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If in the expansion of (x^(3)-(2)/(sqrt(...

If in the expansion of `(x^(3)-(2)/(sqrt(x)))^(n)` a term like `x^(2)` exists and `'n'` is a double digit number, then least value of `'n'` is

A

`10`

B

`11`

C

`12`

D

`13`

Text Solution

Verified by Experts

The correct Answer is:
A
`(a)` Let the term is `T_(r+1)=^(n)C_(r )(x^(3))^(n-r)((-2)/(sqrt(x)))^(r )`
`:.3n-3r-r//2=2impliesn=(4+7r)/(6)`
`:.` Least value of `n` which is double digit `=10`
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