2-y-5-which-are-equidistant-from-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92064/the-line-2-x-3-y-12-meets-the-coordinates-axes-at-a-and-b-respectively-the-line</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92065/let-a-6-7-b-2-3-and-c-2-1-be-the-vertices-of-a-triangle-the-point-p-nearer-to-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92066/the-line-l-given-by-x-5-y-b-1-passes-through-the-point-13-32-if-the-line-k-is-pa</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92067/the-equation-of-the-image-of-line-y-x-with-respect-to-the-line-mirror-2-x-y-1-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92068/in-the-figure-shown-o-a-b-c-is-a-rectangle-with-o-a-3-units-o-c-4-units-if-b-d-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92069/the-point-p-2-1-is-shifted-through-a-distance-of-3-2-units-measured-perpendicula</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92070/if-the-area-of-the-rhombus-enclosed-by-the-lines-x-y-n-0-be-2-square-units-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92071/the-point-a-divides-the-line-segment-joining-the-points-5-1-and-3-5-in-the-ratio</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/92073/if-the-segment-intercepted-between-the-lines-x-6-y-13-0-and-x-y-3-0-is-bisected</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92074/a-line-4-x-y-1-passes-thought-the-point-a-2-7-and-meets-the-line-b-c-at-b-whose</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92075/the-line-x-c-2-divides-the-triangle-with-vertices-0-0-1-1-and-9-1-into-two-regio</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92076/the-number-of-distinct-possible-lines-passing-through-the-point-2-3-and-forming</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92077/if-the-vertex-opposite-to-the-hypotenuse-of-a-right-angled-triangle-lies-on-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92078/let-p-is-a-point-on-the-line-y-2-x-2-and-q-and-r-are-two-points-on-the-line-3-y</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92079/let-the-coordinates-of-two-points-p-and-q-be-1-2-and-7-5-respectively-the-line-p</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92080/let-a-d-c-b-and-a-d-b-c-where-a-b-c-r-if-the-family-of-lines-a-2-x-b-2-y-c-2-d-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92081/let-the-points-p-and-q-lie-on-the-lines-y-x-and-y-2-x-respectively-the-equation</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/92083/for-a-a-b-c-if-b-3-0-c-3-0-and-the-angle-b-a-c-is-90-then-the-locus-of-the-centr</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92084/the-sum-of-all-the-values-of-p-for-which-the-lines-x-y-1-0-p-x-4-y-2-0-and-4-x-p</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92085/let-the-circumcentre-of-a-b-c-is-s-1-0-and-the-midpoints-of-the-sides-a-b-and-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92086/the-equations-of-the-lines-l-1-and-l-2-are-y-m-x-and-y-n-x-respectively-suppose</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92087/let-2-a-2-b-c-0-l-1-and-l-2-are-straight-lines-of-the-family-a-x-b-y-c-0-which-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92088/in-the-equilateral-triangle-a-b-c-the-equation-of-the-side-b-c-is-x-y-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/92089/let-x-2-y-2-r-2-and-x-y-1-intersect-at-a-and-b-in-the-first-quadrant-if-a-b-14-u</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92090/the-area-in-sq-units-of-the-locus-of-the-point-at-which-the-two-circles-x-2-y-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/92092/a-line-passing-through-the-point-a-2-2-encloses-an-area-of-4-sq-units-with-coord</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92093/let-in-and-8710-a-b-c-the-coordinates-of-a-are-0-0-internal-angle-bisector-of-an</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92094/let-the-incentre-of-and-916-a-b-c-is-i-2-5-if-a-1-13-and-b-4-1-then-the-sum-of-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92095/let-a-x-1-y-1-b-x-2-y-2-c-x-3-y-3-and-d-x-4-y-4-are-four-points-which-are-at-equ</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/92118/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>
