JEE Main 2014 Physics Paper

In the circuit shown here, the point $'C'$ is kept connected to point $'A'$ till the current flowing through the circuit becomes constant. Afterward, suddenly, point $'C'$ is disconnected from point $'A'$ and connected to point $'B'$ at time $t = 0.$ Ratio of the voltage across resistance and the inductor at $t = L/R$ will be equal to:

Hydrogen $\left({}_{1}H^{1}\right)$, Deuterium $\left({}_{1}H^{2}\right)$, singly ionised Helium $\left({}_{2}He^{4}\right)^{+}$ and doubly ionised lithium $\left({}_{3}Li^{6}\right)^{++}$ all have one electron around the nucleus. Consider an electron transition from $n = 2$ to $n = 1.$ If the wavelengths of emitted radiation are $\lambda_{1}, \lambda_{2}, \lambda_{3}$ and $\lambda_{4}$ respectively then approximately which one of the following is correct?

The radiation corresponding to $3 \rightarrow 2$ transition of hydrogen atom falls on a metal surface to produce photoelectrons. These electrons are made to enter a magnetic field $3 \times 10^{-4}\text{ T}.$ If the radius of the larger circular path followed by these electrons is $10.0\text{ mm}$, the work function of the metal is close to:

A parallel plate capacitor is made of two circular plates separated by a distance $5\text{ mm}$ and with a dielectric of dielectric constant $2.2$ between them. When the electric field in the dielectric is $3 \times 10^{4}\text{ V/m}$ the charge density of the positive plate will be close to:

In a large building, there are $15$ bulbs of $40\text{ W},\ 5$ bulbs of $100\text{ W},\ 5$ fans of $80\text{ W}$ and $1$ heater of $1\text{ kW}.$ The voltage of electric mains is $220\text{ V}.$ The minimum capacity of the main fuse of the building will be:

Match List - $1$ (Electromagnetic wave type) with List - $2$ (Its association/application) and select the

correct option from the choices given below the lists:

During the propagation of electromagnetic waves in a medium:

Assume that an electric field $\vec{E} = 30x^{2}\hat{i}$ exists in space. Then the potential difference $V_A - V_O,$ where $V_O$ is the potential at the origin and $V_A$ the potential at $x = 2\text{ m}$ is:

An open glass tube is immersed in mercury in such a way that a length of $8\text{ cm}$ extends above the mercury level. The open end of the tube is then closed and sealed and the tube is raised vertically up by additional $46\text{ cm}$. What will be length of the air column above mercury in the tube now? (Atmospheric pressure $= 76\text{ cm}$ of $Hg$)

There is a circular tube in a vertical plane. Two liquids which do not mix and of densities $d_1$ and $d_2$ are filled in the tube. Each liquid subtends $90^\circ$ angle at center. Radius joining their interface makes an angle $\alpha$ with vertical. Ratio $\frac{d_1}{d_2}$ is:

Four particles, each of mass $M$ and equidistant from each other, move along a circle of radius $R$ under the action of their mutual gravitational attraction. The speed of each particle is:

Three rods of Copper, Brass and Steel are welded together to form a $Y$ shaped structure. Area of cross - section of each rod $= 4\text{ cm}^2.$ End of copper rod is maintained at $100^\circ\text{C}$ where as ends of brass and steel are kept at $0^\circ\text{C}$. Lengths of the copper, brass and steel rods are $46,\ 13$ and $12\text{ cms}$ respectively. The rods are thermally insulated from surroundings excepts at ends. Thermal conductivities of copper, brass and steel are $0.92,\ 0.26$ and $0.12\text{ CGS}$ units respectively. Rate of heat flow through copper rod is:

A block of mass $m$ is placed on a surface with a vertical cross section given by $y = \frac{x^3}{6}.$ If the coefficient of friction is $0.5,$ the maximum height above the ground at which the block can be placed without slipping is:

The coercivity of a small magnet where the ferromagnet gets demagnetized is $3 \times 10^{3}\text{ Am}^{-1}.$ The current required to be passed in a solenoid of length $10\text{ cm}$ and number of turns $100,$ so that the magnet gets demagnetized when inside the solenoid, is:

