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The coefficient of x^7 in the expansion ...

The coefficient of `x^7` in the expansion of `(1-x-x^2+x^3)^6` is

A

`4`

B

`6`

C

`8`

D

`12`

Text Solution

Verified by Experts

The correct Answer is:
A
`(a)` The highest power of `x=1+2+3+….+12=78` to get coefficient of `x^(70)`, we have to omit the factors containing `x^(8)`
`(1)` Product of the constant terms of `(x-1)(x^(7)-7)=7`
`(2)` Product of the constant terms of `(x^(2)-2)(x^(6)-6)=12`
`(3)` Product of the constant terms of `(x^(3)-3)(x^(5)-5)=15`
`(4)` Product of the constant terms of `(x-1)(x^(2)-2)(x^(5)-5)=-10`
`(5)` Product of the constant terms of `(x-1)(x^(3)-3)(x^(4)-4)=-12`
Required coefficient `=7+12+15-10-12-8`
`=34-30=4`
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