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If (1+x+x^(2)+x^(3))^(100)=a(0)+a(1)x+a(...

If `(1+x+x^(2)+x^(3))^(100)=a_(0)+a_(1)x+a_(2)x^(2)+…….+a_(300)x^(300)` then which of the following statement(s) is/are correct ?

A

`a_(1)=100`

B

`a_(0)+a_(1)+a_(2)+…..+a_(300)` is divisible by 1024

C

coefficients equidistant from beginning and end are equal

D

`a_(0)+a_(2)+a_(4)+……..+a_(300)=a_(1)+a_(3)+a_(5)+……+a_(299)`

Text Solution

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