The switch $S$ of the circuit shown in the figure is closed at $t = 0$. If $e$ denotes the induced emf in the inductor $L$ and $i$ denotes the current flowing through the circuit at time $t$,which of the following graphs correctly represents the variation of $e$ with time $t$?

$A$ conducting ring of radius $a$ is rotated about a point $O$ on its periphery as shown in the figure in a plane perpendicular to a uniform magnetic field $B$ which exists everywhere. The rotational velocity is $\omega$. Choose the correct statement$(s)$ related to the induced current in the ring.

$A$ 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 $\text{m s}^{-1}$	$(4)$ $0.12$
	$(5)$ $2.00$

$A$ current $I = 10 \ A$ is passed through the part of a circuit shown in the figure. What will be the potential difference between $A$ and $B$ when $I$ is decreased at a constant rate of $10^2 \ A \ s^{-1}$ (in $V$)?

The current $(I)$ in the inductance is varying with time according to the plot shown in the figure. Which one of the following is the correct variation of voltage $(V)$ with time in the coil?

$A$ metallic ring of mass $m$ and radius $l$ (ring being horizontal) is falling under gravity in a region having a magnetic field. If $z$ is the vertical direction,the $z$-component of the magnetic field is $B_z = B_0(1 + \lambda z)$. If $R$ is the resistance of the ring and the ring falls with a velocity $v$,find the energy lost in the resistance per unit time. If the ring has reached a constant velocity,use the conservation of energy to determine $v$ in terms of $m, B_0, l, \lambda, R$ and acceleration due to gravity $g$.