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  <url><loc>https://www.quantrexacademy.com/q/92120/a-plane-p-0-which-is-perpendicular-to-line-x-2-2-y-2-2-z-1-1-is-passing-through</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92121/if-the-image-of-the-point-p-1-2-3-in-the-plane-2-x-3-y-4-z-22-0-measured-paralle</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92122/if-the-point-of-intersection-of-the-plane-4-x-5-y-2-z-6-0-with-the-line-through</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92123/let-p-1-and-160-2-x-y-z-1-0-p-2-and-160-2-x-y-z-3-0-and-p-3-and-160-2-x-3-y-z-5</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92124/image-of-line-x-2-3-y-1-1-z-1-4-in-the-plane-x-y-z-7-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92125/if-the-planes-r-i-j-k-1-r-i-2-a-j-k-2-and-r-a-i-a-2-j-k-3-intersect-in-a-line-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92126/two-intersecting-lines-lying-in-plane-p-1-have-equations-x-1-1-y-3-2-z-4-3-and-x</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92127/the-direction-cosines-l-m-and-n-of-two-lines-are-connected-by-the-relations-l-m</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92128/let-a-be-the-point-1-2-3-and-b-be-a-point-on-the-line-x-1-2-y-1-3-z-5-4-k-the-va</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92129/the-equation-of-a-plane-containing-the-line-formed-by-2-x-y-z-3-0-3-x-y-z-5-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92130/equation-of-the-plane-passing-through-the-point-of-intersection-of-the-line-x-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92131/consider-the-planes-p-1-2-x-y-z-6-and-p-2-x-2-y-z-4-having-normals-n-1-and-n-2-r</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92132/if-the-planes-x-c-y-b-z-0-and-160-c-x-y-a-z-0-and-b-x-a-y-z-0-pass-through-a-str</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92133/the-point-of-intersection-of-the-plane-3-x-5-y-2-z-6-with-the-straight-line-pass</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92134/let-p-1-x-2-y-3-z-5-and-p-2-2-x-3-y-z-4-0-be-two-planes-the-equation-of-the-plan</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92135/lying-in-the-plane-x-y-z-6-is-a-line-l-passing-through-1-2-3-and-perpendicular-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92136/let-a-be-a-vector-parallel-to-the-line-of-intersection-of-the-planes-p-1-and-p-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92137/the-shortest-distance-between-the-line-x-y-z-and-the-line-of-intersection-of-2-x</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92138/a-plane-passes-through-1-2-1-and-is-perpendicular-to-two-planes-2-x-2-y-z-0-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92139/the-plane-2-x-2-y-z-3-is-rotated-about-its-line-of-intersection-with-the-xy-plan</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92140/the-projection-of-the-line-x-1-2-y-1-1-z-2-3-on-a-plane-p-is-x-1-1-y-1-2-z-2-1-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92141/let-p-1-x-y-z-1-0-and-160-p-2-x-y-2-z-1-0-and-p-3-3-x-y-4-z-7-0-be-three-planes</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92142/distance-between-two-non-intersecting-planes-p-1-and-p-2-is-5-units-where-p-1-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92143/if-a-x-13-y-b-z-c-0-is-a-plane-through-the-line-of-intersection-of-2-x-3-y-z-1-0</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92144/if-m-1-and-m-2-are-the-roots-of-the-equation-x-2-3-2-x-3-1-0-then-the-area-in-sq</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92145/a-plane-passes-through-the-point-2-2-2-and-contains-the-line-joining-the-points</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92146/if-the-foot-of-perpendicular-drawn-from-the-point-2-5-1-on-a-line-passing-throug</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92147/the-perpendicular-bisector-of-a-line-segment-with-end-points-1-2-6-and-3-6-2-pas</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92148/the-distance-of-the-plane-x-2-y-z-2-from-the-point-2-1-3-measured-in-the-directi</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92149/the-intercepts-made-on-the-x-and-160-y-and-z-axes-by-the-plane-which-bisects-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92150/the-plane-4-x-7-y-4-z-81-0-is-rotated-through-a-right-angle-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/92151/the-image-of-the-line-x-2-y-1-5-z-1-3-in-the-plane-x-y-2-z-3-meets-the-x-z-plane</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92152/let-p-1-2-3-be-a-point-in-space-and-q-be-a-point-on-the-line