What is the moment of inertia of a ring of mass $M$ and radius $R$ about the axis $PQ$ as shown in the figure?

The moment of inertia of a solid sphere about an axis parallel to its diameter and at a distance $x$ from it is represented by $I$. Which of the following graphs shows the variation of $I$ with $x$?

$A$ uniform square plate of side $a$ and mass $m$ is given. The moment of inertia of this plate about an axis perpendicular to the plate and passing through one of its corners is .......

$A$ square lamina of side $b$ has the same mass as a disc of radius $R$. The moment of inertia of the two objects about an axis perpendicular to the plane and passing through the centre is equal. The ratio $\frac{b}{R}$ is

The moment of inertia of a disc of mass $M$ and radius $R$ about any of its diameters is $\frac{MR^2}{4}$. The moment of inertia of this disc about an axis normal to the disc and passing through a point on its edge will be $\frac{x}{2} MR^2$. The value of $x$ is $..........$.

The moment of inertia of a thin uniform rod of mass $M$ and length $L$,about an axis perpendicular to the length of the rod and at a distance $L/4$ from one end is: