If `(1 + x + x^(2) + x^(3))^(n) = a_(0) + a_(1)x + a_(2)x^(2)+"……….."a_(3n)x^(3n)` then which of following are correct

Options

A. `a_(0) + a_(1) + a_(2) +……+a_(3n) = 2^(2n)`
B. `a_(0) + a_(2) + a_(4) +"……"= a_(1) + a_(3) + a_(5) +"…….."`
C. `a_(0) = a_(3n), a_(1) = a_(3n - 1), a_(2) = a_(3n - 2)`
D. `a_(0) + a_(2) + a_(4) + "……." = 2^(2n - 1)`

Answer

A, B, D

Explanation

Put `x = 1` to get
`4^(n) = a_(0) + a_(1) + a_(2) + "………" + a_(3n)"………"`
Put `x = -1` to get
`rArr a_(0) + a_(2) + a_(4) "…….." = a_(1) + a_(3) + a_(5) "……"`