If $\mathrm{f}(x)=2 x^3+\mathrm{m} x^2-13 x+\mathrm{n}$ and 2,3 are the roots of the equation $\mathrm{f}(x)=0$ then the value of $4 m+5 n$ is

The equation $\mathrm{e}^{\sin x}-\mathrm{e}^{-\sin x}=4$ has ̱_________ solutions.

Let $\alpha, \beta$ be the roots of the equation $x^2-\mathrm{p} x+\mathrm{r}=0$ and $\frac{\alpha}{2}, 2 \beta$ be the roots of the equation $x^2-q x+r=0$. Then the value of r is