JEE Main 2022 · 29 Jun · Shift 2, Mathematics question 27

Let the coefficients of $x^{-1}$ and $x^{-3}$ in the expansion of $\left(2x^{\frac15}-\dfrac1{x^{\frac15}}\right)^{15}$, $x>0$, be $m$ and $n$ respectively. If $r$ is a positive integer such that $mn^2={}^{15}C_r\cdot2^r$, then the value of $r$ is equal to ______.