In an $FM$ system, a $7\, kHz$ signal modulates a $108\, MHz$ carrier such that the frequency deviation is $50\, kHz$. The carrier swing is: (in $ kHz$)

$2 \tanh^{-1} \frac{1}{2}$ is equal to

In a Ruby laser, the colour of laser light is due to ______ atom.

The diagram represents Miller's experiment. Choose the correct combination of labelling.

If the normal to the curve $y = f(x)$ at the point $(3, 4)$ makes an angle $\frac{3\pi}{4}$ with the positive $x$-axis,then $f'(3)$ is equal to

$3$ moles of an ideal monoatomic gas perform an $A B C D A$ cyclic process as shown in the figure. The gas temperatures are $T_A=400 \, K$, $T_B=800 \, K$, $T_C=2400 \, K$, and $T_D=1200 \, K$. The work done by the gas is (approximately) $(R=8.314 \, J / mol K)$. (in $ \, kJ$)