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For n ∈ N , in the expansion of x - 3 4 + a x 5 4 n , the sum of all the binomial coefficients lie between 200 and 400. Also, the term independent of x is 448, then the value of a is

Correct answer

2

Step-by-step solution

200 < n C 0 + n C 1 + … + n C n < 400 ⇒ 200 < 2 n < 400 ⇒ n = 8 T r + 1 = 8 C r x - 3 4 8 - r a x 5 4 r ⇒ T r + 1 = 8 C r a r x 2 r - 6 For this term to be independent of x , 2 r - 6 = 0 ⇒ r = 3 T 4 = 8 C 3 a 3 ⇒ 448 = 56 a 3 ⇒ a 3 = 8 ⇒ a = 2

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