The coefficient of `x^k`d in the expansion of `1+(1+x)+(1+x_)^2+……+(1+x)^n` is (A) `^nC_k` (B) `^(n+1)C_k` (C) `^(n+1)C_(k+1)` (D) none of these

The co-efficient of x^(k)(0<=k<=n) in the expansion of E=1+(1+x)+(1+x)^(2)+....+(1+x)^(n)

The coefficients of x^n in the expansion of (1+x)6(2n) and (1+x0^(2n-1) are in the rtio of (A) 1:2 (B) 1:3 (C) 3:1 (D) 2:1

If n is not a multiple of 3, then the coefficient of x^(n) in the expansion of log_(e)(1+x+x^(2)) is : (A) (1)/(n)(B)(2)/(n)(C)-(1)/(n)(D)-(2)/(n)

Maximum sum of coefficient in the expansion of (1-x sin theta+x^(2))^(n) is 1 b.2^(n) c.3^(n) d.0

The middle term in the expansion of ((2x)/(3)-(3)/(2x^(2)))^(2n) is ^(2n)C_(n) b.(-1)^(n)2nC_(n)x^(-n) c.^(2n)C_(n)x^(-n)d .none of these

Find the coefficient of x^(k) in 1+(1+x)+(1+x)^(2)+...+(1+x)^(n)(0<=k<=n)

The number of terms in the expansion of (x+1/x+1)^n is (A) 2n (B) 2n+1 (C) 2n-1 (D) none of these

If 4th term in the expansion of (kx+ 1/x)^n is 5/2 then (A) n=8 (B) n=6 (C) k=1/4 (D) k=1/2

The coefficient of 1/x in the expansion of (1+x)^(n)(1+1/x)^(n) is (n!)/((n-1)!(n+1)!) b.((2n)!)/((n-1)!(n+1)!) c.((2n-1)!(2n+1)!)/((2n-1)!(2n+1)!) d.none of these