A block kept on a rough inclined plane, as shown in the figure, remains at rest upto a maximum force 2 N…

$2+mg\sin \theta =\mu mg\cos \theta$

$mg\sin \theta -\mu mg\cos \theta =2 ........\left(1\right)$
$mg\sin \theta + \mu mg\cos \theta =10 .......\left(2\right)$

equation (1) devided by (2)

$\frac{mg \left({sin}\theta -\mu {cos}\theta \right)}{mg \left({sin}\theta + \mu {cos}\theta \right)}=\frac{-2}{10}=\frac{-1}{5}$

$\left(1-\mu \sqrt{3}\right)5=-\left(1+\mu \sqrt{3}\right)$

$6=4\sqrt{3} \mu$

$\mu =\frac{\sqrt{3}}{2}$