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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`.

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Verified by Experts

The correct Answer is:
6
`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_(2pi//3)(-1)^(2n//3) = 15 = .^(6)C_(4)`
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