List-I contains four conducting loops lying in the $XY$ plane, as shown in the figures. The loops are rotating about $Z$ axis passing through the point $O$ with time period $T$ in clockwise direction.

The region $x>0$ contains a uniform magnetic field $B$ in the $+z$ direction. List-II contains the qualitative variation of the induced current $i(t)$ for each of these loops. Choose the option which describes the correct match between the entries in List-I to those in List-II.

List-I	List-II
(P)	(1)
(Q)	(2)
(R)	(3)
(S)	(4)
	(5)

A conducting square loop initially lies in the $X Z$ 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:

A conducting square loop of side $L$, mass $M$ and resistance $R$ is moving in the $X Y$ plane with its edges parallel to the $X$ and $Y$ axes. The region $y \geq 0$ has a uniform magnetic field, $\vec{B}=B_0 \widehat{k}$. The magnetic field is zero everywhere else. At time $t=0$, the loop starts to enter the magnetic field with an initial velocity $v_0 \hat{\jmath} \mathrm{~m} / \mathrm{s}$, as shown in the figure. Considering the quantity $K=\frac{B_0^2 L^2}{R M}$ in appropriate units, ignoring self-inductance of the loop and gravity, which of the following statements is/are correct:

A region in the form of an equilateral triangle (in $x-y$ plane) of height $L$ has a uniform magnetic field $\vec{B}$ pointing in the $+z$-direction. A conducting loop $\mathrm{PQR}$, in the form of an equilateral triangle of the same height $L$, is placed in the $x-y$ plane with its vertex $\mathrm{P}$ at $x=0$ in the orientation shown in the figure. At $t=0$, the loop starts entering the region of the magnetic field with a uniform velocity $\vec{v}$ along the $+x$-direction. The plane of the loop and its orientation remain unchanged throughout its motion.

Which of the following graph best depicts the variation of the induced emf $(E)$ in the loop as a function of the distance $(x)$ starting from $x=0$ ?

A current carrying infinitely long wire is kept along the diameter of a circular wire loop, without touching it, the correct statement(s) is(are)

The figure shows certain wire segments joined together to form a coplanar loop. The loop is placed in a perpendicular magnetic field in the direction going into the plane of the figure. The magnitude of the field increases with time. $I_1$ and $I_2$ are the currents in the segments ab and cd. Then,

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 below. When current I is switched on in both the solenoids in 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)

What is the advantage of this system?

What is the disadvantage of this system?

Which force causes the train to elevate upwards

A long solenoid of radius a and number of turns per unit length $n$ is enclosed by cylindrical shell of radius R, thickness $d$ $(d < < R)$ and length L. A variable current $\mathrm{I}=\mathrm{I}_{0} \sin \omega t$ flows through the coil. If the resistivity of the material of cylindrical shell is $\mathrm{P}$, find the induced current in the shell.