JEE Main 2023 Physics April 8 Shift 1 Question Paper with Solution PDF- Download Here

A cylindrical wire of mass (0.4 ± 0.01)g has length (8 ± 0.04) cm and radius (6 ± 0.03) mm. The maximum error in its density will be:

Options:

• (1) 4%
• (2) 1%
• (3) 3.5%
• (4) 5%

The engine of a train moving with speed 10 ms\(^{-1}\) towards a platform sounds a whistle at frequency 400 Hz. The frequency heard by a passenger inside the train is (neglect air speed, speed of sound in air = 330 ms\(^{-1}\)):

Options:

• (1) 400 Hz
• (2) 388 Hz
• (3) 200 Hz
• (4) 412 Hz

The weight of a body on the earth is 400 N. Then weight of the body when taken to a depth half of the radius of the earth will be:

Options:

• (1) 300 N
• (2) Zero
• (3) 100 N
• (4) 200 N

A TV transmitting antenna is 98 m high, and the receiving antenna is at ground level. If the radius of the earth is 6400 km, the surface area covered by the transmitting antenna is approximately:

Options:

• (1) 1240 km\(^2\)
• (2) 1549 km\(^2\)
• (3) 4868 km\(^2\)
• (4) 3942 km\(^2\)

Certain galvanometers have a fixed core made of non-magnetic metallic material. The function of this metallic material is:

Options:

• (1) To produce large deflecting torque on the coil
• (2) To bring the coil to rest quickly
• (3) To oscillate the coil in magnetic field for longer period of time
• (4) To make the magnetic field radial

Dimension of \(\frac{1}{\mu_0 \epsilon_0}\) should be equal to:

Options:

• (1) T/L
• (2) T\(^2\)/L\(^2\)
• (3) L/T
• (4) L\(^2\)/T\(^2\)

Two projectiles A and B are thrown with initial velocities of 40 m/s and 60 m/s at angles 30° and 60° with the horizontal respectively. The ratio of their ranges is (g = 10 m/s\(^2\)):

Options:

• (1) 2 : \(\sqrt{3}\)
• (2) \(\sqrt{3}\) : 2
• (3) 4 : 9
• (4) 1 : 1

In this figure, the resistance of the coil of galvanometer G is 2\(\Omega\). The emf of the cell is 4 V. The ratio of potential difference across \(C_1\) and \(C_2\) is:




Options:

• (1) \(\frac{5}{4}\)
• (2) 1
• (3) \(\frac{4}{5}\)
• (4) \(\frac{3}{4}\)

A charge particle moving in magnetic field B has components of velocity along B and perpendicular to B. The path of the charge particle will be:

Options:

• (1) Helical path with the axis along magnetic field B
• (2) Straight along the direction of magnetic field B
• (3) Helical path with the axis perpendicular to the direction of magnetic field B
• (4) Circular path

Proton (P) and electron (e) will have same de-Broglie wavelength when the ratio of their momentum is (assume \( m_p = 1849 \, m_e \)):

Options:

• (1) 1 : 43
• (2) 43 : 1
• (3) 1 : 1849
• (4) 1 : 1

Graphical variation of electric field due to a uniformly charged insulating solid sphere of radius R, with distance r from the center O is represented by:

For a nucleus \( ^A_ZX \) having mass number A and atomic number Z:

Options:

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

At any instant the velocity of a particle of mass 500 g is \((2t\hat{i} + 3t^2\hat{j})\, ms^{-1}\). If the force acting on the particle at \(t = 1\,s\) is \((\hat{i} + x\hat{j})\,N\), then the value of \(x\) will be:

Options:

• (1) 2
• (2) 6
• (3) 3
• (4) 4

Given below are two statements:

Statement I: If \(E\) be the total energy of a satellite moving around the Earth, then its potential energy will be \(\frac{E}{2}\).

Statement II: The kinetic energy of a satellite revolving in an orbit is equal to the half the magnitude of total energy \(E\).

