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Physics

If two charges \( q_1 \) & \( q_2 \) are separated with distance ‘\( d \)’ and placed in a medium of dielectric constant \( K \). What will be the equivalent distance between charges in air for the same electrostatic force?

2.

\( 1 \, \text{g} \) of a liquid is converted to vapour at \( 3\times10^{5} \, \text{Pa} \) pressure. If \( 10\% \) of the heat supplied is used for increasing the volume by \( 1600 \, \text{cm}^{3} \) during this phase change, then the increase in internal energy in the process will be:

3.

Given below are two statements:
Statement I : An elevator can go up or down with uniform speed when its weight is balanced with the tension of its cable.
Statement II : Force exerted by the floor of an elevator on the foot of a person standing on it is more than his/her weight when the elevator goes does with increasing speed.
In the light of the above statement, choose the correct answer form the options given below:

4.

Match Column I with Column II

Choose the correct answer form the options given below:

5.

A conducting circular loop of radius \( \frac{10}{\sqrt{\pi}} \, \text{cm} \) is placed perpendicular to a uniform magnetic field of \( 0.5 \, \text{T} \). The magnetic field is decreased to zero in \( 0.5 \, \text{s} \) at a steady rate. The induced emf in the circular loop at \( 0.05 \, \text{s} \) is:

6.

Consider the following radioactive decay process
\( {}^{218}_{84}A \xrightarrow{\alpha} A_1 \xrightarrow{\beta^{-}} A_2 \xrightarrow{\gamma} A_3 \xrightarrow{\alpha} A_4 \xrightarrow{\beta^{+}} A_5 \xrightarrow{\gamma} A_6 \)
The mass number and the atomic number of \( A_6 \) are given by:

7.

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Photodiodes are preferably operated in reverse bias condition for light intensity measurement.
Reason (R): The current in the forward bias is more than the current in the reverse bias for a p – n junction diode.
In the light of the above statement, choose the correct answer from the options given below:

8.

The maximum vertical height to which a man can throw a ball is \( 136 \, \text{m} \). The maximum horizontal distance upto which he can throw the same ball is:

9.

Given below are two statements:
Statement I: The temperature of a gas is \( -73^{\circ}\text{C} \). When the gas is heated to \( 572^{\circ}\text{C} \), the root mean square speed of the molecules is doubled.
Statement II: The product of pressure and volume of an ideal gas will be equal to translational kinetic energy of the molecules.
In the light of the above statements, choose the correct answer from the options given below:

10.

A modulating signal is a square wave, as shown in the figure.

If the carrier wave is given as \( c(t) = 2\sin(8\pi t) \) volts, the modulation index is:

11.

A circular loop of radius \( r \) is carrying current \( 1 \, \text{A} \). The ratio of magnetic field at the centre of circular loop and at a distance \( r \) from the center of the loop on its axis is:

12.

From the photoelectric effect experiment, following observations are made. Identify which of these are correct.
I. The stopping potential depends only on the work function of the metal
II. The saturation current increase as the intensity of incident light increases
III. The maximum kinetic energy of a photo electron depends on the intensity of the incident light
IV. Photoelectric effect can be explained using wave theory of light
Choose the correct answer from the options given below:

13.

Two long straight wires \( P \) and \( Q \) carrying equal current \( 10 \, \text{A} \) each were kept parallel to each other at \( 5 \, \text{cm} \) distance. Magnitude of magnetic force experienced by \( 10 \, \text{cm} \) length of wire \( P \) is \( F_1 \). If distance between wires is halved and currents on them are doubled, force \( F_2 \) on \( 10 \, \text{cm} \) length of wire \( P \) will be:

14.

Given below are two statements :
Statement I : If the Brewster’s angle for the light propagating from air to glass is \( \theta_B \), then the Bresster’s angle for the light propagating from glass to air is \( \frac{\pi}{2} - \theta_B \)
Statement II : The Brewster’s angle for the light propagating from glass to air is \( \tan^{-1}(\mu_g) \) where \( \mu_g \) is the refractive index of glass.
In the light of the above statements, choose the correct answer from the options given below:

15.

As per given figure, a weightless pulley \( P \) is attached on a double inclined frictionless surfaces. The tension in the string (massless) will be (if \( g = 10 \, \text{m} \, /\text{s}^{2} \))

16.

A travelling wave is described by the equation \( y(x,t) = [0.05 \sin(8x - 4t)] \, \text{m} \). The velocity of the wave is : [all the quantities are in SI unit]

17.

In \( \vec{E} \) & \( \vec{K} \) represent electric field and propagation vectors of the EM waves in vacuum, then magnetic field vector is given by: ( \( \omega \) - angular frequency)

18.

As shown in the figure, a network of resistors is connected to a battery of \( 24 \, \text{V} \) with an internal resistance of \( 3 \, \Omega \). The currents through the resistors \( R_4 \) & \( R_5 \) are \( I_4 \) & \( I_5 \) respectively. The values of \( I_4 \) & \( I_5 \) are :

19.

