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An AC source rated \( 220 \, \text{V} \), \( 50 \, \text{Hz} \) is connected to a resistor. The time taken by the current to change from its maximum to the rms value is:

2.

A constant power delivering machine has towed a box, which was initially at rest, along a horizontal straight line. The distance moved by the box in time \( t \) is proportional to:

3.

Four identical long solenoids A, B, C and D are connected to each other as shown in the figure. If the magnetic field at the center of A is \( 3 \, \text{T} \), the field at the center of C would be:
(Assume that the magnetic field is confined with in the volume of respective solenoid).

4.

A loop of flexible wire of irregular shape carrying current is placed in an external magnetic field. Identify the effect of the field on the wire.

5.

In a series LCR resonance circuit, if we change the resistance only, from a lower to higher value:

6.

Your friend is having eye sight problem. She is not able to see clearly a distant uniform window mesh and it appears to her as non-uniform and distorted. The doctor diagnosed the problem as:

7.

A thin circular ring of mass \( M \) and radius \( r \) is rotating about its axis with an angular speed \( \omega \). Two particles having mass \( m \) each are now attached at diametrically opposite points. The angular speed of the ring will become:

8.

In the experiment of Ohm’s law, a potential difference of \( 5.0 \, \text{V} \) is applied across the end of a conductor of length \( 10.0 \, \text{cm} \) and diameter of \( 5.00 \, \text{mm} \). The measured current in the conductor is \( 2.00 \, \text{A} \). The maximum permissible percentage error in the resistivity of the conductor is:

9.

In Young’s double slit arrangement, slits are separated by a gap of \( 0.5 \, \text{mm} \), and the screen is placed at a distance of \( 0.5 \, \text{m} \) from them. The distance between the first and the third bright fringe formed when the slits are illuminated by a monochromatic light of 5890 Å is:

10.

Match List-I with List-II

11.

The time period of a satellite in a circular orbit of radius \( R \) is \( T \). The period of another satellite in a circular orbit of radius \( 9R \) is:

12.

A radioactive sample disintegrates via two independent decay processes having half lives \( T_{1/2}^{(1)} \) and \( T_{1/2}^{(2)} \) respectively. The effective half-life, \( T_{1/2} \) of the nuclei is:

13.

A particle is travelling \( 4 \) times as fast as an electron. Assuming the ratio of de-Broglie wavelength of a particle to that of electron is \( 2 : 1 \), the mass of the particle is:

14.

A plane electromagnetic wave of frequency \( 100 \, \text{MHz} \) is travelling in vacuum along the \( x \)-direction. At a particular point in space and time, \( \vec{B} = 2.0 \times 10^{-8} \, \hat{k} \, \text{T} \). (where, \( \hat{k} \) is unit vector along \( z \)-direction) what is \( \vec{E} \) at this point?
(speed of light \( c = 3 \times 10^{8} \, \text{m/s} \))

15.

An oil drop of radius \( 2 \, \text{mm} \) with a density \( 3 \, \text{g} \, \text{cm}^{-3} \) is held stationary under a constant electric field \( 3.55 \times 10^{5} \, \text{V} \, \text{m}^{-1} \) in the Millikan’s oil drop experiment. What is the number of excess electrons that the oil drop will possess? Consider \( g = 9.81 \, \text{m} \, /\text{s}^{2} \)

16.

The position, velocity and acceleration of a particle moving with a constant acceleration can be represented by:

17.

The P–V diagram of a diatomic ideal gas system going under cyclic process as shown in figure. The work done during an adiabatic process \( CD \) is (use \( \gamma = 1.4 \))

18.

What will be the average value of energy along one degree of freedom for an ideal gas in thermal equilibrium at a temperature \( T \)? \( (k_{B} \) is Boltzmann constant\( ) \)

19.

The time period of a simple pendulum is given by \( T = 2\pi \sqrt{\frac{l}{g}} \). The measured value of the length of pendulum is \( 10 \, \text{cm} \) known to a \( 1 \, \text{mm} \) accuracy. The time for \( 200 \) oscillations of the pendulum is found to be \( 100 \, \text{second} \) using a clock of \( 1 \, \text{s} \) resolution. The percentage accuracy in the determination of \( g \) using this pendulum is \( x \). The value of \( x \) to the nearest integer is:

20.

Imagine that the electron in a hydrogen atom is replaced by a muon \( (\mu) \). The mass of muon particle is \( 207 \) times that of an electron and charge is equal to the charge of an electron. The ionization potential of this hydrogen atom will be:

21.