Options:

• (1) Both Statement I and Statement II are incorrect
• (2) Statement I is incorrect but Statement II is correct
• (3) Statement I is correct but Statement II is incorrect
• (4) Both Statement I and Statement II are correct

Two forces having magnitude \(A\) and \(\frac{A}{2}\) are perpendicular to each other. The magnitude of their resultant is:

Options:

• (1) \(\frac{5A}{2}\)
• (2) \(\frac{\sqrt{5A^2}}{2}\)
• (3) \(\frac{\sqrt{5A}}{4}\)
• (4) \(\frac{\sqrt{5A}}{2}\)

For the logic circuit shown, the output waveform at \(Y\) is:

An aluminium rod with Young's modulus \(Y = 7.0 \times 10^{10}\,N/m^2\) undergoes elastic strain of \(0.04%\). The energy per unit volume stored in the rod in SI unit is:

Options:

• (1) 5600
• (2) 2800
• (3) 11200
• (4) 8400

Given below are two statements:

Statement I: If heat is added to a system, its temperature must increase.

Statement II: If positive work is done by a system in a thermodynamic process, its volume must increase.

Options:

• (1) Both Statement I and Statement II are true
• (2) Both Statement I and Statement II are false
• (3) Statement I is true but Statement II is false
• (4) Statement I is false but Statement II is true

An air bubble of volume \(1\,cm^3\) rises from the bottom of a lake \(40\,m\) deep to the surface at a temperature of \(12^\circC\). The atmospheric pressure is \(1 \times 10^5\,Pa\), the density of water is \(1000\,kg/m^3\), and \(g = 10\,m/s^2\). The volume of the air bubble when it reaches the surface will be:

Options:

• (1) \(3\,cm^3\)
• (2) \(4\,cm^3\)
• (3) \(2\,cm^3\)
• (4) \(5\,cm^3\)

In a reflecting telescope, a secondary mirror is used to:

Options:

• (1) Make chromatic aberration zero
• (2) Reduce the problem of mechanical support
• (3) Move the eyepiece outside the telescopic tube
• (4) Remove spherical aberration

The momentum of a body is increased by 50%. The percentage increase in the kinetic energy of the body is:

A nucleus with mass number 242 and binding energy per nucleon as 7.6 MeV breaks into two fragments each with mass number 121. If each fragment nucleus has binding energy per nucleon as 8.1 MeV, the total gain in binding energy is:

An electric dipole of dipole moment \(6.0 \times 10^{-6}\,C\cdotm\) is placed in a uniform electric field of \(1.5 \times 10^3\,N/C\). The work done in rotating the dipole by \(180^\circ\) in this field will be:

An organ pipe 40 cm long is open at both ends. The speed of sound in air is \(360\,m/s\). The frequency of the second harmonic is:

The moment of inertia of a semicircular ring about an axis, passing through the center and perpendicular to the plane of the ring, is \((1/x)MR^2\), where \(R\) is the radius and \(M\) is the mass of the semicircular ring. The value of \(x\) will be:

Two vertical parallel mirrors A and B are separated by 10 cm. A point object O is placed at a distance of 2 cm from mirror A. The distance of the second nearest image behind mirror A from the mirror A is:

The magnetic intensity at the center of a long current carrying solenoid is found to be \(1.6 \times 10^3\,A/m\). If the number of turns is 8 per cm, then the current flowing through the solenoid is:

A current of 2 A through a wire of cross-sectional area \(25.0\,mm^2\). The number of free electrons in a cubic meter is \(2.0 \times 10^{28}\). The drift velocity of the electrons is \(\_\_\_\_ \times 10^{-6}\,m/s\) (given, charge on electron \(= 1.6 \times 10^{-19}\,C\)):

An oscillating LC circuit consists of a \(75\,mH\) inductor and a \(1.2\,\muF\) capacitor. If the maximum charge to the capacitor is \(2.7\,\muC\). The maximum current in the circuit will be:

An air bubble of diameter \(6\,mm\) rises steadily through a solution of density \(1750\,kg/m^3\) at the rate of \(0.35\,cm/s\). The coefficient of viscosity of the solution (neglect density of air) is \(\_\_\_\_\,Pas\) (given, \(g = 10\,m/s^2\)):