JEE Main 2023 Question Paper (01-Feb-2023) (Shift 2)

Question 1

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 \mathrm{C} $, will be

Accepted Answer

$62 \quad K$

Answer

$16.5 \quad K$

Answer

$33 \quad K$

Answer

$66 \quad K$

Question 2

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. The solid sphere will have lower charge than the hollow one. Reason R: The capacitance of metallic spheres depends on the radii of the spheres. In the light of the above statements, choose the correct answer from the options given below.

Accepted Answer

A is true but R is false

Answer

A is false but R is true

Answer

Both $ A $ and $ R $ are true and $ R $ is the correct explanation of $ A $.

Answer

Both $ A $ and $ R $ are true but $ R $ is not the correct explanation of $ A $.

Question 3

As shown in the figure, a long straight conductor with a semicircular arc of radius $ \frac{\pi}{10} \, m $ is carrying current $ I = 3\, A $. The magnitude of the magnetic field at the center $ O $ of the arc is: (The permeability of the vacuum $ \mu_0 = 4\pi \times 10^{-7} \, \mathrm{N A}^{-2} $)

Accepted Answer

$3 \quad \mathrm{\mu T}$

Answer

$6 \quad \mathrm{\mu T}$

Answer

$1 \quad \mathrm{\mu T}$

Answer

$4 \quad \mathrm{\mu T}$

Question 4

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 the coil can be changed by: 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 the 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:

Accepted Answer

A, B and D only

Answer

A and B only

Answer

A, B and C only

Answer

A and C only

Question 5

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

Accepted Answer

$2 \;:\; 1$

Answer

$1 \;:\; 2$

Answer

$1 \;:\; 1$

Answer

$4 \;:\; 1$