As shown in the figure, a particle of mass \( 10 \, \text{kg} \) is placed at a point A. When the particle is slightly displaced to its right, it starts moving and reaches the point B. The speed of the particle at B is \( x \, \text{m}\!/\!\text{s} \). (Take \( g = 10 \, \text{m}\,/\text{s}^{2} \)) The value of \( x \) to the nearest integer is _____________.

22.

An npn transistor operates as a common emitter amplifier with a power gain of \( 10^{6} \). The input circuit resistance is \( 100 \, \Omega \) and the output load resistance is \( 10 \, \text{k}\Omega \). The common emitter current gain \( \beta \) will be ______________. (Round off to the Nearest integer)

23.

The voltage across the \( 10 \, \Omega \) resistor in the given circuit is \( x \) volt.

The value of \( x \) to the nearest integer is _______________.

24.

A ball of mass \( 10 \, \text{kg} \) moving with a velocity \( 10\sqrt{3} \, \text{m}\!/\!\text{s} \) along the x-axis, hits another ball of mass \( 20 \, \text{kg} \) which is at rest. After this collision, first ball comes to rest while the second ball disintegrates into two equal pieces. One piece starts moving along y-axis with a speed of \( 10 \, \text{m}\!/\!\text{s} \). The second piece starts moving at an angle of \( 30^\circ \) with respect to the x-axis. The velocity of the ball moving at \( 30^\circ \) with x-axis is \( x \, \text{m}\!/\!\text{s} \). The configuration of pieces after collision is shown in the figure below. The value of \( x \) to the nearest integer is ____________.

25.

A bullet of mass \( 0.1 \, \text{kg} \) is fired on a wooden block to pierce through it, but it stops after moving a distance of \( 50 \, \text{cm} \) into it. If the velocity of bullet before hitting the wood is \( 10 \, \text{m/s} \) and it slows down with uniform deceleration, then the magnitude of effective retarding force on the bullet is \( 'x' \, \text{N} \).
The value of \( 'x' \) to the nearest integer is __________ .

26.

A parallel plate capacitor has plate area \( 100 \, \text{m}^{2} \) and plate separation of \( 10 \, \text{m} \). The space between the plates is filled up to a thickness \( 5 \, \text{m} \) with a material of dielectric constant of \( 10 \). The resultant capacitance of the system is \( x \, \text{pF}\).
The value of \( \varepsilon_{0} = 8.85 \times 10^{-12} \, \text{F·m}^{-1} \)
The value of \( x \) to the nearest integer is __________ .

27.

Two separate wires A and B are stretched by \( 2 \, \text{mm} \) and \( 4 \, \text{mm} \) respectively, when they are subjected to a force of \( 2 \, \text{N}\). Assume that both the wires are made up of same material and the radius of wire B is \( 4 \) times that of the radius of wire A.
The length of the wires A and B are in the ratio of \( a : b \). Then \( \frac{a}{b} \) can be expressed as \( \frac{1}{x} \) where \( x \) is __________ .

28.

The circuit shown in the figure consists of a charged capacitor of capacity \( 3 \, \mu\text{F} \) and a charge of \( 30 \, \mu\text{C} \). At time \( t = 0 \), when the key is closed, the value of current flowing through the \( 5 \, \text{M}\Omega \) resistor is \(' x' \, \mu\text{A} \).
The value of \( 'x' \) to the nearest integer is __________ .

29.

A person is swimming with a speed of \( 10 \, \text{m/s} \) at an angle of \( 120^\circ \) with the flow and reaches to a point directly opposite on the other side of the river. The speed of the flow is \(' x' \, \text{m/s} \). The value of \( 'x '\) to the nearest integer is __________ .

30.

A particle performs simple harmonic motion with a period of \( 2 \, \text{second} \). The time taken by the particle to cover a displacement equal to half of its amplitude from the mean position is \( \frac{1}{a} \, \text{s} \).
The value of \( 'a' \) to the nearest integer is __________ .

JEE Main 2021 18th March Morning Shift

Physics Chemistry Mathematics

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In the experiment of Ohm’s law, a potential difference of \( 5.0 \, \text{V} \) is applied across the end of a conductor of length \( 10.0 \, \text{cm} \) and diameter of \( 5.00 \, \text{mm} \). The measured current in the conductor is \( 2.00 \, \text{A} \). The maximum permissible percentage error in the resistivity of the conductor is:

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JEE Mains | PYQ