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If the constant term in the binomial exp...

If the constant term in the binomial expansion of `(x^2-1/x)^n ,n in N` is 15, then find the value of `n`.

A

`6`

B

`9`

C

`12`

D

`15`

Text Solution

Verified by Experts

The correct Answer is:
A
`(a)` For `(x^(2)-(1)/(x))^(n)`
`T_(r+1)=^(n)C_(r )(x^(2))^(n-r)(-1)^(r )x^(-r)=^(n)C_(r )x^(2n-3r)(-1)^(r )`
Constant term `=^(n)C_(r )(-1)^(r )` if `2n=3r` i.e. coefficient of `x=0`
Hence `.^(n)C_(2n//3)(-1)^(2n//3)=15=^(6)C_(4)impliesn=6`
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