By what minimum angle the mirror must be rotated anticlockwise such that the reflected ray will become vertical?

The correct option is B ${15}^{\circ }$

From the above figure, reflected ray must be rotated by ${30}^{\circ }$ anticlockwise to make it vertical.
We know that when a mirror is rotated by an angle $\theta$ (say anti-clockwise), keeping the incident ray fixed then
the reflected ray rotates by $2\theta$ along the same direction, i.e. anti-clockwise.
$\therefore 2\theta ={30}^{\circ }$
$\Rightarrow \theta =\frac{{30}^{\circ }}{2}={15}^{\circ }$ anticlockwise
Hence, option $\left(b\right)$ is the correct answer.