Find the coefficient of `x^(r)` in the following expression :
`(x+n)^(n)+(x+2)^(n-1)(x+1)+(x+2)^(n-2)(x+1)^(2)+.....+(x+1)^(n)`

Find the coefficient of x^(r) in the expansion of (x+4)^(n)+(x+4)^(n-1)(x+3)+(x+4)^(n-2)(x+3)^(2)+.....+(x+3)^(n)

Find the coefficient of x^(r) in the expansion of n of 1+(1+x)+(1+x)^(2)+......+(1+x)^(n)

Coefficient of x^(n-1) in the expansion of.(x+3)^(n)+(x+3)^(n-1)(x+2)+(x+3)^(n-2)(x+2)^(2)+.........+(x+2)^(n) is :

The coefficients of x^(n) in the expansion of (1+x)^(2n) and (1+x)^(2n-1) are in the ratio

Find the sum (x+2)^(n-1)+(x+2)^(n-2)(x+1)^+(x+2)^(n-3)(x+1)^2++(x+1)^(n-1)

The coefficients fo x^(n) in the expansion of (1+x)^(2n) and (1+x)^(2n-1) are in the ratio

The coefficient of x^n in the expansion of (1+x)^(2n) and (1+x)^(2n-1) are in the ratio.

The coefficient of x^r[0lt=rlt=(n-1)] in the expansion of (x+3)^(n-1)+(x+3)^(n-2)(x+2)+(x+3)^(n-3)(x+2)^2+.... +(x+2)^(n-1) is a.^n C_r(3^r-2^n) b.^n C_r(3^(n-r)-2^(n-r)) c.^n C_r(3^r+2^(n-r)) d. none of these