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In the expansion of (3^(-x//4)+3^(5x//4)...

In the expansion of `(3^(-x//4)+3^(5x//4))^(pi)` the sum of binomial coefficient is 64 and term with the greatest binomial coefficient exceeds the third by `(n-1)` , the value of `x` must be `0` b. `1` c. `2` d. `3`

A

`x` is integer

B

value of `n` is `4`

C

`n` is a composite number

D

`n` and `x` are so prime

Text Solution

Verified by Experts

The correct Answer is:
A, C, D
Given that sum of all binomical coefficient is `64` so putting
`3^(-x//4) = 3^(9x//4) = 1`.
`(1+1)^(n)=64 :. 2n^(2) = 64 :. n = 6`
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