If the constant term in the binomial expansion of${\left(x^2-\frac{1}{x}\right)}^n$ , $n\in N$ is 15 then the value of n is equal to _____.

$T_{r+1}$ in ${\left(x^2-\frac{1}{x}\right)}^n$ is${ }^n{C}_r{\left(x^2\right)}^{n-r}{\left(-1\right)}^r{x}^{-r}$ 

                            = ${ }^n{C}_r{\left(x\right)}^{2n-3r}{\left(-1\right)}^r$

Constant term = ${ }^n{C}_r{\left(-1\right)}^r$ ,if$2n=3r$ i.e coefficient off $x=0$

Hence${ }^n{C}_{2n/3}{(-1)}^{{ }^{2n/3}}=15\text{}$

${ }^6\text{}{C}_4\Rightarrow n=6$