JEE Main 2021 March 16 Shift 1 Question Paper & Solutions - JEE MCQ

The pressure acting on a submarine is 3 × 10⁵ Pa at a certain depth. If the depth is doubled, the percentage increase in the pressure acting on the submarine would be: (Assume that atmospheric pressure is 1 × 10⁵ Pa, density of water is 10³ kg m^-3, g = 10 ms^-2)

The angle of deviation through a prism is minimum when:

(A) Incident ray and emergent ray are symmetric to the prism.
(B) The refracted ray inside the prism becomes parallel to its base.
(C) Angle of incidence is equal to the angle of emergence.
(D) Angle of emergence is double the angle of incidence.
Choose the correct answer from the options given below:

A plane electromagnetic wave of frequency 500 MHz is travelling in vacuum along y-direction. At a particular point in space and time,  . The value of electric field at this point is:
(speed of light = 3 × 108 ms-1) 
 are unit vectors along x, y and z directions.

The maximum and minimum distances of a comet from the Sun are 1.6 × 10¹² m and 8.0 × 10¹⁰ m, respectively. If the speed of the comet at the nearest point is 6 × 10⁴ m/s, the speed at the farthest point is:

A bar magnet of length 14 cm is placed in the magnetic meridian with its north pole pointing towards the geographic north pole. A neutral point is obtained at a distance of 18 cm from the centre of the magnet. If B_H = 0.4G, the magnetic moment of the magnet is (1 G = 10^-4 T)

The volume V of an enclosure contains a mixture of three gases, 16 g of oxygen, 28 g of nitrogen and 44 g of carbon dioxide at absolute temperature T. Consider R as universal gas constant. The pressure of the mixture of gases is:

In thermodynamics, heat and work are:

Four equal masses m each are placed at the corners of a square of length (l) as shown in the figure. The moment of inertia of the system about an axis passing through A and parallel to DB would be:

A conducting wire of length 'l', area of cross-section A and electric resistivity ρ is connected between the terminals of a battery. A potential difference V is developed between its ends, causing an electric current.
If the length of the wire of the same material is doubled and the area of cross-section is halved, the resultant current would be:

Time period of a simple pendulum is T inside a lift when the lift is stationary. If the lift moves upwards with an acceleration g/2, the time period of pendulum will be:

The velocity-displacement graph describing the motion of a bicycle is shown in the figure.

The acceleration-displacement graph of the bicycle's motion is best described by:

A 25 m long antenna is mounted on an antenna tower. The height of the antenna tower is 75 m. The wavelength (in metres) of the signal transmitted by this antenna would be:

For an electromagnetic wave travelling in free space, the relation between average energy densities due to electric (U_e) and magnetic (U_m) fields is:

An RC circuit as shown in the figure is driven by an AC source generating a square wave. The output wave pattern monitored by CRO would look close to:

The stopping potential in the context of photoelectric effect depends on the following property of incident electromagnetic radiation:

A block of 200 g mass moves with a uniform speed in a horizontal circular groove, with vertical side walls of radius 20 cm. If the block takes 40 s to complete one round, the normal force by the side walls of the groove is:

A conducting bar of length L is free to slide on two parallel conducting rails as shown in the figure.

Two resistors R₁ and R₂ are connected across the ends of the rails. There is a uniform magnetic field  pointing into the page. An external agent pulls the bar to the left at a constant speed v.
The correct statement about the directions of induced currents I₁ and I₂ flowing through R₁ and R₂ respectively is:

In the figure given, the electric current flowing through the 5 kΩ resistor is 'x' mA.

The value of x, to the nearest integer, is ________.

A fringe width of 6 mm was produced for two slits separated by 1 mm apart. The screen is placed 10 m away. The wavelength of light used is 'x' nm. The value of 'x', to the nearest integer, is ______.

Consider a 20 kg uniform circular disk of radius 0.2 m. It is pin supported at its centre and is at rest initially. The disk is acted upon by a constant force F = 20 N through a massless string wrapped around its periphery as shown in the figure.

Suppose the disk makes n number of revolutions to attain an angular speed of 50 rad s^-1. The value of n, to the nearest integer, is __________. [Given: In one complete revolution, the disk rotates by 6.28 rad.]

The first three spectral lines of H-atom in the Balmer series are given λ₁,λ₂ and λ₃. Considering the Bohr atomic model, the wavelengths of first and third spectral lines λ₁ / λ₃ are related by a factor of approximately 'x' × 10^-1. The value of x, to the nearest integer, is __________.

The value of power dissipated across the zener diode (V_z = 15 V) connected in the circuit as shown in the figure is x × 10^-1 Watt.

The value of x, to the nearest integer, is ________.

A sinusoidal voltage of peak value 250 V is applied to a series LCR circuit, in which R = 8 Ω, L = 24 mH and C = 60μF. The value of power dissipated at resonant condition is 'x' kW. The value of x, to the nearest integer, is ________.

In the logic circuit shown in the figure, if inputs A and B are 0 to 1 respectively, the output at Y would be 'x'. The value of x is ________.

The resistance R = V/I , where V = (50 ± 2) V and I = (20 ± 0.2) A. The percentage error in R is x%. The value of 'x', to the nearest integer, is ___________.

Consider a frame that is made up of two thin massless rods AB and AC as shown in the figure.
A vertical force  of magnitude 100 N is applied at point A of the frame.

Suppose the force is  resolved parallel to the arms AB and AC of the frame. The magnitude of the resolved component along the arm AC is xN. The value of x, to the nearest integer, is _________.
[Given: sin (35°) = 0.573, cos (35°) = 0.819 sin (110°) = 0.939, cos (110°) = -0.342]

A ball of mass 10 kg moving with a velocity 10√3ms^-1 along X-axis hits another ball of mass 20 kg which is at rest. After collision, the first ball comes to rest and the second one disintegrates into two equal pieces. One of the pieces starts moving along Y-axis at a speed of 10 m/s. The second piece starts moving at a speed of 20 m/s at an angle θ (degree) with respect to X-axis.
The configuration of pieces after collision is shown in the figure. The value of θ, to the nearest integer, is ________.