The magnetic field varies as $B = B_0 e^{-t}$. The coil has a radius $r$ and resistance $R$. What is the power dissipated when the key $K$ is closed at $t = 0$?

Which of the following is not a unit of permeability?

Two inductor coils of self-inductance $3\,H$ and $6\,H$ respectively are connected with a resistance $10\,\Omega$ and a battery $10\,V$ as shown in the figure. The ratio of the total energy stored at steady state in the inductors to that of the heat developed in the resistance in $10\,s$ at the steady state is (neglect mutual inductance between $L_1$ and $L_2$):-

$A$ thin conducting rod $MN$ of mass $20 \text{ g}$,length $25 \text{ cm}$ and resistance $10 \text{ }\Omega$ is held on frictionless,long,perfectly conducting vertical rails as shown in the figure. There is a uniform magnetic field $B_0 = 4 \text{ T}$ directed perpendicular to the plane of the rod-rail arrangement. The rod is released from rest at time $t = 0$ and it moves down along the rails. Assume air drag is negligible. Match each quantity in List-$I$ with an appropriate value from List-$II$,and choose the correct option. [Given: The acceleration due to gravity $g = 10 \text{ m s}^{-2}$ and $e^{-1} = 0.4$]

List-$I$	List-$II$
$(P)$ At $t = 0.2 \text{ s}$,the magnitude of the induced emf in Volt	$(1)$ $0.07$
$(Q)$ At $t = 0.2 \text{ s}$,the magnitude of the magnetic force in Newton	$(2)$ $0.144$
$(R)$ At $t = 0.2 \text{ s}$,the power dissipated as heat in Watt	$(3)$ $1.20$
$(S)$ The magnitude of terminal velocity of the rod in $\text{m s}^{-1}$	$(4)$ $0.12$
	$(5)$ $2.00$

$A$ conducting square loop initially lies in the $XZ$ plane with its lower edge hinged along the $X$-axis. Only in the region $y \geq 0$,there is a time-dependent magnetic field pointing along the $Z$-direction,$\vec{B}(t) = B_0(\cos \omega t) \hat{k}$,where $B_0$ is a constant. The magnetic field is zero everywhere else. At time $t=0$,the loop starts rotating with constant angular speed $\omega$ about the $X$-axis in the clockwise direction as viewed from the $+X$ axis (as shown in the figure). Ignoring self-inductance of the loop and gravity,which of the following plots correctly represents the induced e.m.f. $(V)$ in the loop as a function of time?

The current $i$ in an inductance coil varies with time $t$ according to the following graph. Which one of the following plots shows the variations of voltage $V$ in the coil?