Find the coefficient of `x^n` in the expansion of: `(a+bx+cx^2)/e^x` .

Find the coefficient of x^4 in the expansion of (2-x+3x^2)^6dot

Find the coefficient of x^5 in the expansion of (x+3)^6 is :

Find the coefficient of x^8 in the expansion of (x^2-1/x)^(10)

The coefficient of x in the expansion of (x+3)^3 is

Find the coefficient of x^10 in the expansion of : (1+x+x^2+x^3 +.....+ x^10)^4 .

Find the coefficient of x^7 in the expansion of (1 - x -x^2 + x^3)^(6)dot

Find the coefficient of x^5 in the expansion of : (1 + 2x)^6 (1- x)^7 using binomial theorem.

Find the coefficient of x^5 in the expansion of : (1 + x)^21+ (1 + x)^22+ .............+ (1 + x)^30 .

Find the coefficient of x^(n-r) in the expansion of (x+1)^n (1+x)^n . Deduce that C_0C_r+C_1C_(r-1)+......+C_(n-r) C_n= ((2n!))/((n+r)!(n-r)!) .

Find the coefficient of x^n in the expansion of e^(a+bx) in powers of x.