Moment of Inertia Questions

One solid sphere $A$ and another hollow sphere $B$ are of same mass and same outer radii. Their moment of inertia about their diameters are respectively $I_A$ and $I_B$ such that:

Four point masses, each of value $m$, are placed at the corners of a square $ABCD$ of side $\ell$. The moment of inertia through $A$ and parallel to $BD$ is:

For a given uniform square lamina $ABCD$ with centre $O$, let $I_{AC}$ and $I_{EF}$ be the moments of inertia about the diagonal $AC$ and the line $EF$ passing through $O$ and parallel to side $AB$ respectively. Then:

The moment of inertia of a uniform semicircular disc of mass $M$ and radius $r$ about a line perpendicular to the plane of the disc through the centre is:

A circular disc $X$ of radius $R$ is made from an iron plate of thickness $t$, and another disc $Y$ of radius $4R$ is made from an iron plate of thickness $t/4$. The relation between the moment of inertia $I_X$ and $I_Y$ is:

Consider a uniform square plate of side ‘$a$ ’ and mass ‘$m$ ’. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is: