Let α be the constant term in the binomial expansion of x - 6 x 3 2 n , n ≤ 15 . If the sum of the coefficients of the remaining terms in the expansion is 649 and the coefficient of x - n is λ α , then λ is equal to _ _ _ _ _ _ _ _ .

Step-by-step solution

Given, x - 6 x 3 2 n , n ≤ 15 Now r t h term is given by T r + 1 = C r n x 1 2 n - r - 6 x - 3 2 r ⇒ T r + 1 = - 6 r · C r n · x n - r 2 · x - 3 r 2 ⇒ T r + 1 = - 6 r · C r n · x n - 4 r 2 Now we have to take, n = 4 r for constant term so n is divisible by 4 . So, α = C n 4 n - 6 n 4 And sum of all coefficients will be 1 - 6 1 3 2 n = - 5 n Also given, - 5 n - C n 4 n - 6 n 4 = 649 Now by hit and trial we get, n = 4 Hence, α = C 1 4 - 6 4 4 = - 24 Now for coeffic