JEE Main 2018 Physics Paper: 15 Apr, Shift 1

An ideal capacitor of capacitance $0.2\,\mu F$ is charged to a potential difference of $10\ V.$ The charging battery is then disconnected. The capacitor is then connected to an ideal inductor of self inductance $0.5\ mH.$ The current at a time when the potential difference across the capacitor is $5\ V,$ is:

The energy required to remove the electron from a singly ionized Helium atom is $2.2$ times the energies required to remove an electron from Helium atom. The total energy required to ionize the Helium atom completely is:

The equivalent capacitance between $A$ and $B$ in the circuit given below, is:

In the given circuit all resistances are of value $R\text{ ohm}$ each. The equivalent resistance between $A$ and $B$ is:

In a meter bridge, as shown in the figure, it is given that resistance $Y = 12.5\ \Omega$ and that the balance is obtained at a distance $39.5\text{ cm}$ from end $A$ (by Jockey J). After interchanging the resistances $X$ and $Y$, a new balance point is found at a distance $l_2$ from end $A.$ What are the value of $X$ and $l_2$?

Two electrons are moving with non-relativistic speed perpendicular to each other. If corresponding de Broglie wavelength are $\lambda_1$ and $\lambda_2,$ their de Broglie wavelength in the frame of reference attached to their center of masses:

A monochromatic beam of light has a frequency $\nu = \frac{3}{2\pi} \times 10^{12}\text{ Hz}$ and is propagating along the direction $\frac{\hat{i} + \hat{j}}{\sqrt{2}}.$

It is polarized along the $\hat{k}$ direction. The acceptable form for the magnetic field is:

A charge $Q$ is placed at a distance $a/2$ above the center of the square surface of edge a as shown in the figure.

The electric flux through the square surface is

A body of mass $M$ and charge $q$ is connected to spring of spring constant $k.$ It is oscillating along $x$-direction about its equilibrium position, taken to be at $x = 0,$ with an amplitude $A$. An electric field $E$ is applied along the $x$-direction. Which of the following statements is correct?

A thin uniform tube is bent into a circle of radius $r$ in the vertical plane. Equal volumes of two immiscible liquids, whose densities are $\rho_1$ and $\rho_2\ (\rho_1 > \rho_2),$ fill half the circle. The angle $\theta$ between the radius vector passing through the common interface and the vertical is:

Take the mean distance of the moon and the sun from the earth to be $0.4 \times 10^{6}$ km and $150 \times 10^{6}$ km respectively. Their masses are $8 \times 10^{22}$ kg and $2 \times 10^{30}$ kg respectively. The radius of the earth is $6400$ km. Let $\Delta F_1$ be the difference in the forces exerted by the moon at the nearest and farthest points on the earth and $\Delta F_2$ be the difference in the force exerted by the sun at the nearest and farthest points on the earth. Then, the number closest to $\frac{\Delta F_1}{\Delta F_2}$ is:

A body of mass m is moving in a circular orbit of radius R about a planet of mass M. At some instant, it splits into two equal masses. The first mass moves in a circular orbit of radius $\frac{R}{2},$ and the other mass, in a circular orbit of radius $\frac{3R}{2}$. The difference between the final and initial total energies is:

A given object takes n times more time to slide down a $45^\circ$ rough inclined plane as it takes to slide down a perfectly smooth $45^\circ$ incline. The coefficient of kinetic friction between the object and the incline is:

The $B\text{-}H$ curve for a ferromagnet is shown in the figure. The ferromagnet is placed inside a long solenoid with $1000$ turns/cm. The current that should be passed in the solenoid to demagnetise the ferromagnet completely is:

An automobile, travelling at $40$ km/h, can be stopped at a distance of $40$ m by applying brakes. If the same automobile is travelling at $80$ km/h, the minimum stopping distance, in metres, is (assume no skidding):

The velocity-time graphs of a car and a scooter are shown in the figure. (i) The difference between the distance travelled by the car and the scooter in $15\text{ s}$ and (ii) the time at which the car will catch up with the scooter are, respectively.

