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

Question

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

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

Monjur Alahi

5 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - B
`(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.

5 views Answered 2023-02-05 15:29