The moment of inertia of a ring about one of its diameters is $I$. What will be its moment of inertia about a tangent parallel to the diameter?

Suppose there is a uniform circular disc of mass $M$ and radius $r$ shown in the figure. Two shaded circular regions, each of radius $r/4$, are cut out from the disc. The centers of these cut-out discs are at a distance of $3r/4$ from the center of the original disc. The moment of inertia of the remaining part about the axis $A$ (passing through the center of the disc and perpendicular to its plane) is given by $\frac{x}{256} Mr^2$. The value of $x$ is . . . . . . .

$A$ 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 rectangular plate shown in the figure is rotated in turn about $x-x'$,$y-y'$ and $z-z'$ axes passing through its centre of mass $O$. Its moment of inertia is

Will the theorem of perpendicular axis be applicable to a solid sphere?

For the given uniform square lamina $ABCD$,whose centre is $O$,which of the following relations is correct?