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`

Question

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`

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`

Monjur Alahi

4 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
`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`

4 views Answered 2023-02-05 15:29