A Helmholtz coil has a pair of loops, each with $N$ turns and radius $R$. They are placed coaxially at distance $R$ and the same current $I$ flows through the loops in the same direction. The magnitude of the magnetic field at $P,$ midway between the centers $A$ and $C$, is given by [Refer to figure given below]:

A containing active cobalt ${}^{60}_{27}\text{Co}$ having activity of $0.8\ \mu\text{Ci}$ and decay constant $\lambda$ is injected in an animal's body. If $1\text{ cm}^3$ of blood is drawn from the animal's body after $10$ hrs of injection, the activity found was $300$ decays per minute What is the volume of blood that is flowing in the body? $(\text{Ci} = 3.7 \times 10^{10}$ decays per second and at $t = 10$ hrs $e^{-\lambda t} = 0.84)$

A planoconvex lens becomes an optical system of $28\text{ cm}$ focal length when its plane surface is silvered and illuminated from left to right as shown in Fig-A.

If the same lens is instead silvered on the curved surface and illuminated from other side as in Fig- B, it acts like an optical system of focal length $10\text{ cm.}$ The refractive index of the material of lens is:

A particle is oscillating on the $X$-axis with an amplitude $2\text{ cm}$ about the point $x_0 = 10\text{ cm},$ with a frequency $\omega$. A concave mirror of focal length $5\text{ cm}$ is placed at the origin (see figure).

Identify the correct statements.

(A) The image executes periodic motion.

(B) The image executes non-periodic motion.

(C) The turning points of the image are asymmetric w.r.t. the image of the point at $x = 10\text{ cm}$. (D) The distance between the turning points of the oscillation of the image is $\frac{100}{21}\text{ cm.}$

A force of $40\text{ N}$ acts on a point $B$ at the end of an $L$-shaped object, as shown in the figure. The angle $\theta$ that will produce maximum moment of the force about point $A$ is given by:

A uniform rod $AB$ is suspended from a point $X,$ at a variable distance $x$ from $A$, as shown. To make the rod horizontal, a mass $m$ is suspended from its end $A.$ A set of $(m, x)$ values is recorded. The appropriate variables that give a straight line, when plotted, are:

In a common emitter configuration with suitable bias, it is given that $R_L$ is the load resistance and $R_{BE}$ is small signal dynamic resistance (input side). Then, voltage gain, current gain and power gain are given, respectively, by:

$\beta$ is current gain, $\mathrm{I}_B, \mathrm{I}_C$ and $\mathrm{I}_E$ are respectively base, collector and emitter currents.

A Carnot's engine works as a refrigerator between $250$ K and $300$ K. It receives $500$ cal heat from the reservoir at the lower temperature. The amount of work done in each cycle to operate the refrigerator is:

One mole of an ideal monoatomic gas is compressed isothermally in a rigid vessel to double its pressure at room temperature, $27^\circ\text{C}.$ The work done on the gas will be:

The relative error in the determination of the surface area of sphere is $\alpha$. Then the relative error in the determination of its volume is:

In a screw gauge, $5$ complete rotations of the screw cause it to move a linear distance of $0.25\text{ cm}$ There are $100$ circular scale divisions. The thickness of a wire measured by this screw gauge gives a reading of $4$ main scale divisions and $30$ circular scale divisions. Assuming negligible zero error, the thickness of the wire is:

A tuning fork vibrates with frequency $256\text{ Hz}$ and gives one beat per second with the third normal mode of vibration of an open pipe. What is the length of the pipe? (Speed of sound in air is $340\text{ ms}^{-1}$)

Light of wavelength $550\text{ nm}$ falls normally on a slit of width $22.0 \times 10^{-5}\text{ cm.}$ The angular position of the second minima from the central maximum will be (in radians):