Two circuits A and B are connected to identical d.c. sources each of e.m.f. 10 volt. Self-inductances of circuits A and B are respectively $\mathrm{L}_{\mathrm{A}}=10 \mathrm{H}$ and $\mathrm{L}_{\mathrm{B}}=10 \mathrm{mH}$. The total resistance of each circuit is $40 \Omega$. The ratio of energy consumed in circuit A and circuit B to build up the current to steady value is

The ratio of the frequencies of two simple pendulums is $4: 3$ at the same place. The ratio of their respective lengths is

A source of sound emits sound wave of frequency ' f ' and moves towards an observer with a velocity $\frac{\mathrm{V}}{3}$ where V is the velocity of sound. If the observer moves away from the source with a velocity $\frac{\mathrm{V}}{5}$ the apparent frequency heard by him will be

In Young's double slit experiment, the distance between the slits is 2 mm and the slits are 1 m away, from the screen. Two interference patterns can be obtained on the screen due to light of wavelength ' $\lambda_1$ ' and ' $\lambda_2$ ' respectively. The separation on the screen between the $3^{\text {rd }}$ order bright fringes on the two interference patterns is ( $\lambda_2=1.5 \lambda_1$ )