The middle term in the expansion of `(1-3x+3x^2-x^3)^(2n)` is

Options

A. `((6n)!x^(n))/((3n)!(3n)!)`
B. `((6n)!x^(3n))/((3n)!)`
C. `((6n))/((3n)!(3n)!)(-x)^(3n)`
D. None of these

Answer

C

Explanation

`(c )` `(1-3x+3x^(2)-x^(3))^(2n)=(1-x)^(6n)`
middle term is `((6n)/(2)+1)^(th)`
i.e., `(3n+1)^(th)` term is middle term,
`T_(3n+1)=^(6n)C_(3n)(-x)^(3n)=(6n!)/(3n!3n!)(-x)^(3n)`