The moment of inertia of a thin circular disc about an axis passing through its centre and perpendicular to its plane is $I$. Then, the moment of inertia of the disc about an axis parallel to its diameter and touching the edge of the rim 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 $..........$.

Consider a uniform square plate of mass $m$ and side length $a$. What is the moment of inertia of this plate about an axis passing through one of its vertices and perpendicular to its plane?

Match Column-$I$ with Column-$II$:

Column-$I$	Column-$II$
$(1)$ Perpendicular Axis Theorem	$(a)$ $I = I_C + Md^2$
$(2)$ Parallel Axis Theorem	$(b)$ $I_z = I_x + I_y$

Where, $d =$ distance between two parallel axes.

The moment of inertia of a rod of length $l$ about an axis passing through its centre of mass and perpendicular to the rod is $I$. The moment of inertia of a hexagonal shape formed by six such rods,about an axis passing through its centre of mass and perpendicular to its plane,will be (in $I$)

The moment of inertia of a triangular plate $ABC$ of mass $M$ and side $BC = a,$ about an axis passing through $A$ and perpendicular to the plane of the plate is :-