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99 Percentile Qs Bank for JEE MainMathematicsBinomial Theorem

If L and M are respectively the coefficient of x - 7 in a x + b x 2 11 and the coefficient of x 7 in b x 2 + a x 11 then L + M =

Options

  1. A1 b coefficient   of   x - 6   in   a x + b x 2 12
  2. B1 a coefficient   of   x 6   in   a x 2 + b x 12
  3. Ca coefficient   of   x - 10   in   a x + b x 2 11
  4. Db coefficient   of   x 4   in   a x 2 + b x 11

Correct answer

B. 1 a coefficient   of   x 6   in   a x 2 + b x 12

Step-by-step solution

General term of a + b x 2 is T r + 1 = C r 11 a x 11 - r × b x 2 r ⇒ T r + 1 = C r 11   a 11 - r · b r x 11 - 3 r For coefficient of x - 7 , 11 - 3 r = - 7 ⇒   3 r = 18 ⇒     r = 6 So, T 6 + 1 = C 6 11   a 11 - 6   b 6     x - 7 T r + 1 = C 6 11   a 5 b 6 x - 7 So, L = C 6 11 a 5 b 6 Similarly, general term of b x 2 + a x 11 is T r + 1 = C r 11   b x 2 11 - r × a x r ⇒ T r + 1 = C r 11   b 11 - r × a r × x 22 - 3

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