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JEE Main 2019 April 9 Shift 1 Paper & Solutions - Question 1

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

The rms value of the force experienced by a stationary charge Q =10^{–4}C at z = 0 is

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JEE Main 2019 April 9 Shift 1 Paper & Solutions - Question 2

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:

Detailed Solution for JEE Main 2019 April 9 Shift 1 Paper & Solutions - Question 2

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JEE Main 2019 April 9 Shift 1 Paper & Solutions - Question 3

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

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JEE Main 2019 April 9 Shift 1 Paper & Solutions - Question 4

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

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JEE Main 2019 April 9 Shift 1 Paper & Solutions - Question 5

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

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JEE Main 2019 April 9 Shift 1 Paper & Solutions - Question 6

The pressure wave, P = 0.01sin[1000t – 3x]Nm^{–2} , corresponds to the sound produced

by a vibrating blade on a day when atmospheric temperature is 0ºC. 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 336ms^{–1} . Approximate value of T is:

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JEE Main 2019 April 9 Shift 1 Paper & Solutions - Question 7

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 center of mass at the bottom of the incline is same, theratio of the maximum heights they climb is:

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JEE Main 2019 April 9 Shift 1 Paper & Solutions - Question 8

An NPN transistor is used in common emitter configuration as an amplifier with1kΩ load resistance. Signal voltage of 10 mV is applied across the base-emitter. Thisproduces a 3 mA change in the collector current and 15μ A change in the basecurrent of the amplifier. The input resistance and voltage gain are:

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JEE Main 2019 April 9 Shift 1 Paper & Solutions - Question 9

A ball is thrown vertically up (taken as +z-axis) from the ground. The correct momentum – height (p-h) diagram is:

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JEE Main 2019 April 9 Shift 1 Paper & Solutions - Question 10

The electric field of light wave is given as .

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

photo-electrons is:Given, E (in eV)

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JEE Main 2019 April 9 Shift 1 Paper & Solutions - Question 11

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

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JEE Main 2019 April 9 Shift 1 Paper & Solutions - Question 12

A signal Acosωt is transmitted using ν_{0} sin ω_{0}t as carrier wave. The correct amplitude modulated (AM) signal is:

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JEE Main 2019 April 9 Shift 1 Paper & Solutions - Question 13

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:

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JEE Main 2019 April 9 Shift 1 Paper & Solutions - Question 14

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 of the material of the bob. If the bob is inside liquid all the time, its period of oscillation in this liquid is:

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JEE Main 2019 April 9 Shift 1 Paper & Solutions - Question 15

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:

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JEE Main 2019 April 9 Shift 1 Paper & Solutions - Question 16

Following figure shows two process A and B for a gas. If ΔQ_{A} and ΔQ_{B} are the amount of heat absorbed by the system in two cases, and ΔU_{A} and ΔU_{B }are changes in internal energies, respectively, then:

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JEE Main 2019 April 9 Shift 1 Paper & Solutions - Question 17

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:

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JEE Main 2019 April 9 Shift 1 Paper & Solutions - Question 18

A uniform cable of mass ‘M’ and length ‘L’ is placed on a horizontal surface such

that its 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:

Detailed Solution for JEE Main 2019 April 9 Shift 1 Paper & Solutions - Question 18

JEE Main 2019 April 9 Shift 1 Paper & Solutions - Question 19

A body of mass 2 kg makes an elastic collision with a second body at rest andcontinues to move in the original direction but with one fourth of its original speed.What is the mass of the second body?

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JEE Main 2019 April 9 Shift 1 Paper & Solutions - Question 20

A capacitor with capacitance 5μF is charged to5μC. If the plates are pulled apart to reduce the capacitance to 2μF , how much work is done?

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JEE Main 2019 April 9 Shift 1 Paper & Solutions - Question 21

A rectangular coil (Dimension5cm × 2.5cm) with 100 turns, carrying a current of 3A 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 45º about Z-axis, then the torque on the coil is

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JEE Main 2019 April 9 Shift 1 Paper & Solutions - Question 22

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 λ,t will be:

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JEE Main 2019 April 9 Shift 1 Paper & Solutions - Question 23

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)

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JEE Main 2019 April 9 Shift 1 Paper & Solutions - Question 24

A rigid square loop of side ‘a’ and carrying current I_{2} is lying on a horizontal surface near a long current I_{1} carrying wire in the same plane as shown in figure. The net force on the loop due to the wire will be:

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JEE Main 2019 April 9 Shift 1 Paper & Solutions - Question 25

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

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JEE Main 2019 April 9 Shift 1 Paper & Solutions - Question 26

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 θ , where θ is the angle by which it has rotated, is given as kθ^{2} . If its moment of inertia is I then the angular acceleration of the disc is:

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JEE Main 2019 April 9 Shift 1 Paper & Solutions - Question 27

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:

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JEE Main 2019 April 9 Shift 1 Paper & Solutions - Question 28

An HCl molecule has rotational, translational and vibrational motions. If the rms velocity of HCl molecules in its gaseous phase is , m is its mass and K_{B}is Boltzman constant, then its temperature will be :

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JEE Main 2019 April 9 Shift 1 Paper & Solutions - Question 29

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:

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JEE Main 2019 April 9 Shift 1 Paper & Solutions - Question 30

Determine the charge on the capacitor in the following circuit:

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