The theorem of perpendicular axes is applicable to which type of body?

$A$ thin wire of length $l$ having linear mass density $\rho$ is bent into a circular loop with $C$ as its centre, as shown in the figure. The moment of inertia of the loop about the line $AB$ is

The moment of inertia of a solid cylinder of mass $M$, length $L = 2R$ and radius $R$ about an axis passing through the centre of mass and perpendicular to the axis of the cylinder is $I_1$, and about an axis passing through one end of the cylinder and perpendicular to the axis of the cylinder is $I_2$. Then:

The moment of inertia of a uniform hollow hemisphere about the given axes $I_A$ and $I_B$ is:

$A$ thin uniform rod has mass $M$ and length $L$. The moment of inertia about an axis perpendicular to it and passing through the point at a distance $\frac{L}{3}$ from one of its ends,will be

State and prove the theorem of perpendicular axes and the theorem of parallel axes.