Question

The coefficient of `x^(7)` in the expansion of `(1-x-x^(3)+x^(4))^(8)` is equal to
A. `-648`
B. `792`
C. `-792`
D. `648`

Answer 1

Correct Answer - C
`(1-x-x^(2)+x^(4))^(8)=(1-x)^(8)(1-x^(3))^(8)`
`= (1-.^(8)C_(1)x+.^(8)C_(1)x^(2)-.^(8)C_(3)x^(3)+"….")xx(1-.^(8)C_(1)x^(3)+.^(8)C_(2)x^(6)-.^(8)C_(3)x^(9)+"…..")`
`:.` Coefficient of `x^(7)= -.^(8)C_(7)-.^(8)C_(1)xx.^(8)C_(4)-.^(8)C_(1) xx.^(8)C_(2)`
`= - 792`