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Physics

If \( 1000 \) droplets of water of surface tension \( 0.07 \, \text{N/m} \), having same radius \( 1 \, \text{mm} \) each, combine to from a single drop. In the process the released surface energy is: (Take \( \pi = \frac{22}{7} \))

2.

A bar magnet with a magnetic moment \( 5.0 \, \text{A m}^2 \) is placed in parallel position relative to a magnetic field of \( 0.4 \, \text{T} \). The amount of required work done in turning the magnet from parallel to antiparallel position relative to the field direction is:

3.

The drift velocity of electrons for conductor connected in an electrical circuit is \( V_d \). The conductor in now replaced by another conductor with same material and same length but double the area of cross section. The applied voltage remains same. The new drift velocity of electrons will be:

4.

The pressure of a gas changes linearly with volume from \( A \) to \( B \) as shown in figure. If no heat is supplied to or extracted from the gas then change in the internal energy of the gas will be:

5.

Which of the following correctly represents the variation of electric potential \( (V) \) of a charged spherical conductor of radius \( (R) \) with radial distance \( (r) \) from the centre?

6.

If \( R \), \( X_L \), and \( X_C \) represent resistance, inductive reactance and capacitive reactance. Then which of the following is dimensionless:

7.

Two polaroide A and B are placed in such a way that the pass-axis of polaroids are perpendicular to each other. Now, another polaroid C is placed between A and B bisecting angle between them. If intensity of unpolarized light is \( I_0 \) then intensity of transmitted light after passing through polaroid B will be:

8.

At a certain depth “\( d \)” below surface of earth, value of acceleration due to gravity becomes four times that of its value at a height \( 3R \) above earth surface. Where \( R \) is Radius of earth (Take \( R = 6400 \, \text{km} \)). The depth \( d \) is equal to:

9.

The initial speed of a projectile fired from ground is \( u \). At the highest point during its motion, the speed of projectile is \( \frac{\sqrt{3}}{2}u \). The time of flight of the projectile is:

10.

Spherical insulating ball and spherical metallic ball of same size and mass are dropped from the same height. Choose the correct statement out of the following (Assume negligible air friction)

11.

If a source of electromagnetic radiation having power \( 15 \, \text{kW} \) produces \( 10^{16} \) photons per second, the radiation belongs to a part of spectrum is: (Take constant \( h = 6 \times 10^{-34} \, \text{J s} \) )

12.

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: The beam of electrons show wave nature and exhibit interference and diffraction.
Reason R: Davisson germer experimentally verified the wave nature of electrons.
In the list of the above statements, choose the most appropriate answer from the options given below:

13.

The amplitude of \( 15\sin(1000\pi t) \) is modulated by \( 10\sin(4\pi t) \) single. The amplitude modulated signal contains frequency (ies) of.
(A) \( 500\,\text{Hz} \) (B) \( 2\,\text{Hz} \) (C) \( 250\,\text{Hz} \) (D) \( 498\,\text{Hz} \) (E) \( 502\,\text{Hz} \)
Choose the correct answer from the options given below:
(1) A and B only (2) B only (3) A only (4) A, D and E only

14.

A rod with circular cross–section area \( 2\,\text{cm}^2 \) and length \( 40\,\text{cm} \) is wound uniformly with \( 400 \) turns of an insulated wire. If a current of \( 0.4\,\text{A} \) flows in the wire windings, the total magnetic flux produced inside windings is \( 4\pi\times10^{-6}\,\text{Wb} \). The relative permeability of the rod is:
(Given: Permeability of vacuum \( \mu_0 = 4\pi\times10^{-7}\,\text{N}\,\text{A}^{-2} \))

15.

A free neutron decays into a proton but a free proton does not decay into neutron. This is because

16.

The effect of increase in temperature on the number of electrons in conduction band \( (n_e) \) and resistance of a semiconductor will be is:

17.

The correct relation between \( \gamma=\frac{C_p}{C_v} \) and temperature \( T \) is:

18.

The maximum potential energy of a block executing simple harmonic motion is \( 25\,\text{J} \). \( A \) is amplitude of oscillation. At \( \frac{A}{2} \), the kinetic energy of the block is:

19.

\( 100 \) balls each of mass \( m \) moving with speed \( v \) simultaneously strike a wall normally and reflected back with same speed, in time \( t \, \text{s} \). the total force exerted by the balls on the wall is:

20.

As shown in figure, a \( 70 \, \text{kg} \) garden roller is pushed with a force of \( \vec{F} = 200 \, \text{N} \) at an angle of \( 30^\circ \) with horizontal. The normal on the roller is:
(Given \( g = 10 \, \text{m s}^{-2} \))

21.

In a medium the speed of light wave decrease to \( 0.2 \) times to its speed in free space the ratio of relative permittivity to the refractive index of the medium is \( x:1 \). The value of \( x \) is_____ :
(Given speed of light in free space = \( 3 \times 10^8 \, \text{m s}^{-1} \) and for the given medium \( \mu_r = 1 \) )

22.

The speed of a swimmer is \( 4 \, \text{km h}^{-1} \) in still water. If the swimmer makes his strokes normal to the flow of river of width \( 1 \, \text{km} \), he reaches a point \( 750 \, \text{m} \) down the stream on the opposite bank.
The speed of the river water is, ______ \( \text{km h}^{-1} \)

23.

A lift of mass \( M = 500 \, \text{kg} \) is descending with speed of \( 2 \, \text{m s}^{-1} \). Its supporting cable begins to slip thus allowing it to fall with a constant acceleration of \( 2 \, \text{m s}^{-2} \). The kinetic energy of the lift at the end of fall through to a distance of \( 6 \, \text{m} \) will be ______\( \text{kJ} \).

24.

In the figure given below, a block of mass \( M = 490 \, \text{g} \) placed on a frictionless table is connected with two springs have same spring constant \( \left( K = 2 \, \text{N m}^{-1} \right) \). If the block is horizontally displaced through ‘\( X \)’ \( \text{m} \) then the number of complete oscillations it will make in \( 14\pi \) seconds will be_____.

25.

A thin rod having a length of \( 1 \, \text{m} \) and area of cross–section \( 3 \times 10^{-6} \, \text{m}^2 \) is suspended vertically from one end. The rod is cooled from \( 210^{\circ}\text{C} \) to \( 160^{\circ}\text{C} \). After cooling, a mass \( M \) is attached at the lower end of the rod such that the length of rod again becomes \( 1 \, \text{m} \). Young's modulus and coefficient of linear expansion of the rod are \( 2 \times 10^{11} \, \text{N m}^{-2} \) and \( 2 \times 10^{-5} \, \text{K}^{-1} \), respectively. The value of \( M \) is _____ \( \text{kg} \). (Take \( g = 10 \, \text{m s}^{-2} \))

26.

An inductor of \( 0.5 \, \text{mH} \), a capacitor of \( 20 \, \mu \text{F} \) and resistance of \( 20 \, \Omega \) are connected in series with a \( 220 \, \text{V} \) \( \text{ac} \) source. If the current is in phase with the emf, the amplitude of current of the circuit is \( \sqrt{x} \) \( \text{A} \). The value of \( x \) is:

27.

Expression for an electric field is given by \( \vec{E} = 4000 x^{2} \hat{i} \, \dfrac{\text{V}}{\text{m}} \). The electric flux through the cube of side \( 20 \, \text{cm} \) when placed in electric field (as shown in the figure) is _____ \( \text{V cm} \).

28.

For hydrogen atom, \( \lambda_1 \) and \( \lambda_2 \) are the wavelengths corresponding to the transitions \( 1 \) and \( 2 \) respectively as shown in figure. The ratio of \( \lambda_1 \) and \( \lambda_2 \) is \( \dfrac{x}{32} \). The value of \( x \) is _____.

29.

A solid sphere of mass \( 1 \, \text{kg} \) rolls without slipping on a plane surface. Its kinetic energy is \( 7 \times 10^{-3} \, \text{J} \), the speed of the centre of mass of the sphere is _____ \( \text{cm s}^{-1} \).

30.

Two identical cells, when connected either in parallel or in series gives same current in an external resistance \( 5 \, \Omega \). The internal resistance of each cell will be ____ \( \Omega \).

JEE Main 2023 31st Jan Morning Shift

Physics Chemistry Mathematics

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A rod with circular cross–section area \( 2\,\text{cm}^2 \) and length \( 40\,\text{cm} \) is wound uniformly with \( 400 \) turns of an insulated wire. If a current of \( 0.4\,\text{A} \) flows in the wire windings, the total magnetic flux produced inside windings is \( 4\pi\times10^{-6}\,\text{Wb} \). The relative permeability of the rod is:
(Given: Permeability of vacuum \( \mu_0 = 4\pi\times10^{-7}\,\text{N}\,\text{A}^{-2} \))

JEE MainsJEE AdvanceBITSATJEE Mains | PYQ

JEE Mains JEE Advance BITSAT
JEE Mains | PYQ