In the expansion of `(1+3x+2x^2)^6` , the coefficient of `x^(11)` is a. 144 b. 288 c. 216 d. 576

In the expansion of (2x + 3)^(5) the coefficient of x^(2) is:

In the expansion of (1+x+x^3+x^4)^10, the coefficient of x^4 is ^40 C_4 b. ^10 C_4 c. 210 d. 310

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

Statement 1: In the expansion of (1+x)^(41)(1-x+x^2)^(40), the coefficient of x^(85) is zero. Statement 2: In the expansion of (1+x)^(41)a n d(1-x+x^2)^(40), x^(85) term does not occur.

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 .

The middle term in the expansion of (x//2+2)^8 is 1120, then x in R is equal to a. -2 b. 3 c. -3 d. 2

Coefficient of x^(11) in the expansion of (1+x^2)^4(1+x^3)^7(1+x^4)^(12) is 1051 b. 1106 c. 1113 d. 1120

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