Where is the $Central$ $Drug$ $Research$ $Institute$ $(CDRI)$ located?

If $f(x) = \int \frac{5x^8 + 7x^6}{(x^2 + 1 + 2x^7)^2} dx, (x \ge 0)$ and $f(0) = 0$,then the value of $f(1)$ is

When an unpolarized light of intensity $I_0$ is incident on a polarizing sheet,the intensity of the light which does not get transmitted is

If $\tan ^{-1} x = y$,then . . . . . . .

$A$ child is standing at one end of a long trolley moving with a speed $v$ on a smooth horizontal floor. If the child starts running towards the other end of the trolley with a speed $u$,the centre of mass of the system (trolley + child) will move with a speed:

The ratio of momenta of an electron and an $\alpha$-particle which are accelerated from rest by a potential difference of $100\, V$ is