-x-1-2-y-3-5-z-1-3-s</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92153/if-the-lines-x-1-1-y-3-1-z-2-and-x-1-y-3-2-z-4-1-intersect-at-a-point-then-the-v</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92154/a-plane-p-0-passing-through-the-point-1-1-1-is-perpendicular-to-the-planes-2-x-y</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92155/the-shortest-distance-between-the-lines-x-2-2-y-3-2-z-0-1-and-x-4-1-y-7-8-z-5-4</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92156/the-length-of-two-opposite-edges-of-a-tetrahedron-are-12-and-15-units-and-the-sh</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92157/if-the-length-of-the-projection-of-the-line-segment-joining-the-points-1-2-1-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92158/the-distance-of-the-point-2-3-2-from-the-plane-3-x-4-y-4-z-23-measured-parallel</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92159/direction-cosines-of-the-normal-to-the-plane-containing-the-lines-x-2-y-3-z-5-an</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92160/if-the-distance-of-point-p-3-2-6-from-the-line-x-1-2-y-2-3-z-3-4-measured-parall</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92161/the-length-of-the-perpendicular-in-units-from-the-point-1-2-4-on-the-straight-li</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92162/if-the-direction-ratios-of-a-line-are-1-2-4-and-if-it-makes-an-angle-of-6-0-o-wi</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92163/equation-of-the-plane-passing-through-the-point-1-1-3-parallel-to-the-vector-i-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92164/if-the-magnitude-of-the-projection-of-the-vector-i-j-2-k-on-the-vector-perpendic</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92165/a-line-l-passing-through-1-2-3-and-perpendicular-to-the-line-l-1-x-1-2-y-1-3-z-5</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92166/a-ray-of-light-through-the-point-a-1-2-3-strikes-the-plane-x-y-z-12-at-a-point-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92167/the-equation-of-the-plane-passing-through-the-point-of-intersection-of-the-lines</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92168/two-lines-x-1-2-y-2-3-z-3-4-and-x-4-5-y-1-2-z-1-intersect-at-a-point-p-if-the-di</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92169/the-length-of-the-perpendicular-from-1-0-2-on-the-line-x-1-3-y-2-2-z-1-1-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92170/the-equation-of-the-plane-through-the-points-2-1-0-3-4-5-and-parallel-to-a-line</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92171/let-l-1-x-y-z-and-l-2-x-1-y-2-z-3-be-two-lines-the-foot-of-perpendicular-drawn-f</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92172/the-direction-ratios-of-the-normal-to-the-plane-passing-through-the-points-1-2-3</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92173/consider-the-line-l-and-8801-x-1-2-y-2-3-z-7-6-point-p-2-5-0-and-q-are-such-that</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92174/let-a-be-the-foot-of-the-perpendicular-from-the-origin-to-the-plane-x-2-y-2-z-6</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92175/let-p-1-x-y-2-z-4-0-and-p-2-2-x-y-3-z-5-0-be-two-planes-let-a-1-3-4-and-b-3-2-7</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92176/let-p-1-3-y-z-1-0-and-p-2-2-x-y-3-z-7-0-and-the-equation-of-line-a-b-is-x-1-2-y</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92177/if-the-lines-x-1-y-1-1-z-2-2-x-2-y-1-1-z-2-1-x-1-y-1-1-z-2-1-intersect-the-plane</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92178/let-p-1-x-y-2-z-3-and-p-2-x-2-y-z-4-be-two-planes-let-a-2-4-5-and-b-4-3-8-be-two</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92179/a-line-passes-through-the-point-a-2-3-5-and-is-parallel-to-the-vector-2-i-j-k-if</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92180/a-line-l-lies-in-the-plane-2-x-y-z-4-such-that-it-is-perpendicular-to-the-line-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/92182/if-the-line-x-1-1-y-k-2-z-3-lies-in-the-plane-3-x-4-y-2-z-6-then-5-k-3-is-equal</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92183/if-the-line-x-1-5-y-3-2-z-3-2-intersects-the-curve-x-2-y-2-k-2-and-160-z-0-then</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/92184/consider-a-plane-p-2-x-y-z-5-a-line-l-x-3-2-y-1-3-z-2-1-and-a-point-a-3-4-1-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/92192/a-line-makes-an-angle-with-the-x-axis-and-the-y-axis-if-it-makes-an-angle-with-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/93035/electromagnetic-waves-travel-in-a-medium-with-a-speed-of-2-10-8-m-s-1-the-relati</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/93755/a-liquid-drop-having-surface-energy-e-is-spread-into-512-droplets-of-same-size-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/93757/when-a-large-bubble-rises-from-the-bottom-of-a-lake-to-the-surface-its-radius-do</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93758/water-flows-out-of-a-big-tank-along-a-tube-bent-at-right-angles-the-inside-radiu</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93759/water-from-a-tap-emerges-vertically-downwards-with-an-initial-speed-of-1-0-m-s-1</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93760/the-level-of-water-in-a-tank-is-5-m-high-a-hole-of-the-area-10-c-m-2-is-made-in</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93761/the-density-of-a-liquid-contained-in-a-tank-of-area-0-5-m-2-is-1200-k-g-m-3-the</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93762/the-radius-r-of-the-soap-bubble-is-doubled-under-isothermal-condition-if-t-be-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93763/two-communicating-vessels-contain-mercury-the-diameter-of-one-vessel-is-n-times</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93764/the-pressures-inside-two-soap-bubbles-are-1-02-a-t-m-and-1-03-a-t-m-respectively</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93765/the-compressibility-of-water-is-4-10-5-per-unit-atmospheric-pressure-the-decreas</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93766/water-is-being-poured-in-a-vessel-at-a-constant-rate-m-3-s-1-there-is-a-small-ho</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93767/a-solid-cone-of-height-h-radius-r-suspended-by-a-string-is-just-submerged-in-a-l</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93768/surface-tension-of-the-liquid-is-s-work-done-in-increasing-the-radius-of-soap-bu</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93769/the-atmospheric-pressure-at-the-surface-of-a-lake-of-depth-h-is-p-0-if-the-press</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93770/a-large-tank-filled-with-water-to-a-height-h-is-to-be-emptied-through-a-small-ho</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93771/there-are-two-identical-small-holes-of-the-area-of-cross-section-a-on-the-opposi</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93772/a-water-drop-is-divided-into-eight-equal-droplets-then-the-pressure-difference-b</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93773/a-soap-bubble-has-radius-r-and-thickness-d-r-as-shown-in-the-diagram-it-collapse</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93774/the-frequency-of-a-sonometer-wire-is-f-but-when-the-weight-producing-the-tension</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93775/a-glass-capillary-tube-is-of-the-shape-of-a-truncated-cone-with-an-apex-angle-so</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93776/a-wide-cylindrical-vessel-50-cm-in-height-is-filled-with-water-and-rests-on-a-ta</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93777/the-lower-end-of-a-glass-capillary-tube-is-dipped-in-water-water-rises-to-a-heig</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93778/water-from-a-tap-emerges-vertically-downwards-with-an-initial-velocity-v-0-assum</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93779/a-body-p-floats-in-water-with-half-its-volume-immersed-another-body-q-floats-in</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93780/a-coaxial-cylinder-made-of-glass-is-immersed-in-a-liquid-of-surface-tension-s-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93781/the-glycerin-of-density-1-25-10-3-k-g-m-3-is-flowing-through-a-conical-tube-with</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93782/a-cone-of-radius-r-and-height-h-is-hanging-inside-a-liquid-of-density-by-means-o</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93783/in-a-cylinder-piston-arrangement-the-air-is-under-a-pressure-p-1-a-soap-bubble-o</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93784/the-velocity-of-water-in-a-river-is-18-km-h-1-near-the-surface-if-the-river-is-5</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