If the number average molecular weight and weight average molecular weight of a polymer are $40000$ and $60000$ respectively,the polydispersity index of the polymer will be

Consider the following statements $A$ and $B$ and identify the correct answer:
$A$. When a person walks on a rough surface, the direction of the frictional force exerted by the surface on the person is in the direction of his motion.
$B$. When a cycle is in motion, the force of friction exerted by the ground on the front wheel is in the backward direction.

The angle between the asymptotes of the hyperbola $x^2-3y^2=3$ is

If $\int \frac{dx}{\cos^3 x \sqrt{2 \sin 2x}} = (\tan x)^A + C(\tan x)^B + k,$ where $k$ is a constant of integration,then $A + B + C$ equals

There are two identical small holes of cross-sectional area $a$ on the opposite sides of a tank containing a liquid of density $\rho$. The difference in height between the holes is $h$. The tank is resting on a smooth horizontal surface. The horizontal force which will have to be applied on the tank to keep it in equilibrium is

If the angles made by a straight line with the coordinate axes are $\alpha, \frac{\pi}{2}-\alpha, \beta$,then $\beta$ is equal to