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JEE Main201910 Apr 2019Morning ShiftMathematicsBinomial TheoremActual

If the coefficients of x 2 and x 3 , are both zero, in the expansion of the expression 1 + a x + b x 2 1 - 3 x 15 , in powers of x , then the ordered pair a , b is equal to

Options

  1. A28 , 315
  2. B- 21 , 714
  3. C28 , 861
  4. D- 54 , 315

Correct answer

A. 28 , 315

Step-by-step solution

1 + a x + b x 2 1 - 3 x 15 = 1 + a x + b x 2 C 0 15 - 15 C 1   3 x   +   15 C 2   3 x 2 - 15 C 3 3 x 3 + … - 15 C 15 3 x 15 ∴   Coefficient of x 2 is:   b . 15 C 0 - 3 . a 15 C 1 + 3 2 . . 15 C 2 = 0 (Given) ⇒ b - 45 a + 945 = 0 . . . . . . i Coefficient of x 3 is: - b . 3 . 15 C 1 + 9 a . 15 C 2 - 27 . 15 C 3 = 0 ⇒   - 45 b + 9 a × 15 2 × 14 1 - 27 × 15 3 × 14 2 × 13 1 = 0 ⇒   - b + 21 a - 273 = 0 ⇒   b - 21 a

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