93785/a-manometer-connected-to-a-close-tap-reads-3-5-10-5-n-m-2-when-the-valve-is-open</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93786/glycerine-is-filled-in-25-mm-wide-space-between-two-large-plane-horizontal-surfa</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93787/a-u-tube-has-a-liquid-of-density-0-at-0-c-in-the-two-limbs-they-are-kept-to-a-le</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93788/the-graph-between-the-mass-of-liquid-inside-the-capillary-and-radius-of-the-capi</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93789/a-block-is-being-hung-in-the-air-from-a-wire-which-is-stretched-over-a-sonometer</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93790/a-liquid-is-kept-in-a-cylindrical-vessel-which-is-rotated-along-its-axis-the-liq</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93791/the-cylindrical-tube-of-a-spray-pump-has-a-cross-section-of-8-c-m-2-one-end-of-w</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93792/a-spherical-drop-of-water-has-radius-1-mm-if-the-surface-tension-of-water-is-70</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93793/a-wooden-stick-of-length-l-radius-r-and-density-has-a-small-metal-piece-of-mass</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93794/a-slender-homogeneous-rod-of-length-2l-floats-partly-immersed-in-water-being-sup</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93795/a-concrete-sphere-of-the-radius-r-has-a-cavity-of-radius-r-which-is-packed-with</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93796/a-vessel-contains-oil-density-0-8-g-m-cm-3-over-mercury-density-13-6-g-m-cm-3-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93797/a-tube-of-length-l-and-radius-r-carries-a-steady-flow-of-fluid-whose-density-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93798/a-bucket-contains-water-filled-upto-a-height-15-cm-the-bucket-is-tied-to-a-rope</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93799/two-metal-strips-are-riveted-together-at-their-ends-by-four-rivets-each-of-diame</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93800/a-solid-sphere-made-out-of-metal-having-a-bulk-modulus-of-2-10-11-nm-2-is-charge</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93801/a-cube-of-aluminium-of-side-6-and-160-cm-is-subjected-to-a-tangential-force-such</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93802/a-stone-of-mass-1-3-and-160-kg-is-being-rotated-in-a-horizontal-plane-as-a-conic</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93803/a-uniform-rod-of-length-l-is-acted-upon-by-a-force-f-in-a-gravity-free-region-as</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93804/a-particular-force-f-applied-on-a-wire-increases-its-length-by-2-10-3-m-if-we-we</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93805/one-of-the-square-faces-of-a-metal-slab-of-side-50-and-160-cm-and-thickness-20-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93806/two-wires-of-the-same-material-young-s-modulus-y-and-same-length-l-but-radii-r-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93807/a-thin-rod-of-negligible-mass-and-area-of-cross-section-4-10-6-m-2-suspended-ver</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93808/a-wire-fixed-to-the-ceiling-at-one-end-is-being-pulled-slowly-by-a-force-f-at-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93809/the-elastic-limit-of-brass-is-379-m-p-a-the-minimum-diameter-of-a-brass-rod-if-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93810/a-heavy-plank-of-mass-100-kg-hangs-on-three-vertical-wires-of-equal-length-arran</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93811/two-blocks-of-masses-5-kg-and-10-kg-are-connected-by-a-metal-wire-going-over-a-s</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93812/a-bottle-has-an-opening-of-radius-a-and-length-b-a-cork-of-length-b-and-radius-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93813/a-wire-suspended-vertically-from-one-of-its-ends-is-stretched-by-attaching-a-wei</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93814/there-is-no-change-in-the-volume-of-a-wire-due-to-the-change-in-its-length-on-st</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93815/a-body-of-mass-m-10-k-g-is-attached-to-one-end-of-a-wire-of-length-0-3-m-what-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93816/a-steel-rod-is-projecting-out