A uniform cylinder of height h and radius r is placed with its circular face on a rough in inclined plane and the inclination of the plane to the horizontal is gradually increased. If $\mathrm{\mu }$ is the coefficient of friction

The cylinder will slide if $\mathrm{mgsin}\mathrm{\theta }\ge \mathrm{\mu mgcos}\mathrm{\theta }\Rightarrow \tan \mathrm{\theta }>\mathrm{\mu }$
The cylinder will topple if $(\mathrm{mgsin}\mathrm{\theta })\frac{\mathrm{h}}{2}>(\mathrm{mgcos}\mathrm{\theta })\mathrm{r}\Rightarrow \tan \mathrm{\theta }>\frac{2\mathrm{r}}{\mathrm{h}}$
$\therefore$Condition for sliding is $\tan \mathrm{\theta }>\mathrm{\mu }$ and condition of toppling is $\tan \mathrm{\theta }>\frac{2\mathrm{r}}{\mathrm{h}}$. 

Hence the cylinder will topple before toppling if $\mathrm{\mu }>\frac{2\mathrm{r}}{\mathrm{h}}$, Similarly the cylinder will slide before toppling if $\mathrm{\mu }<\frac{2\mathrm{r}}{\mathrm{h}}$