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JEE Main2018MathematicsBinomial TheoremActual

The sum of the co-efficient of all odd degree terms in the expansion of x + x 3 - 1 5 + x - x 3 - 1 5 , x > 1 is

Options

  1. A2
  2. B- 1
  3. C0
  4. D1

Correct answer

A. 2

Step-by-step solution

x + x 3 - 1 5 + x - x 3 - 1 5 ,   ( x > 1 ) f x = 2 x 5 +   5 C 2 x 3 x 3 - 1 +   5 C 4 x x 3 - 1 2 Sum of coefficients of odd power of x = f 1 - f - 1 2 f 1 = 2 f - 1 = 2 - 1 +   5 C 2 × 2 -   5 C 4 × 4 f - 1 = 2 - 1 + 20 - 20 = - 2 ⇒ f 1 - f - 1 2 = 2 - - 2 2 = 2

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