A \( 100 \, \text{m} \) long wire having cross-sectional area \( 6.25 \times 10^{-4} \, \text{m}^{2} \) and Young’s modulus is \( 10^{10} \, \text{N m}^{-2} \) is subjected to a load of \( 250 \, \text{N} \), then the elongation in the wire will be:

20.

The weight of a body at the surface of earth is \( 18 \, \text{N} \). The weight of the body at an altitude of \( 3200 \, \text{km} \) above the Earth’s surface is (given, radius of earth \( R_e = 6400 \, \text{km} \) ):

21.

A spherical body of mass \( 2 \, \text{kg} \) starting from rest acquires a kinetic energy of \( 10000 \, \text{J} \) at the end of \( 5^{\text{th}} \) second. The force acted on the body is \( \text{N} \).

22.

A block of a mass \( 2 \, \text{kg} \) is attached with two identical springs of spring constant \( 20 \, \text{N/m} \) each. The block is placed on a frictionless surface and the ends of the springs are attached to rigid supports (see in figure). When the mass is displaced from its equilibrium position, it executes a simple harmonic motion. The time period of oscillation is \( \frac{\pi}{\sqrt{x}} \) in SI unit. The value of \( x \) is ________.

23.

Assume that protons and neutrons have equal masses. Mass of a nucleon is \( 1.6 \times 10^{-27} \, \text{kg} \) and radius of nucleus is \( 1.5 \times 10^{-15} A^{1/3} \, \text{m} \). The approximate ratio of the nuclear density and water density is \( n \times 10^{13} \). The value of \( n \) is ________.

24.

In the circuit shown in the figure, the ratio of the quality factor and the band width is ______ \( \text{s} \).

25.

A stream of a positively charged particles having \( \frac{q}{m} = 2 \times 10^{11} \, \frac{\mathrm{C}}{\mathrm{kg}} \) and velocity \( \vec{v}_0 = 3 \times 10^{7} \, \hat{i} \, \frac{\mathrm{m}}{\mathrm{s}} \) is deflected by an electric field \( 1.8 \, \hat{j} \, \mathrm{kV}/\mathrm{m} \). The electric field exists in a region of \( 10 \, \mathrm{cm} \) along \( x \) direction. Due to the electric field, the deflection of the charge particles in the \( y \) direction is ______.

26.

Solid sphere \( A \) is rotating about an axis \( PQ \). If the radius of the sphere is \( 5 \, \mathrm{cm} \) then its radius of gyration about \( PQ \) will be \( \sqrt{x} \, \mathrm{cm} \). The value of \( x \) is ______.

27.

A hole is drilled in a metal sheet. At \( 27^{\circ}\mathrm{C} \), the diameter of hole is \( 5 \, \mathrm{cm} \). When the sheet is heated to \( 177^{\circ}\mathrm{C} \) the change in the diameter of hole is \( d \times 10^{-3} \, \mathrm{cm} \). The value of \( d \) will be ______ if coefficient of linear expansion of the metal is \( 1.6 \times 10^{-5} \,/ {^{\circ}}\mathrm{C}^{} \).

28.

Vector \( a\hat{i} + b\hat{j} + \hat{k} \) & \( 2\hat{i} - 3\hat{j} + 4\hat{k} \) are perpendicular to each other when \( 3a + 2b = 7 \) the ratio of \( a \) to \( b \) is \( \frac{x}{2} \). The value of \( x \) is ______.

29.

A hollow cylindrical conductor has length of \( 3.14 \, \mathrm{m} \), while its inner and outer diameters are \( 4 \, \mathrm{mm} \) and \( 8 \, \mathrm{mm} \) respectively. The resistance of the conductor is \( n \times 10^{-3} \, \Omega \). If the resistivity of the material is \( 2.4 \times 10^{-8} \, \Omega \, \mathrm{m} \). The value of \( n \) is ______.

30.

As shown in the figure, a combination of thin plano concave lens and a thin plano convex lens is used to image an object at infinity. The radius of curvature of both the lenses is \( 30 \, \mathrm{cm} \) and refraction index of the material for both the lenses is \( 1.75 \). Both the lenses are placed at distance of \( 40 \, \mathrm{cm} \) from each other. Due to the combination, the image of the object is formed at distance \( x = \) ______ \( \mathrm{cm} \) from concave lens.

JEE Main 2023 24th Jan Morning Shift

Physics Chemistry Mathematics

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As shown in the figure, a network of resistors is connected to a battery of \( 24 \, \text{V} \) with an internal resistance of \( 3 \, \Omega \). The currents through the resistors \( R_4 \) & \( R_5 \) are \( I_4 \) & \( I_5 \) respectively. The values of \( I_4 \) & \( I_5 \) are :

JEE MainsJEE AdvanceBITSATJEE Mains | PYQ

JEE Mains JEE Advance BITSAT
JEE Mains | PYQ