-of-a-rigid-wall-the-shearing-strength-of-steel-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/93819/a-sphere-of-radius-0-1-and-160-m-and-mass-8-and-960-and-160-kg-is-attached-to-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93820/one-end-of-a-long-metallic-wire-of-length-l-is-tied-to-the-ceiling-the-other-end</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93821/a-rigid-bar-of-mass-15-kg-is-supported-symmetrically-by-three-wires-each-of-leng</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/93824/a-wire-of-cross-sectional-area-a-is-stretched-horizontally-between-two-clamps-lo</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93825/when-a-metallic-wire-is-held-under-a-tensile-force-f-1-the-length-of-the-wire-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93826/a-load-of-31-4-kg-is-suspended-from-a-wire-of-radius-10-3-m-and-density-9-10-3-k</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93827/32-g-of-o-2-is-contained-in-a-cubical-container-of-side-1-m-and-maintained-at-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93828/there-is-some-change-in-length-when-a-33000-n-tensile-force-is-applied-on-a-stee</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93829/a-solid-sphere-of-radius-r-made-up-of-a-material-of-bulk-modulus-k-is-surrounded</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93830/two-wires-of-diameter-0-25-cm-one-made-of-steel-and-other-made-of-brass-are-load</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93831/an-open-cylindrical-vessel-filled-with-water-is-rotated-together-with-water-at-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93832/a-sphere-of-radius-0-1-and-160-m-and-mass-8-and-960-and-160-kg-is-attached-to-th</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93833/the-edge-of-an-aluminium-cube-is-10-cm-long-one-face-of-the-cube-is-firmly-fixed</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93834/a-particle-goes-from-a-to-b-with-a-speed-of-40-km-h-and-b-to-c-with-a-speed-of-6</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/93835/two-trains-a-and-b-of-length-400-m-each-are-moving-on-two-parallel-tracks-with-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/94253/an-object-and-a-concave-mirror-are-approaching-each-other-with-velocities-10-m-s</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94254/a-narrow-parallel-beam-of-light-is-incident-on-a-transparent-sphere-of-refractiv</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94255/a-ray-of-light-travelling-in-medium-a-is-incident-on-plane-interface-of-two-medi</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94256/a-glass-rod-of-rectangular-cross-section-is-bent-into-the-shape-shown-in-the-fig</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94257/a-plano-convex-lens-1-5-has-maximum-thickness-of-1-mm-if-the-diameter-of-its-ape</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94258/an-observer-whose-least-distance-of-distinct-vision-is-d-views-his-own-face-in-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94259/a-plane-glass-plate-is-placed-over-various-coloured-letters-violet-green-yellow</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94260/image-of-an-object-approaching-a-convex-mirror-of-radius-of-curvature-20-m-along</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94261/an-astronomical-telescope-has-objective-and-eyepiece-of-focal-lengths-40-cm-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94262/the-x-z-plane-separates-two-media-a-and-b-of-refractive-indices-n-1-1-5-and-n-2</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94263/a-thin-plano-convex-lens-fits-exactly-into-a-plano-concave-lens-with-their-plane</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94264/an-object-is-kept-at-a-distance-of-16-cm-from-a-thin-lens-and-the-image-formed-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94265/a-diminished-image-of-an-object-is-to-be-obtained-on-a-screen-1-0-m-away-from-it</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94266/a-thin-glass-refractive-index-1-5-lens-has-an-optical-power-of-5-d-in-the-air-it</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94267/the-image-of-a-small-electric-bulb-fixed-on-the-wall-of-a-room-is-to-be-obtained</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94268/a-lens-is-made-of-flint-glass-refractive-index-1-5-when-the-lens-is-immersed-in</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94269/a-point-object-o-is-placed-on-the-principal-axis-of-a-convex-lens-of-focal-lengt</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94270/a-thin-biconvex-lens-of-refractive-index-3-2-is-placed-on-a-horizontal-plane-mir</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94271/an-object-is-placed-at-a-distance-of-15-cm-from-a-convex-lens-of-focal-length-10</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94272/when-a-mass-is-rotated-in-a-plane-about-a-fixed-point-its-angular-momentum-is-di</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94273/a-chain-of-mass-m-forming-a-circle-of-radius-r-is-slipped-on-a-smooth-round-cone</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94274/the-moment-of-inertia-of-a-rigid-body-in-terms-of-its-angular-momentum-l-and-kin</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94275/a-solid-sphere-of-radius-r-and-mass-m-is-rolled-by-a-force-f-acting-at-the-top-o</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94276/a-uniform-rod-of-mass-m-1-is-hinged-at-its-upper-end-as-shown-in-the-figure-a-pa</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94277/in-the-given-arrangement-the-rod-is-free-to-rotate-about-the-hinge-and-it-is-in</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94278/a-uniform-rod-a-b-is-hinged-at-its-end-a-and-the-other-end-of-the-rod-is-connect</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94279/the-toy-top-initially-at-rest-shown-in-the-figure-has-a-moment-of-inertia-4-10-4</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94280/a-circular-platform-is-free-to-rotate-in-a-horizontal-plane-about-a-vertical-axi</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94281/four-solid-spheres-each-of-mass-m-and-radius-r-are-placed-at-four-corners-of-a-l</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94282/a-bar-of-mass-m-and-length-l-is-in-pure-translational-motion-with-its-centre-of</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94283/a-solid-cylinder-is-given-a-velocity-v-0-and-an-angular-speed-and-969-0-in-the-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94284/a-uniform-cubical-box-of-side-a-is-placed-on-a-rough-floor-and-it-is-to-be-moved</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94285/a-uniform-rod-of-length-l-is-free-to-rotate-in-a-vertical-plane-about-a-fixed-ho</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94286/two-beads-each-of-mass-m-are-fixed-on-a-light-rigid-rod-of-length-2-l-which-is-f</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94287/a-motor-generates-an-output-power-of-220-w-at-an-angular-velocity-of-2100-rpm-ca</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94288/a-nonuniform-rod-o-m-of-length-l-has-linear-mass-density-that-varies-with-the-di</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94289/three-solid-spheres-each-of-mass-m-and-diameter-d-are-stuck-together-such-that-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94290/a-sphere-is-rotating-between-two-rough-inclined-walls-as-shown-in-figure-coeffic</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94291/in-a-continuous-printing-process-paper-roll-is-wrapped-on-a-cylindrical-core-whi</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94292/a-disc-of-mass-m-and-radius-r-is-attached-to-a-rectangular-plate-of-the-same-mas</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94293/a-door-1-6-m-wide-requires-a-minimum-force-of-1-n-to-be-applied-at-the-free-end</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94294/a-uniform-thin-hemispherical-shell-is-kept-at-rest-and-in-equilibrium-on-an-incl</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94295/four-holes-of-radius-r-are-cut-from-a-thin-square-plate-of-side-4-r-and-mass-m-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94296/a-uniform-ball-of-radius-r-rolls-without-slipping-down-from-the-top-of-a-sphere</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94297/in-the-diagram-shown-a-rod-of-mass-m-has-been-fixed-on-a-ring-of-the-same-mass-t</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94298/a-solid-sphere-of-radius-r-is-gently-placed-on-a-rough-horizontal-surface-with-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94299/a-spool-of-mass-m-and-radius-2-r-lies-on-an-inclined-plane-as-shown-in-figure-