JEE Main 2019 Physics Paper: 9 Apr, Shift 1

Taking the wavelength of first Balmer line in hydrogen spectrum (n = 3 to n = 2) as 660 nm, the wavelength of the 2nd Balmer line (n = 4 to n = 2) will be:

Determine the charge on the capacitor in the following circuit:

A capacitor with capacitance 5μF is charged to 5μC. If the plates are pulled apart to reduce the capacitance to 2μF, how much work is done?

A wire of resistance R is bent to form a square ABCD as shown in the figure. The effective resistance between E and C is: (E is mid-point of arm CD)

A moving coil galvanometer has resistance 50$\Omega$ and it indicates full deflection at 4mA current. A voltmeter is made using this galvanometer and a 5 k$\Omega$ resistance. The maximum voltage, that can be measured using this voltmeter, will be close to:

The electric field of light wave is given as

$\vec{E} = 10^{-3}\cos\left(\frac{2\pi x}{5 \times 10^{-7}} - 2\pi \times 6 \times 10^{14}t\right)\hat{x}\,\frac{\text{N}}{\text{C}}$

This light falls on a metal plate of work function 2eV. The stopping potential of the photoelectrons is:

Given, E (in eV) = 12375/$\lambda$(inÅ)

The total number of turns and cross-section area in a solenoid is fixed. However, its length L is varied by adjusting the separation between windings. The inductance of solenoid will be proportional to:

The magnetic field of a plane electromagnetic wave is given by:

$\vec{B} = B_0 \hat{i} [\cos(kz - \omega t)] + B_0 \hat{j} \cos(kz + \omega t)$

B0 = 3 × 10–5 T and B1 = 2 × 10–6 T.

The rms value of the force experienced by a stationary charge Q = 10–4 C at z = 0 is closest to:

A system of three charges are placed as shown in the figure:

If D >> d, the potential energy of the system is best given by:

A solid sphere of mass 'M' and radius 'a' is surrounded by a uniform concentric spherical shell of thickness 2a and mass 2M. The gravitational field at distance '3a' from the centre will be:

An HCl molecule has rotational, translational and vibrational motions. If the rms velocity of HCl molecules in its gaseous phase is $\bar{v}$, m is its mass and kB is Boltzmann constant, then its temperature will be:

For a given gas at 1 atm pressure, rms speed of the molecule is 200 m/s at 127°C. At 2 atm pressure and at 227°C, the rms speed of the molecules will be:

A rectangular coil (Dimension 5 cm × 2.5 cm) with 100 turns, carrying a current of 3 A in the clock- wise direction is kept centered at the origin and in the X-Z plane. A magnetic field of 1 T is applied along X-axis. If the coil is tilted through 45° about Z-axis, then the torque on the coil is:

A rigid square loop of side 'a' and carrying current I2 is lying on a horizontal surface near a long current I1 carrying wire in the same plane as shown in figure. The net force on the loop due to wire will be:

A simple pendulum oscillating in air has period T. The bob of the pendulum is completely immersed in a non-viscous liquid. The density of the liquid is 1/16 th of the material of the bob. If the bob is inside liquid all the time, its period of oscillation in this liquid is:

The stream of a river is flowing with a speed of 2km/h. A swimmer can swim at a speed of 4km/h. What should be the direction of the swimmer with respect to the flow of the river to cross the river straight?

A concave mirror for face viewing has focal length of 0.4 m. The distance at which you hold the mirror from your face in order to see your image upright with a magnification of 5 is:

The following bodies are made to roll up (without slipping) the same inclined plane from a horizontal plane.: (i) a ring of radius R, (ii) a solid cylinder of radius R/2 and (iii) a solid sphere of radius R/4. If in each case, the speed of the centre of mass at the bottom of the incline is same, the ratio of the maximum heights they climb is:

A stationary horizontal disc is free to rotate about its axis. When a torque is applied on it, its kinetic energy as a function of $\theta$, where $\theta$ is the angle by which it has rotated, is given as k$\theta$2. If its moment of inertia is I then the angular acceleration of the disc is:

An NPN transistor is used in common emitter configuration as an amplifier with 1 k$\Omega$ load resistance. Signal voltage of 10 mV is applied across the base-emitter. This produces a 3 mA change in the collector current and 15μA change in the base current of the amplifier. The input resistance and voltage gain are:

If 'M' is the mass of water that rises in a capillary tube of radius 'r', then mass of water which will rise in a capillary tube of radius '2r' is:

Following figure shows two processes A and B for a gas. If $\Delta$QA and $\Delta$QB are the amount of heat absorbed by the system in two cases, and $\Delta$UA and $\Delta$UB are changes in internal energies, respectively, then:

In the density measurement of a cube, the mass and edge length are measured as (10.00 ± 0.10) kg and (0.10 ± 0.01) m, respectively. The error in the measurement of density is:

The pressure wave, P = 0.01 sin [1000t – 3x] Nm–2, corresponds to the sound produced by a vibrating blade on a day when atmospheric temperature is 0°C. On some other day, when temperature is T, the speed of sound produced by the same blade and at the same frequency is found to be 336 ms–1. Approximate value of T is

A string is clamped at both the ends and it is vibrating in its 4th harmonic. The equation of the stationary wave is Y = 0.3 sin(0.157x) cos(200$\pi$t). The length of the string is: (All quantities are in SI units.)

The figure shows a Young's double slit experimental setup. It is observed that when a thin transparent sheet of thickness t and refractive index μ is put in front of one of the slits, the central maximum gets shifted by a distance equal to n fringe widths. If the wavelength of light used is $\lambda$, t will be:

A uniform cable of mass 'M' and length 'L' is placed on a horizontal surface such that its (1/n)th part is hanging below the edge of the surface. To lift the hanging part of the cable upto the surface, the work done should be: