$5.6 \, \text{liter}$ of helium gas at $STP$ is adiabatically compressed to $0.7 \, \text{liter}$. Taking the initial temperature to be $T_1$,the work done in the process is

$\int \frac{1+\cos 4 x}{\cot x-\tan x} d x$ is equal to

Which of the following $statement(s)$ is/are not correct?
$(i)$ Reproduction is the production of progeny possessing features dissimilar to their parents.
$(ii)$ The fungi,the filamentous algae,the protonema of mosses,all multiply by budding.
$(iii)$ Many organisms like mules,sterile worker bees do not reproduce.
$(iv)$ Reproduction is not an all-inclusive defining characteristic of living organisms.

$A$ ball is dropped from a height of $5 \ m$. The time after which the ball stops rebounding,if the coefficient of restitution between the ball and the ground is $e = 1/2$,is ................. $s$.

The $V-Q$ graph is shown below. What does the area of $\Delta OAB$ represent in this graph?