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94300/a-t-shaped-uniform-density-object-with-dimensions-shown-in-the-figure-is-lying-o</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94301/a-metre-stick-is-balanced-on-a-knife-edge-at-its-centre-when-two-coins-each-of-m</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94302/a-disc-of-radius-r-rolls-without-slipping-at-a-speed-v-along-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/94303/the-figure-shows-a-fixed-incline-plane-on-which-a-plank-is-being-pulled-upwards</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94304/a-block-of-mass-m-is-attached-to-one-end-of-a-light-string-which-is-wrapped-on-a</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94305/a-disc-of-mass-2-kg-and-radius-0-2-m-is-rotating-with-an-angular-velocity-of-30</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94306/a-solid-spherical-ball-of-radius-5-9-m-is-connected-to-a-point-a-on-the-wall-wit</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94307/four-solid-spheres-each-of-diameter-5-cm-and-mass-0-5-kg-are-placed-with-their-c</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94308/a-lamina-is-made-by-removing-a-small-disc-of-diameter-2-r-from-a-bigger-disc-of</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94309/a-solid-spherical-ball-of-mass-m-is-released-from-the-topmost-point-of-the-shown</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94310/a-solid-cylinder-is-kept-on-one-edge-of-a-plank-of-same-mass-and-length-25-m-pla</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94311/a-thin-circular-metal-disc-of-the-radius-500-mm-is-set-rotating-about-a-central</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94312/a-small-ball-of-mass-m-and-radius-r-r-10-rolls-without-slipping-along-the-track</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94313/a-solid-cylinder-is-made-of-radius-r-and-height-3r-having-mass-density-now-two-h</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/94315/a-uniform-rod-ab-of-mass-2-kg-and-length-1-m-is-placed-on-a-sharp-support-o-such</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94316/a-merry-go-round-is-at-rest-pivoted-on-a-frictionless-axis-a-child-of-mass-m-run</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/94318/the-pulley-system-shown-in-the-figure-has-two-pulleys-of-radii-2-m-and-1-m-respe</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94319/an-equilateral-prism-of-mass-m-rests-on-a-rough-horizontal-surface-with-a-coeffi</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94320/two-uniform-discs-a-and-b-of-equal-radii-but-having-different-masses-1-and-160-k</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94321/a-thin-uniform-equilateral-plate-rests-in-a-vertical-plane-with-one-of-its-verte</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94322/a-spool-of-mass-m-3-kg-and-radius-r-20-cm-has-an-axle-of-radius-r-10-cm-around-w</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94323/a-uniform-solid-sphere-of-mass-m-and-radius-r-is-lying-on-a-rough-horizontal-pla</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94324/a-particle-of-mass-m-moves-in-the-x-y-plane-with-a-velocity-v-along-the-straight</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94325/a-particle-of-mass-m-is-projected-at-t-0-from-a-point-o-on-the-ground-with-a-spe</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94326/a-uniform-rod-ab-of-length-l-and-mass-m-is-free-to-rotate-about-point-a-the-rod</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94327/one-fourth-length-of-a-uniform-rod-is-placed-on-a-rough-horizontal-surface-and-i</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94328/two-loops-p-and-q-are-made-from-a-uniform-wire-the-radii-of-p-and-q-are-r-1-and</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94329/a-bullet-of-mass-10-g-and-speed-500-m-s-1-is-fired-into-a-door-and-gets-embedded</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94330/a-uniform-smooth-rod-mass-m-and-length-l-placed-on-a-smooth-horizontal-floor-is</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
  <url><loc>https://www.quantrexacademy.com/q/94331/a-smooth-rod-o-p-is-fixed-vertically-a-disc-of-mass-m-and-radius-r-is-rolling-wi</loc><lastmod>2026-08-30</lastmod><changefreq>weekly</changefreq><priority>0.8</priority></url>
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