A thin uniform metal rod of mass ' $M$ ' and length ' $L$ ' is swinging about a horizontal axis passing through its end. Its maximum angular velocity is ' $\omega$ '. Its centre of mass rises to a maximum height of ( $\mathrm{g}=$ Acceleration due to gravity)

When the number of turns in a coil are made 3 times without any change in the length of the coil, its self inductance becomes

When a system is taken from state ' $a$ ' to state ' $c$ ' along a path abc, it is found that $\mathrm{Q}=80 \mathrm{cal}$ and $\mathrm{W}=35 \mathrm{cal}$. Along path adc $\mathrm{Q}=65 \mathrm{cal}$ the work done W along path adc is

The driver of a car travelling with a speed ' $V_1$ ' $\mathrm{m} / \mathrm{s}$ towards a wall sounds a siren of frequency ' $n$ ' Hz. If the velocity of sound in air is $\mathrm{V} \mathrm{m} / \mathrm{s}$, then the frequency of sound reflected from the wall and as heard by the driver, in Hz , is