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JEE Main201912 Apr 2019Morning ShiftMathematicsBinomial TheoremActual

The coefficient of x 18 in the product 1 + x 1 - x 10 1 + x + x 2 9 is

Options

  1. A84
  2. B- 84
  3. C- 126
  4. D126

Correct answer

A. 84

Step-by-step solution

1 + x 1 - x 10 1 + x + x 2 9 = 1 + x 1 - x 1 - x 9 1 + x + x 2 9 = 1 - x 2 1 - x 1 + x + x 2 9 = 1 - x 2 1 - x 3 9 So, Coefficient of x 18 in 1 + x 1 - x 10 1 + x + x 2 9 = Coefficient of x 18 in 1 - x 2 1 - x 3 9 =   Coefficient of x 18 in 1 - x 2 C 0   9 + C 1   9 - x 3 + C 2 - x 3 2 + …   9 = C 6   9 - 1 6 = C 3   9 = 9.8 . 7 1.2 . 3 = 84

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