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The coefficient of x^70 in the product (...

The coefficient of `x^70` in the product `(x-1)(x^2-2)(x^3-3)....(x^12-12)` is (a) `4`. (b) `6` (c) `8` (d) `12`

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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