How does the moment of inertia depend on the angular momentum?

Let $l$ 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:

$A$ long slender rod is welded to a thin circular disc of diameter $0.5 \ m$ at a point on its circumference. The rod is in the same plane as that of the disc and forms a tangent to the disc. The radius of gyration of the disc about the rod (in $m$) is

Two rings of the same radius and mass are placed such that their centers are at the same point and their planes are mutually perpendicular. The moment of inertia of this system about an axis passing through the center and perpendicular to the plane of one of the rings is (mass of ring = $m$,radius = $r$):

$A$ spherical shell has a mass one-fourth that of a solid sphere,and both have the same moment of inertia $(M.I.)$ about their respective diameters. The ratio of their radii will be:

$A$ straight rod of length $L$ is made of a material having mass per unit length $m(x) = \lambda|x|$, where $x$ is measured from the center of the rod. The moment of inertia about an axis perpendicular to the rod and passing through one end of the rod is to be calculated. Given $L = 1 \ m$ and $\lambda = 16 \ kg/m^2$.