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)!)/((2n-1)!(2n+1)!)` d. none of these

The coefficient of x^(n) in expansion of (1 + x)(1 - x)^(n) is

If x^m occurs in the expansion (x+1//x^2)^ 2n then the coefficient of x^m is ((2n)!)/((m)!(2n-m)!) b. ((2n)!3!3!)/((2n-m)!) c. ((2n)!)/(((2n-m)/3)!((4n+m)/3)!) d. none of these

Prove that the coefficient of x^n in the expansion of 1/((1-x)(1-2x)(1-3x))i s1/2(3^(n+2)-2^(n+3)+1)dot

If (1+x)^n=C_0+C_1x+C_2x^2++C_n x^n ,t h e nC_0C_2+C_1C_3+C_2C_4++C_(n-2)C_n= ((2n)!)/((n !)^2) b. ((2n)!)/((n-1)!(n+1)!) c. ((2n)!)/((n-2)!(n+2)!) d. none of these

If A and B are co efficients of x^(n) in the expasion of (1+x)^(2n)and(1+x)^(2n-1) respectively then (A)/(B) …………..

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

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

(d^n)/(dx^n)(logx)= (a) ((n-1)!)/(x^n) (b) (n !)/(x^n) (c) ((n-2)!)/(x^n) (d) (-1)^(n-1)((n-1)!)/(x^n)

Find the coefficient of x^n in the polynomial (x+^n C_0)(x+3^n C_1)xx(x+5^n C_2)[x+(2n+1)^n C_n]dot

If x^p occurs in the expansion of (x^2+1//x)^(2n) , prove that its coefficient is ((2n)!)/([1/3(4n-p)]![1/3(2n+p)]!) .