When the observer moves towards a stationary source with velocity $\mathrm{V}_1$, the apparent frequency of emitted note is $F_1$. When observer moves away from the source with velocity $\mathrm{V}_1$, the apparent frequency is $\mathrm{F}_2$. If V is the velocity of sound in air and $F_1 / F_2=2$ then $V / V_1$ is equal to

An ideal gas taken through a process ABCA as shown in figure. If the net heat supplied to gas in the cycle is 5 J , then the work done by the gas in process from C to A is

In Young's double slit experiment, in an interference pattern second minimum is observed exactly in front of one slit. The distance between the two coherent sources is ' $d$ ' and the distance between source and screen is ' $D$ '. The wavelength of light source used is

In an a.c. circuit containing $L, C, R$ in series the ratio of true power to apparent power is ( $\mathrm{Z}=$ impedance of the circuit and R is the resistance)