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JEE Main202225 Jul 2022Morning ShiftMathematicsBinomial TheoremActual

If the maximum value of the term independent of t in the expansion of t 2 x 1 5 + 1 - x 1 10 t 15 , x ≥ 0 , is K , then 8 K is equal to _____ .

Correct answer

0

Step-by-step solution

Given, t 2 x 1 5 + 1 - x 1 10 t 15 Now r t h term is given by, T r + 1 = C r 15 t 2 x 1 5 15 - r · 1 - x r 10 t r For independent of t , 2 15 - r - r = 0 30 - 2 r - r = 0 ⇒ r = 10 So, Maximum value of C 10 15 x 1 - x will be at x = 1 2 as  d y d x x - x 2 = 1 -2 x   &   1 - 2 x = 0 ⇒ x = 1 2 = C 10 15 1 2 × 1 2 = 3003 4 So, K = 3003 4 and 8 K = 6006

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