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

The number of points in $(-\infty, \infty)$ for which $x^2 - x \sin x - \cos x = 0$ is

If the circle $x^2 + y^2 + 2gx + 2fy + c = 0$ touches the $x$-axis,then:

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

$\int \frac{1+x+\sqrt{x+x^2}}{\sqrt{x}+\sqrt{1+x}} d x$ is equal to

If $T$ is the surface tension of a soap solution,the amount of work done in blowing a soap bubble from a diameter $D$ to $2D$ is (in $\pi D^2T$)