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If n is a positive integer and if (1+x+...

If n is a positive integer and if `(1+x+x^(2))^(2n)=underset(r=0)overset(2n)(sum)a_(r)x^(r)`, then

A

`a_(r)=a_(2n-r),` for `0 le r le 2n`

B

`a_(0)+a_(1)+ . . .+a_(n-1)=(1)/(2)(3^(n)-a_(n))`

C

`a_(0)^(2)-a_(1)^(2)+a_(2)^(2)-a_(3)^(2)+ . . . .+2_(2n)^(2)=a_(n)`

D

`a_(0)+a_(2)+ . . .+a_(2n)=(1)/(2)(3^(n)+1)`

Text Solution

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The correct Answer is:
A, B, C, D
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