$A$ square plate of mass $M$ and edge $L$ is shown in the figure. The moment of inertia of the plate about the axis in the plane of the plate passing through one of its vertices making an angle $15^{\circ}$ with the horizontal is:

$ABC$ is a plane lamina in the shape of an equilateral triangle. $D$ and $E$ are the midpoints of $AB$ and $AC$,respectively,and $G$ is the centroid of the lamina. The moment of inertia of the lamina about an axis passing through $G$ and perpendicular to the plane $ABC$ is $I_{0}$. If the part $ADE$ is removed,the moment of inertia of the remaining part about the same axis is $\frac{NI_{0}}{16}$,where $N$ is an integer. The value of $N$ is

The moment of inertia of a circular ring of mass $M$ and diameter $r$ about a tangential axis lying in the plane of the ring is

Two discs $A$ and $B$ each of radius $r$ and mass $m$ are attached as shown to form a system. The moment of inertia of this system about an axis perpendicular to the plane of the discs and passing through the center of disc $A$ is

Let $I$ be the moment of inertia of a uniform square plate about an axis $AB$ that passes through its centre and is parallel to two of its sides. $CD$ is a line in the plane of the plate that passes through the centre of the plate and makes an angle $\theta$ with $AB$. The moment of inertia of the plate about the axis $CD$ is then equal to:

The moment of inertia of a square plate of side $l$ and mass $M$ about an axis passing through one of its corners and perpendicular to the plane of the square plate is given by: