Let m and n be the coefficients of seventh and thirteenth terms respectively in the expansion of 1 3 x 1 3 + 1 2 x 2 3 18 . Then n m 1 3 is:

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Correct answer: D. 9 4

Given expansion is 1 3 x 1 3 + 1 2 x 2 3 18 . ⇒ T 7 = C 6 18 1 3 x 1 3 12 1 2 x 2 3 6 ⇒ m = C 6 18 1 3 12 1 2 6 ⇒ T 13 = C 12 18 1 3 x 1 3 6 1 2 x 2 3 12 ⇒ n = C 12 18 1 3 6 1 2 12 ⇒ m n = C 6 18 1 3 12 1 2 6 C 12 18 1 3 6 1 2 12 ⇒ m n = 1 3 6 1 2 6 ⇒ m n = 2 3 6 ⇒ m n 1 3 = 4 9 ⇒ n m 1 3 = 9 4

Let m and n be the coefficients of seventh and thirteenth terms respectively in the expansion of 1 3 x 1 3 + 1 2 x 2 3 18 . Then n m 1 3 is:

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