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JEE Main20198 Apr 2019Morning ShiftMathematicsBinomial TheoremActual

The sum of the co-efficient of all even degree terms in x in the expansion of x + x 3 - 1 6 + x - x 3 - 1 6 , x > 1 is equal to

Options

  1. A2 6
  2. B32
  3. C24
  4. D29

Correct answer

C. 24

Step-by-step solution

x + x 3 - 1 6 + x - x 3 - 1 6 = 2 6 C 0   x 6   +   6 C 2 x 4 x 3 - 1 +   6 C 4   x 2 x 3 - 1 2   +   6 C 6   x 3 - 1 3   = 2 6 C 0   x 6   +   6 C 2   x 7 - x 4 +   6 C 4   x 2 x 6 - 2 x 3 + 1   + 6 C 6   x 9 - 3 x 6 + 3 x 3 - 1   ∴   Sum of the coefficient of even power of x   = 2 6 C 0 - 6 C 2 + 6 C 4 + 6 C 4 - 3 - 6 C 6 = 2 1 - 15 + 15 + 15 - 3 - 1 = 24

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