The moment of inertia of a uniform semi circular disc of mass M and radius ‘r’ about a line perpendicular to the plane of disc through the centre is

The mass of a circular disc will be double that of a semicircular disc.
the circular disc's moment of inertia at mass 2M is

${\mathrm{I}}_{\mathrm{circulardisc}}=\frac{1}{2}\left(2\mathrm{M}\right){\mathrm{R}}^2$

${\mathrm{I}}_{\mathrm{circulardisc}}={\mathrm{MR}}^2$

Due to symmetry, the semi-circular disc's moment of inertia is half that of the circular disc.

${\mathrm{I}}_{\mathrm{semicirculardisc}}=\frac{1}{2}{\mathrm{I}}_{\mathrm{circulardisc}}=\frac{1}{2}{\mathrm{MR}}^2$

Hence the correct answer is $\frac{1}{2}{\mathrm{MR}}^2.$