Question

Coefficient of `x^(2009)` in `(1+x+x^(2)+x^(3)+x^(4))^(1001) (1-x)^(1002)` is
A. `0`
B. `4."^(1001)C_(501)`
C. `-2009`
D. none of these

Answer 1

Correct Answer - A
`(a)` `(1+x+x^(2)+x^(3)+x^(4))^(1001)(1-x)^(1002)`
`((1-x^(5))/(1-x))^(1001)(1-x)^(1002)=(1-x)(1-x^(5))^(1001`, so all the powers of `x` will be of the `5m` or `5m+1(m in I)`
So coefficient of `x^(2009)` will be `0`