The moment of inertia of a uniform circular disc is maximum about an axis perpendicular to the disc and passing through which of the following points?

The moment of inertia of a square frame about an axis passing through its center of mass and perpendicular to its plane is $20 \ kg \cdot m^2$. The moment of inertia about an axis touching its side and lying in the plane of the frame is ........ $kg \cdot m^2$.

Two identical solid spheres each of mass $2\,kg$ and radii $10\,cm$ are fixed at the ends of a light rod. The separation between the centres of the spheres is $40\,cm$. The moment of inertia of the system about an axis perpendicular to the rod passing through its middle point is $........... \times 10^{-3}\,kg\,m^2$.

Moment of inertia of a body about two perpendicular axes $X$ and $Y$ in the plane of the lamina are $20 \text{ kg m}^2$ and $25 \text{ kg m}^2$ respectively. Its moment of inertia about an axis perpendicular to the plane of the lamina and passing through the point of intersection of $X$ and $Y$ axes 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

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 . . . . . . .