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The coefficient of x^5 in the expansion ...

The coefficient of `x^5` in the expansion of `(1+x^2)(1+x)^4` is

A

`12`

B

`5`

C

`4`

D

`56`

Text Solution

Verified by Experts

The correct Answer is:
C
`(1+x)^(21) + (1+x)^(22)+"……"+(1+x)^(30)`
`=(1+x)^(21)[((1+x)^(10)-1)/((1+x)-1)]=1/x[(1+x)^(3!)-(1+x)^(21)]`
`rArr` Coefficient of `x^(5)` in the given expression.
`=` Coefficient of `x^(5)` in `{(1)/(x)[(1+x)^(31)-(1+x)^(21)]}`
`=` Coefficient of `x^(6)` in `[(1+x)^(31)-(1+x)^(21)]`
`= .^(31)C_(6)- .^(21)C_(6)`
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