Co-efficient of `x^n` in the expansion

Find the Co-efficient of x^(4) in the expansion of (1+x^(3))^(50)(x^(2)+1/x)^(5) .

Find the co-efficient of x^(2) in the expansion of (x + 2)^(6) .

Find the co-efficient of x^(4) in the expansion of (3-4x+x^(2))/e^(2x) .

Find the co-efficient of x^(5) in the expansion of (1+x^(2))^(5)(1+x)^(4)

Find the co-efficient of x^4 in the expansion of (2x^2+1/x)^20 .

The co-efficient of x^(5) in the expansion of (1+x)^(21)+(1+x)^(22)+(1+x)^(23)+....+(1+x)^(30)

'Prove that the co-efficient of x^n of the expansion of (1+x)^(2n) is the double of the coefficient of x^n of the expansion of '(1+x)^(2n-1)'

The co-efficient of x in the expansion of (1-x+2x^(2))^(11) is

The co-efficient of x^(401) in the expansion of (1+x+x^(2)+.....+x^(9))^(-1),(|x| lt 1) is