Question

The coefficients of `x^(13)` in the expansion of
` (1 - x)^(5) (1 + x + x^(2) + x^(3) )^(4)` , is
A. 4
B. -4
C. 9
D. none of these

Answer 1

Correct Answer - a
We have,
`(1- x)^(5) (1 + x + x^(2) + x^(3) )^(4)`
`= (1 x)^(5) (1 | x)^(4) (1 | x^(2))^(4)`
` = (1 - x) (1 - x^(2))^(4) (1 + x^(2))^(4)`
` = (1 -x )(1 - x^(4))^(4)`
` = (1 - x) (""^(4)C_(0) - ""^(4)C_(1)x^(4) + ""^(4)C_(2) x^(8) - ""^(4)C_(3)x^(12) + ""^(4)C_(4) x^(16))`
`therefore ` Coefficient of ` x^(13) = ""^(4)C_(3) = 4` .