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The coefficient of x 9 in the expansion of x 3 + 1 2 l o g 2 x 3 2 11 is equal to

Options

  1. A- 5
  2. B330
  3. C520
  4. D5 + l o g 2 3

Correct answer

B. 330

Step-by-step solution

l o g 2 x 3 2 = l o g 2 1 2 x 3 2 = 3 2 1 2 l o g 2 x = l o g 2 x 3 ⇒ 2 l o g 2 x 3 2 = 2 l o g 2 x 3 = x 3 We consider the expansion of x 3 + 1 x 3 11 . t r + 1 = 11 C r x 3 11 - r 1 x 3 r = 11 C r x 33 - 3 r - 3 r = 11 C r x 33 - 6 r For the coefficient of x 9 , we get 33 - 6 r = 9 ⇒ 6 r = 24 ⇒ r = 4 . Thus, the coefficient of x 9 is 11 C 4 = 11 × 10 × 9 3 × 8 4 × 3 × 2 = 330 .

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