The term independent of `a` in the expansion of `(1+sqrt(a)+1/(sqrt(a)-1))^(-30)i s` `^30 C_(20)` b. `0` c. `^30 C_(10)` d. none of these

Options

A. `.^(30)C_(20)`
B. `0`
C. `.^(30)C_(10)`
D. none of these

Answer

B

Explanation

`(1+sqrt(a) + (1)/(sqrt(a)-1))^(-30)`
`= (a/(sqrt(a)-1))^(-30)`
`= ((sqrt(a)-1)/(a))^(30)`
`= (1)/(a^(30)) (1-sqrt(a))^(30)`
`=(1)/(a^(30)){.^(30)C_(0)-.^(30)C_(1)sqrt(a) + "...."+.^(30)C_(30)(sqrt(a))^(30)}`
There is no term independent of a.