Let the coefficients of x^-1 and x^-3 in the expansion of (2 x^(1/5)-1/(x^(1/5)))^15, x>0, be m and n respectively. If r is a positive integer such…

Let the coefficients of $\displaystyle x^{-1}$ and $\displaystyle x^{-3}$ in the expansion of $\displaystyle \left(2 x^{\frac{1}{5}}-\frac{1}{x^{\frac{1}{5}}}\right)^{15}, x>0$, be $\displaystyle m$ and $\displaystyle n$ respectively. If $\displaystyle r$ is a positive integer such that $\displaystyle m n^2={ }^{15} C_r \cdot 2^r$, then the value of $\displaystyle r$ is equal to \_\_\_\_.