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

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 .

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

If the number of terms in the expansion of (1-2/x+4/(x^2))^n , x!=0, is 28, then the sum of the coefficients of all the terms in this expansion, is : (1) 64 (2) 2187 (3) 243 (4) 729

In the expansion of (3^(-x//4)+3^(5x//4))^(n) the sum of binomial coefficient is 64 and term with the greatest binomial coefficient exceeds the third by (n-1) , the value of x must be

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

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

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 the expansion in powers of x of the function 1//[(1-a x)(1-b x)] is a a_0+a_1x+a_2x^2+a_3x^3+ ,then coefficient of x^n is (b^n-a^n)/(b-a) b. (a^n-b^n)/(b-a) c. (b^(n+1)-a^(n+1))/(b-a) d. (a^(n+1)-b^(n+1))/(b-a)

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