If $^nP_4 = 30 \times ^nC_5$,then $n = \dots$

The value of $\cos ^{-1} \left[ \cot \left\{ \sin ^{-1} \sqrt{\frac{2 - \sqrt{3}}{4}} + \cos ^{-1} \frac{\sqrt{12}}{4} + \sec ^{-1} \sqrt{2} \right\} \right]$ is

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

What is a phycobiont?

$A$ point object is placed at a distance of $10\,cm$ and its real image is formed at a distance of $20\,cm$ from a concave mirror. If the object is moved by $0.1\,cm$ towards the mirror,the image will shift by about:

The $P-V$ diagram of an ideal gas is as shown in the figure. The work done by the gas in the process $ABCD$ is: