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The positive value of lambda for which t...

The positive value of `lambda` for which the coefficient of `x^(2)` in the expression `x^(2) (sqrt(x) + (lambda)/(x^(2)))^(10)` is 720 is

A

`2sqrt(2)`

B

3

C

`sqrt(5)`

D

4

Text Solution

Verified by Experts

The correct Answer is:
D
Coefficient of `x^(2)` in `x^(2)(sqrt(x)+(lambda)/(x^(2)))^(10)`
Coefficient of `x^(0)` in `(sqrt(x)+(lambda)/(x^(2)))^(10)=""^(10)C_(2)(sqrt(x))^(8)*((lambda )/(x^(2)))^(2)=""^(10)C_(2) lambda^(2)=720`
`lambda^(2)=(720)/(45)`
`lambda^(2)=16 `
`lambda =pm4 `
`lambda=4`
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