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JEE Main202126 Feb 2021Morning ShiftMathematicsBinomial TheoremActual

The maximum value of the term independent of t in the expansion of t x 1 5 + 1 - x 1 10 t 10 where x ∈ 0 , 1 is:

Options

  1. A10 ! 3 5 ! 2
  2. B10 ! 3 5 ! 2
  3. C2 . 10 ! 3 3 5 ! 2
  4. D2 . 10 ! 3 5 ! 2

Correct answer

C. 2 . 10 ! 3 3 5 ! 2

Step-by-step solution

T r + 1 = C r 10 t x 1 / 5 10 - r 1 - x 1 10 t r = C r 10 t 10 - 2 r x 10 - r 5 1 - x r 10 For the term independent of t , ⇒ 10 - 2 r = 0 ⇒ r = 5 T 6 = f x = C 5 10 x 1 - x ; for maximum f ' x = 0 ⇒ x = 2 3 & f ' ' 2 3 < 0 so f x m a x . = C 5 10 2 3 · 1 3 = 2 . 10 ! 3 3 5 ! 2

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