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)]!)` .

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

In the expansion of (x^3-1/x^2)^n, n in N if sum of the coefficients of x^5 and x^(10) is 0 then n is

Prove that the coefficient of x^n in the expansion of (1+x)^2n is twice the coefficient of x^n in the expansion of (1+x)^2n-1 .

If the sum of the coefficients in the expansion of (1 -3x + 10x^2)^(n) is a and the sum of the coefficients in the expansion of (1 - x^(2))^(n) is b , then

In the expansion of [(1+x)//(1-x)]^2, the coefficient of x^n will be 4n b. 4n-3 c. 4n+1 d. none of these

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

In the expansion of (x^2+1+1/(x^2))^n ,n in N , (a)number of terms is 2n+1 (b)coefficient of constant terms is 2^(n-1) (c)coefficient of x^(2n-1)i sn (d)coefficient of x^2 in n