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The term independent of x in (1+x+x^(-2)...

The term independent of x in `(1+x+x^(-2)+x^(-3))^(10)` is n then the last digit of `(n+2)^(n)` is

A

1

B

3

C

7

D

9

Text Solution

Verified by Experts

The correct Answer is:
C
`(1+x+(1)/(x^(2))+(1)/(x^(3)))^(10)=((x+x+x^(3)+x^(4)))/(x^(30))`
Coefficient of `x^(30) "in" (1+x+x^(3)+x^(4))^(10)=(1+x)^(10)(1+x^^(3))^(10)`
`=""^(10)C_(10)+""^(10)C_(0)+""^(10)C_(3)+""^(10)C_(8)+""^(10)C_(6)+""^(10)C_(7)""^(10)C_(9)`
`=1+1200+9450+1200`
`=11851`
last digit of `(11853)^(11851)=7`
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