If the term independent of x in the (sqr...

If the term independent of `x` in the `(sqrt(x)-k/(x^2))^(10)` is 405, then `k` equals `2,-2` b. `3,-3` c. `4,-4` d. `1,-1`

A

`2,-2`

B

`3,-3`

C

`4,-4`

D

`1,-1`

Text Solution

Verified by Experts

The correct Answer is:

B

`T_(r+1) = .^(10)C_(r)(sqrt(x))^(10-r) ((-k)/(x^(2)))^(r) = .^(10)C_(r)x^(5-5r//2)(-k)^(r)`
For this to be important of x,r must be 2, so these
`.^(10)C_(2)k^(2) = 405` or `k = +-3`

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