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In the binomial expansion of 2 3 + 1 3 3 n , the ratio of the 7 t h term from the beginning to the 7 t h term from the end is 1 : 6 , then the value of n is

Options

  1. A13
  2. B16
  3. C9
  4. D23

Correct answer

C. 9

Step-by-step solution

7 t h term from the beginning is C 6 n 2 n - 6 3 1 3 6 3 7 t h term from the end is C 6 n 1 3 n - 6 3 2 6 3 ⇒ n C 6 2 n 3 - 2 1 3 2 n C 6 2 2 1 3 n 3 - 2 = 1 6 ⇒ 2 n 3 - 4 1 3 4 - n 3 = 1 6 ⇒ 2 × 3 n 3 - 4 = 2 × 3 - 1 ⇒ n = 9

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