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JEE Main2014MathematicsBinomial TheoremActual

If the coefficients of x 3 and x 4 in the expansion of 1 + a x + b x 2 1 - 2 x 18 in powers of x are both zero, then a , b is equal to

Options

  1. A1 4 , 2 7 2 3
  2. B1 6 , 2 7 2 3
  3. C1 6 , 2 5 1 3
  4. D1 4 , 2 5 1 3

Correct answer

B. 1 6 , 2 7 2 3

Step-by-step solution

We have, 1 + a x + b x 2 1 - 2 x 18 = a 0 + a 1 x + a 2 x 2 + . . . . . . . = 1 + ax + bx 2 1 - 18 C 1 · 2 x + 18 C 2 · 2 2 x 2 + ..... 18 C 18 2 x 18 ⇒ a 3 = - 18 C 3 × 8 + 18 C 2 × 4 a - 36 b ⇒ a 4 = 18 C 4 × 16 - 18 C 3 × 8 a + 18 C 2 × 4 × b 102 a - 6 b = 1088     . . . i 64 a - 6 b = 480     . . . i i Solution of the above two equation gives. a = 16 b = 2 7 2 3

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