JEE Main 2013 Physics Paper

In an $LCR$ circuit as shown below both switches are open initially. Now switch $S_1$ is closed, $S_2$ kept open. ($q$ is charge on the capacitor and $\tau = RC$ is Capacitance time constant). Which of the following statements is correct?

In a hydrogen like atom electron make transition from an energy level with quantum number $n$ to another with quantum number $(n-1)$. If $n \gg 1,$ the frequency of radiation emitted is proportional to:

Two capacitors $C_1$ and $C_2$ are charged to $120\text{ V}$ and $200\text{ V}$ respectively. It is found that connecting them together the potential on each one can be made zero. Then

The supply voltage to room is $120\text{ V}.$ The resistance of the lead wires is $6\ \Omega$. A $60\text{ W}$ bulb is already switched on. What is the decrease of voltage across the bulb, when a $240\text{ W}$ heater is switched on in parallel to the bulb?

This questions has Statement - $\text{I}$ and Statement - $\text{II}$. Of the four choices given after the Statements, choose the one that best describes into two Statements.

Statement - $\text{I}$: Higher the range, greater is the resistance of ammeter.

Statement - $\text{II}$: To increase the range of ammeter, additional shunt needs to be used across it.

The anode voltage of a photocell is kept fixed. The wavelength $\lambda$ of the light falling on the cathode is gradually changed. The plate current $I$ of the photocell varies as follows:

A circular loop of radius $0.3\text{ cm}$ lies parallel to a much bigger circular loop of radius $20\text{ cm}$. The center of the small loop is on the axis of the bigger loop. The distance between their centers is $15\text{ cm.}$ If a current of $2.0\text{ A}$ flows through the smaller loop, then the flux linked with bigger loop is

A metallic rod of length $'\ell'$ is tied to a string of length $2\ell$ and made to rotate with angular speed $\omega$ on a horizontal table with one end of the string fixed. If there is a vertical magnetic field $'B'$ in the region, the $e.m.f$ induced across the ends of the rod is

The magnetic field in a travelling electromagnetic wave has a peak value of $20\text{ nT}$. The peak value of electric field strength is:

A charge $Q$ is uniformly distributed over a long rod $AB$ of length $L$ as shown in the figure. The electric potential at the point $O$ lying at distance $L$ from the end $A$ is

Two charges, each equals to $q,$ are kept at $x = -a$ and $x = a$ on the $x$-axis. A particle of mass $m$ and charge $q_0 = \frac{q}{2}$ is placed at the origin. If charge $q_0$ is given a small displacement $(y \ll a)$ along the $y$-axis, the net force acting on the particle is proportional to

What is the minimum energy required to launch a satellite of mass $m$ from the surface of a planet of mass $M$ and radius $R$ in a circular orbit at an altitude of $2R$?

Two short bar magnets of length $1\text{ cm}$ each have magnetic moments $1.20\text{ Am}^{2}$ and $1.00\text{ Am}^{2}$ respectively. They are placed on a horizontal table parallel to each other with their $N$ poles pointing towards the South. They have a common magnetic equator and are separated by a distance of $20.0\text{ cm.}$ The value of the resultant horizontal magnetic induction at the mid-point $O$ of the line joining their centres is close to $($ Horizontal component of earth's magnetic induction is $3.6 \times 10^{-5}\text{ Wb/m}^{2})$

The amplitude of a damped oscillator decreases to $0.9$ times its original magnitude in $5\text{ s}$. In another $10\text{ s}$ it will decrease to $\alpha$ times its original magnitude, where $\alpha$ equals

An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass $M.$ The piston and the cylinder have equal cross sectional area $A$. When the piston is in equilibrium, the volume of the gas is $V_0$ and its pressure is $P_0.$ The piston is slightly displaced from the equilibrium position and released. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frequency

A projectile is given an initial velocity of $\left(\hat{i} + 2\hat{j}\right)$ m/s, where $\hat{i}$ is along the ground and $\hat{j}$ is along the vertical. If g = 10 m/s2, the equation of its trajectory is:

The graph between angle of deviation $(\delta)$ and angle of incidence $(i)$ for a triangular prism is represented by

Diameter of a plano-convex lens is $6\text{ cm}$ and thickness at the center is $3\text{ mm}$. If speed of light in material of lens is $2 \times 10^{8}\text{ m/s},$ the focal length of the lens is

A hoop of radius $r$ and mass $m$ rotating with an angular velocity $\omega_0$ is placed on a rough horizontal surface. The initial velocity of the center of the hoop is zero. What will be the velocity of the center of the hoop when it ceases to slip?

The $\text{I-}V$ characteristic of an $LED$ is

Assume that a drop of liquid evaporates by decreases in its surface energy, so that its temperature remains unchanged. What should be the minimum radius of the drop for this to be possible? The surface tension is $T,$ density of liquid is $\rho$ and $L$ is its latent heat of vaporization.

The above $p\text{-}v$ diagram represents the thermodynamic cycle of an engine, operating with an ideal monatomic gas. The amount of heat, extracted from the source in a single cycle is

Let [$\varepsilon_0$] denote the dimensional formula of the permittivity of vacuum. If M = mass, L = length, T = time and A = electric current, then:

A sonometer wire of length $1.5\text{ m}$ is made of steel. The tension in it produces an elastic strain of $1\%$. What is the fundamental frequency of steel if density and elasticity of steel are $7.7 \times 10^{3}\text{ kg/m}^{3}$ and $2.2 \times 10^{11}\text{ N/m}^{2}$ respectively?

A beam of unpolarised light of intensity $I_0$ is passed through a polaroid $A$ and then through another polaroid $B$ which is oriented so that its principal plane makes an angle of $45^\circ$ relative to that of $A$. The intensity of the emergent light is

Two coherent point sources $S_1$ and $S_2$ are separated by a small distance $'d'$ as shown. The fringes obtained on the screen will be