$A$ short bar magnet passes at a steady speed right through a long solenoid. $A$ galvanometer is connected across the solenoid. Which graph best represents the variation of the galvanometer deflection $\theta$ with time $t$?

Two inductors $L_1$ (inductance $1 \text{ mH}$,internal resistance $3 \text{ } \Omega$) and $L_2$ (inductance $2 \text{ mH}$,internal resistance $4 \text{ } \Omega$),and a resistor $R$ (resistance $12 \text{ } \Omega$) are all connected in parallel across a $5 \text{ V}$ battery. The circuit is switched on at time $t=0$. The ratio of the maximum to the minimum current $(I_{\max} / I_{\min})$ drawn from the battery is:

Radio frequency choke uses a core of

$A$ conducting circular loop of resistance $20 \Omega$ and cross-sectional area $20 \times 10^{-2} \,m^{2}$ is placed perpendicular to a spatially uniform magnetic field $B$, which varies with time $t$ as $B = 2 \sin(50 \pi t) \,T$. Find the net charge flowing through the loop in $20 \,ms$ starting from $t = 0$. (in $\,C$)

Two metallic rings $A$ and $B$,identical in shape and size but having different resistivities $\rho_A$ and $\rho_B$,are kept on top of two identical solenoids as shown in the figure. When current $I$ is switched on in both the solenoids in an identical manner,the rings $A$ and $B$ jump to heights $h_A$ and $h_B$,respectively,with $h_A > h_B$. The possible relation$(s)$ between their resistivities and their masses $m_A$ and $m_B$ is(are):
$(A)$ $\rho_A > \rho_B$ and $m_A = m_B$
$(B)$ $\rho_A < \rho_B$ and $m_A = m_B$
$(C)$ $\rho_A > \rho_B$ and $m_A > m_B$
$(D)$ $\rho_A < \rho_B$ and $m_A < m_B$

The network shown in the figure is part of a complete circuit. If at a certain instant,the current $I$ is $5 \ A$ and it is decreasing at a rate of $10^3 \ A \ s^{-1}$,then $V_B - V_A$ equals.....$V$.