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The coefficient of x 7 in a x 2 + 1 b x 11 and the coefficient of x - 7 in a x - 1 b x 2 11 are equal, then the value of a b is equal to

Correct answer

1

Step-by-step solution

For a x 2 + 1 b x 11 T r + 1 = C r 11 a x 2 11 - r 1 b x r = C r 11 a 11 - r b - r x 22 - 3 r For x 7 ,   22 - 3 r = 7 ⇒ 3 r = 15 ⇒ r = 5 Coefficient of x 7 = C 11 5 a 6 b - 5 For a x - 1 b x 2 11 T r + 1 = C r 11 a x 11 - r - 1 r 1 b x 2 r = C 11 r a 11 - r b - r - 1 r x 11 - 3 r For x - 7 ,   11 - 3 r = - 7 ⇒ r = 6 ⇒ coefficient of x - 7 = C 11 6 a 5 b - 6 According to the question, C 6 11 a 5 b - 6 = C 5 11 a 6 b - 5 ⇒ a b = 1.

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