The pressure that has to be applied to the ends of a steel wire of length $10\text{ cm}$ to keep its length constant when its temperature is raised by $100^\circ\text{C}$ is: (For steel Young's modulus is $2 \times 10^{11}\text{ Nm}^{-2}$ and coefficient of thermal expansion is $1.1 \times 10^{-5}\text{ K}^{-1}$)

From a tower of height H, a particle is thrown vertically upwards with a speed u. The time taken by the particle, to hit the ground, is n times that taken by it to reach the highest point of its path. The relation between H, u and n is:

A conductor lies along the $z$-axis at $-1.5 \le z < 1.5\text{ m}$ and carries a fixed current of $10.0\text{ A}$ in $-\hat{a}_z$ direction (see figure). For a field $\vec{B} = 3.0 \times 10^{-4}\, e^{-0.2x}\, \hat{a}_y\text{ T},$ find the power required to move the conductor at constant speed to $x = 2.0\text{ m},\ y = 0\text{ m}$ in $5 \times 10^{-3}\text{ s}.$ Assume parallel motion along the $x$-axis.

A particle moves with simple harmonic motion in a straight line. In first $\tau s,$ after starting from rest it travels a distance $a,$ and in next $\tau s$ it travels $2a,$ in same direction, then:

A thin convex lens made from crown glass $\left(\mu = \frac{3}{2}\right)$ has focal length $f$. When it is measured in two different liquids having refractive indices $\frac{4}{3}$ and $\frac{5}{3},$ it has the focal lengths $f_1$ and $f_2$ respectively. The correct relation between the focal lengths is:

A green light is incident from the water to the air - water interface at the critical angle $(\theta)$. Select the correct statement.

A bob of mass $m$ attached to an inextensible string of length $l$ is suspended from a vertical support. The bob rotates in a horizontal circle with an angular speed $\omega\, rad/s$ about the vertical. About the point of suspension:

A mass $'m'$ is supported by a massless string wound around a uniform hollow cylinder of mass $m$ and radius $R.$ If the string does not slip on the cylinder, with what acceleration will the mass fall on release?

The forward biased diode connection is:

The current voltage relation of diode is given by $I = \left(e^{1000V/T} - 1\right)\text{ mA},$ where the applied voltage $V$ is in volts and the temperature $T$ is in degree kelvin. If a student makes an error measuring $\pm 0.01\,V$ while measuring the current of $5\,mA$ at $300\,K,$ what will be the error in the value of current in $mA$?

On heating water, bubbles being formed at the bottom of the vessel detach and rise. Take the bubbles to be spheres of radius $R$ and making a circular contact of radius $r$ with the bottom of the vessel. If $r \ll R$ and the surface tension of water is $T,$ value of $r$ just before bubbles detach is: (density of water is $\rho_w$)

One mole of a diatomic ideal gas undergoes a cyclic process $ABC$ as shown in figure. The process $BC$ is adiabatic. The temperatures at $A, B$ and $C$ are $400\text{ K},\ 800\text{ K}$ and $600\text{ K}$ respectively. Choose the correct statement:

A student measured the length of a rod and wrote it as 3.50 cm. Which instrument did he use to measure it?

A pipe of length $85\text{ cm}$ is closed from one end. Find the number of possible natural oscillations of air column in the pipe whose frequencies lie below $1250\text{ Hz}$. The velocity of sound in air is $340\text{ m/s}$.

Two beams, $A$ and $B$, of plane polarized light with mutually perpendicular planes of polarization are seen through a polaroid. From the position when the beam $A$ has maximum intensity (and beam $B$ has zero intensity), a rotation of polaroid through $30^\circ$ makes the two beams appear equally bright. If the initial intensities of the two beams are $\mathrm{I}_A$ and $\mathrm{I}_B$ respectively, then $\frac{\mathrm{I}_A}{\mathrm{I}_B}$ equals:

When a rubber-band is stretched by a distance $x$, it exerts restoring force of magnitude $F = ax + bx^2$ where $a$ and $b$ are constants. The work done in stretching the unstretched rubber-band by $L$ is: