JEE Main 2023 Physics Question Paper Feb 1 Shift 2- Download PDF

A Carnot engine operating between two reservoirs has efficiency \( \frac{1}{3} \). When the temperature of the cold reservoir is raised by x, its efficiency decreases to \( \frac{1}{6} \). The value of x, if the temperature of the hot reservoir is 99\(^\circ\)C, will be:

• (1) 16.5 K
• (2) 33 K
• (3) 66 K
• (4) 62 K

Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: Two metallic spheres are charged to the same potential. One of them is hollow and another is solid, and both have the same radii. Solid sphere will have lower charge than the hollow one.

Reason R: Capacitance of metallic spheres depend on the radii of spheres.

In the light of the above statements, choose the correct answer from the options given below.

• (1) A is false but R is true
• (2) Both A and R are true and R is the correct explanation of A
• (3) A is true but R is false
• (4) Both A and R are true but R is not the correct explanation of A

As shown in the figure, a long straight conductor with a semicircular arc of radius \( \frac{\pi}{10} \) m is carrying current I = 3A. The magnitude of the magnetic field at the center O of the arc is:
(The permeability of the vacuum = \(4\pi \times 10^{-7} NA^{-2}\))

• (1) 6µT
• (2) 1µT
• (3) 4µT
• (4) 3µT

A coil is placed in a magnetic field such that the plane of the coil is perpendicular to the direction of the magnetic field. The magnetic flux through a coil can be changed:

A. By changing the magnitude of the magnetic field within the coil.

B. By changing the area of the coil within the magnetic field.

C. By changing the angle between the direction of magnetic field and the plane of the coil.

D. By reversing the magnetic field direction abruptly without changing its magnitude.

Choose the most appropriate answer from the options given below:

• (1) A and B only
• (2) A, B and C only
• (3) A, B and D only
• (4) A and C only

In an amplitude modulation, a modulating signal having amplitude of X V is superimposed with a carrier signal of amplitude Y V in the first case. Then, in the second case, the same modulating signal is superimposed with a different carrier signal of amplitude 2Y V. The ratio of modulation index in the two cases respectively will be:

• (1) 1 : 2
• (2) 1 : 1
• (3) 2 : 1
• (4) 4 : 1

For a body projected at an angle with the horizontal from the ground, choose the correct statement.

• (1) Gravitational potential energy is maximum at the highest point.
• (2) The horizontal component of velocity is zero at the highest point.
• (3) The vertical component of momentum is maximum at the highest point.
• (4) The kinetic energy (K.E.) is zero at the highest point of projectile motion.

Two objects A and B are placed at 15 cm and 25 cm from the pole in front of a concave mirror having radius of curvature 40 cm. The distance between images formed by the mirror is:

• (1) 40 cm
• (2) 60 cm
• (3) 160 cm
• (4) 100 cm

The Young's modulus of a steel wire of length 6 m and cross-sectional area 3 mm\(^{2}\), is \(2 \times 10^{11}\) N/m\(^{2}\). The wire is suspended from its support on a given planet. A block of mass 4 kg is attached to the free end of the wire. The acceleration due to gravity on the planet is \( \frac{1}{4} \) of its value on the earth. The elongation of wire is (Take g on the earth = 10 m/s\(^{2}\)):

• (1) 1 cm
• (2) 1 mm
• (3) 0.1 mm
• (4) 0.1 cm

Equivalent resistance between the adjacent corners of a regular n-sided polygon of uniform wire of resistance R would be:

• (1) \(\frac{(n-1)R}{n^2}\)
• (2) \(\frac{(n-1)R}{2n-1}\)
• (3) \(\frac{n^2 R}{n-1}\)
• (4) \(\frac{(n-1)R}{n}\)

As shown in the figure, a block of mass 10 kg lying on a horizontal surface is pulled by a force F acting at an angle 30\(^\circ\) with horizontal. For \(\mu_s = 0.25\), the block will just start to move for the value of F:
[Given g = 10 ms\(^{-2}\)]

• (1) 33.3 N
• (2) 25.2 N
• (3) 20 N
• (4) 35.7 N

Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: For measuring the potential difference across a resistance of 600 \(\Omega\), the voltmeter with resistance 1000 \(\Omega\) will be preferred over voltmeter with resistance 4000 \(\Omega\).

Reason R: Voltmeter with higher resistance will draw smaller current than voltmeter with lower resistance.

In the light of the above statements, choose the most appropriate answer from the options given below.

• (1) A is not correct but R is correct
• (2) Both A and R are correct and R is the correct explanation of A
• (3) Both A and R are correct but R is not the correct explanation of A
• (4) A is correct but R is not correct

Choose the correct statement about Zener diode:

• (1) It works as a voltage regulator in reverse bias and behaves like simple pn junction diode in forward bias.
• (2) It works as a voltage regulator in both forward and reverse bias.
• (3) It works a voltage regulator only in forward bias.
• (4) It works as a voltage regulator in forward bias and behaves like simple pn junction diode in reverse bias.

Choose the correct length (L) versus square of time period (T\(^{2}\)) graph for a simple pendulum executing simple harmonic motion.

The escape velocities of two planets A and B are in the ratio 1 : 2. If the ratio of their radii respectively is 1 : 3, then the ratio of acceleration due to gravity of planet A to the acceleration due to gravity of planet B will be:

• (1) \(\frac{4}{3}\)
• (2) \(\frac{3}{2}\)
• (3) \(\frac{2}{3}\)
• (4) \(\frac{3}{4}\)

An electron of a hydrogen-like atom, having Z = 4, jumps from 4\(^{th}\) energy state to 2\(^{nd}\) energy state. The energy released in this process, will be:
(Given Rch = 13.6 eV)
Where R = Rydberg constant

c = Speed of light in vacuum

h = Planck's constant

• (1) 13.6 eV
• (2) 10.5 eV
• (3) 3.4 eV
• (4) 40.8 eV

Figures (a), (b), (c) and (d) show variation of force with time. The impulse is highest in figure:

• (1) Fig (c)
• (2) Fig (b)
• (3) Fig (a)
• (4) Fig (d)

If the velocity of light c, universal gravitational constant G and Planck's constant h are chosen as fundamental quantities. The dimensions of mass in the new system is:

• (1) \( [h^{\frac{1}{2}} c^{-\frac{1}{2}} G^{1}] \)
• (2) \( [h^{1} c^{-1} G^{-1}] \)
• (3) \( [h^{-\frac{1}{2}} c^{\frac{1}{2}} G^{\frac{1}{2}}] \)
• (4) \( [h^{\frac{1}{2}} c^{\frac{1}{2}} G^{-\frac{1}{2}}] \)

For three low density gases A, B, C pressure versus temperature graphs are plotted while keeping them at constant volume, as shown in the figure.


The temperature corresponding to the point 'K' is:

• (1) -273\(^\circ\)C
• (2) -100\(^\circ\)C
• (3) -373\(^\circ\)C
• (4) -40\(^\circ\)C

The ratio of average electric energy density and total average energy density of electromagnetic wave is:

• (1) 2
• (2) 1
• (3) 3
• (4) \(\frac{1}{2}\)

The threshold frequency of metal is \(f_0\). When the light of frequency \(2f_0\) is incident on the metal plate, the maximum velocity of photoelectron is \(v_1\). When the frequency of incident radiation is increased to \(5f_0\), the maximum velocity of photoelectrons emitted is \(v_2\). The ratio of \(v_1\) to \(v_2\) is:

• (1) \(\frac{v_1}{v_2} = \frac{1}{2}\)
• (2) \(\frac{v_1}{v_2} = \frac{1}{8}\)
• (3) \(\frac{v_1}{v_2} = \frac{1}{16}\)
• (4) \(\frac{v_1}{v_2} = \frac{1}{4}\)

For a train engine moving with a speed of 20 ms\(^{-1}\), the driver must apply brakes at a distance of 500 m before the station for the train to come to rest at the station. If the brakes were applied at half of this distance, the train engine would cross the station with speed \(\sqrt{x}\) ms\(^{-1}\). The value of x is ____________.
(Assuming the same retardation is produced by brakes)

A force F = (5 + 3y\(^{2}\)) acts on a particle in the y-direction, where F is newton and y is in meter. The work done by the force during a displacement from y = 2m to y = 5m is ____________ J.

Moment of inertia of a disc of mass M and radius 'R' about any of its diameter is \(\frac{MR^2}{4}\). The moment of inertia of this disc about an axis normal to the disc and passing through a point on its edge will be, \(\frac{x}{2} MR^2\). The value of x is ____________.

Nucleus A having Z = 17 and equal number of protons and neutrons has 1.2 MeV binding energy per nucleon. Another nucleus B of Z = 12 has total 26 nucleons and 1.8 MeV binding energy per nucleons. The difference of binding energy of B and A will be ____________ MeV.

A square shaped coil of area 70 cm\(^{2}\) having 600 turns rotates in a magnetic field of 0.4 wbm\(^{-2}\), about an axis which is parallel to one of the side of the coil and perpendicular to the direction of field. If the coil completes 500 revolution in a minute, the instantaneous emf when the plane of the coil is inclined at 60\(^\circ\) with the field, will be ____________ V. (Take \(\pi = \frac{22}{7}\))

A block is fastened to a horizontal spring. The block is pulled to a distance x = 10 cm from its equilibrium position (at x = 0) on a frictionless surface from rest. The energy of the block at x = 5 cm is 0.25 J. The spring constant of the spring is ____________ Nm\(^{-1}\).

In the given circuit the value of \( \left| \frac{I_1 + I_3}{I_2} \right| \) is ____________.

As shown in the figure, in Young's double slit experiment, a thin plate of thickness t = 10 \(\mu\)m and refractive index \(\mu\) = 1.2 is inserted in front of slit \(S_1\). The experiment is conducted in air (\(\mu\) = 1) and uses a monochromatic light of wavelength \(\lambda\) = 500 nm. Due to the insertion of the plate, central maxima is shifted by a distance of \(x\beta_0\). \(\beta_0\) is the fringe-width before the insertion of the plate. The value of the x is ____________.
 

A cubical volume is bounded by the surfaces x = 0, x = a, y = 0, y = a, z = 0, z = a. The electric field in the region is given by \(\vec{E} = E_0 x \hat{i}\). Where \(E_0 = 4 \times 10^4\) NC\(^{-1}\) m\(^{-1}\). If a = 2 cm, the charge contained in the cubical volume is \(Q \times 10^{-14}\) C. The value of Q is ____________.
(Take \(\epsilon_0 = 9 \times 10^{-12}\) C\(^{2}\)/Nm\(^{2}\))

The surface of water in a water tank of cross section area 750 cm\(^{2}\) on the top of a house is h m. above the tap level. The speed of water coming out through the tap of cross section area 500 mm\(^{2}\) is 30 cm/s. At that instant, \(\frac{dh}{dt}\) is \(x \times 10^{-3}\) m/s. The value of x will be ____________.