The frequency of the whistle of a train moving with a constant speed is observed by a stationary detector on the platform to be $v_1$. The frequency of the same whistle is detected to be $v_2$ inside another train moving on a parallel track, at a speed $v$ towards the frst train. If the speed of sound in air is taken to be $v_s$ ound, what is the ratio $v / v_s$ ound?

A current $I$ flows through a cylindrical cable of length $L$ and uniform cross-sectional area $A$. The power dissipated due to the current is $P_1$. The cable is cut into two equal halves. If the cross-sectional area and the current flowing through the two halves remain unchanged and the power dissipated in each half is $P_2$, which of these options is correct?

Particle A with charge $Q$ and particle B with charge $2 Q$ are fixed at positions $\vec{r}_A$ and $\vec{r}_B$, respectively. The force on $A$ due to $B$ is $\vec{F}_{B A}$, and that on $B$ due to $A$ is $\vec{F}_{A B}$. Which of the following options is correct?

The magnetic fux $\phi_B(t)$ through a coil at a time $t$ is given by $\phi_B(t)=\phi_0 \cos \omega t$, where $0 \leq$ $\omega t \leq \pi$ and $\phi_0$ is a non-zero constant. At what time is the magnitude of the induced emf a maximum?