Question

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

Answer 1

Correct Answer - A
To get sum of coefficients put `x = 0` Given that sum of coefficient is
`2^(n) = 64`
or `n = 6`
The greatest binomial coefficeint is `.^(6)C_(3)`.
No given that
`T_(4) - T_(3) = 6-1 = 5`
`rArr .^(6)C_(3) (3^(-x//4))^(3)(3^(5x//4))^(3)-.^(6)C_(2)(3^(-x//4))^(4)(3^(5x//4))^(2) = 5`.
Which is satisfied by `x = 0`