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 passing through its center is:

How many $g$ of a dibasic acid $(Mol. wt. = 200)$ should be present in $100 \ ml$ of its aqueous solution to give a decinormal strength?

There are two wires of the same material and same length. If the diameter of the second wire is $2$ times the diameter of the first wire,then the ratio of the extension produced in the wires by applying the same load will be:

Two spheres $A$ and $B$ are kept very near to each other. $A$ is negatively charged and $B$ is earthed. The true statements are:
$(A)$ Charge on $B$ is zero
$(B)$ Potential at $B$ is zero
$(C)$ Charge is uniformly distributed on $A$
$(D)$ Charge is non-uniformly distributed on $A$

In which of the following is incomplete double circulation observed?

If $\int e^x(1+x) \cdot \sec ^2(x e^x) \, dx = f(x) + \text{constant}$, then $f(x)$ is equal to