NTA JEE Main 2025 April 4th Shift 1 - Physics

The mean free path and the average speed of oxygen molecules at 300 K and 1 atm are $$3 \times 10^{-7}$$ m and 600 m/s, respectively. Find the frequency of its collisions.

A small mirror of mass m is suspended by a massless thread of length $$l$$. Then the small angle through which the thread will be deflected when a short pulse of laser of energy E falls normal on the mirror (c = speed of light in vacuum and g = acceleration due to gravity)

Two liquids A and B have $$\theta_A$$ and $$\theta_B$$ as contact angles in a capillary tube. If $$K = \cos\theta_A / \cos\theta_B$$, then identify the correct statement:

Which of the following are correct expressions for torque acting on a body?
A. $$\vec{\tau} = \vec{r} \times \vec{L}$$
B. $$\vec{\tau} = \dfrac{d}{dt}(\vec{r} \times \vec{p})$$
C. $$\vec{\tau} = \vec{r} \times \dfrac{d\vec{p}}{dt}$$
D. $$\vec{\tau} = I\vec{\alpha}$$
E. $$\vec{\tau} = \vec{r} \times \vec{F}$$
($$\vec{r}= position vector;$$ $$\vec{p}=linear momentum;$$ $$\vec{L}= angular momentum;$$ $$\vec{\alpha} = angular acceleration;$$ $$I = moment of inertia;$$ $$\vec{F} = force; t = time$$)
Choose the correct answer from the options given below :

In a Young's double slit experiment, the slits are separated by 0.2 mm. If the slits separation is increased to 0.4 mm, the percentage change of the fringe width is:

An alternating current is represented by the equation $$i = 100\sqrt{2} \sin(100\pi t)$$ ampere. The RMS value of current and the frequency of the given alternating current are

Consider the sound wave travelling in ideal gases of He, $$CH_4$$, and $$CO_2$$. All the gases have the same ratio $$\dfrac{p}{\rho}$$, where P is the pressure and $$\rho$$ is the density. The ratio of the speed of sound through the gases $$v_{He} : v_{CH_4} : v_{CO_2}$$ is given by

In an electromagnetic system, the quantity representing the ratio of electric flux and magnetic flux has dimension of $$M^P L^Q T^R A^S$$, where value of 'Q' and 'R' are

When an object is placed 40 cm away from a spherical mirror an image of magnification $$\dfrac{1}{2}$$ is produced. To obtain an image with magnification of $$\dfrac{1}{3}$$, the object is to be moved:

Given below are two statements:
Assertion A: In photoelectric effect, on increasing the intensity of incident light the stopping potential increases.
Reason R: Increase in intensity of light increases the rate of photoelectrons emitted, provided the frequency of incident light is greater than threshold frequency.
Choose the correct answer:

If $$\vec{L}$$ and $$\vec{P}$$ represent the angular momentum and linear momentum respectively of a particle of mass 'm' having position vector $$\vec{r} = a(\hat{i}\cos\omega t + \hat{j}\sin\omega t)$$. The direction of force is

A body of mass m is suspended by two strings making angles $$\theta_1$$ and $$\theta_2$$ with the horizontal ceiling with tensions $$T_1$$ and $$T_2$$ simultaneously. $$T_1$$ and $$T_2$$ are related by $$T_1 = \sqrt{3}T_2$$. The angles $$\theta_1$$ and $$\theta_2$$ are

Current passing through a wire as function of time is given as $$I(t) = 0.02t + 0.01$$ A. The charge that will flow through the wire from $$t = 1$$ s to $$t = 2$$ s is:

Given below are two statements:
Assertion A: The kinetic energy needed to project a body of mass m from earth surface to infinity is $$\dfrac{1}{2}mgR$$, where R is the radius of earth.
Reason R: The maximum potential energy of a body is zero when it is projected to infinity from earth surface.
In the light of the above statements, choose the correct answer from the option given below

The Boolean expression $$Y = \overline{A}BC + \overline{A}C$$ can be realised with which of the following gate configurations.
A. One 3-input AND gate, 3 NOT gates and one 2-input OR gate, One 2-input AND gate,
B. One 3-input AND gate, 1 NOT gate, One 2-input NOR gate and one 2-input OR gate
C. 3-input OR gate, 3 NOT gates and one 2-input AND gate
Choose the correct answer:

In an experiment with a closed organ pipe, it is filled with water by $$\left(\dfrac{1}{5}\right)$$th of its volume. The frequency of the fundamental note will change by

Two simple pendulums having lengths $$l_1$$ and $$l_2$$ with negligible string mass undergo angular displacements $$\theta_1$$ and $$\theta_2$$, from their mean positions, respectively. If the angular accelerations of both pendulums are same, then which expression is correct?

Two infinite identical charged sheets and a charged spherical body of charge density '$$\rho$$' are arranged as shown in figure. Then the correct relation between the electrical fields at A, B, C and D points is:

Two small spherical balls of mass 10g each with charges $$-2\mu C$$ and $$2\mu C$$, are attached to two ends of very light rigid rod of length 20 cm. The arrangement is now placed near an infinite non-conducting charge sheet with uniform charge density $$100 \mu C/m^2$$ such that length of rod makes an angle of 30° with electric field generated by charge sheet. Net torque acting on the rod is: (Take $$\varepsilon_0 : 8.85 \times 10^{-12} C^2/Nm^2$$)

Considering the Bohr model of hydrogen like atoms, the ratio of the radius $$5^{\text{th}}$$ orbit of the electron in $$Li^{2+}$$ and $$He^+$$ is

A circular ring and a solid sphere having same radius roll down on an inclined plane from rest without slipping. The ratio of their velocities when reached at the bottom of the plane is $$\sqrt{\dfrac{x}{5}}$$ where x = ________.

Two slabs with square cross section of different materials (1, 2) with equal sides ($$l$$) and thickness $$d_1$$ and $$d_2$$ such that $$d_2 = 2d_1$$ and $$l \gt d_2$$. Considering lower edges of these slabs are fixed to the floor, we apply equal shearing force on the narrow faces. The angle of deformation is $$\theta_2 = 2\theta_1$$. If the shear moduli of material 1 is $$4 \times 10^9$$ N/m$$^2$$, then shear moduli of material 2 is $$x \times 10^9$$, where value of x is ________.

Distance between object and its image (magnified by $$-\dfrac{1}{3}$$) is 30 cm. The focal length of the mirror used is $$\left(\dfrac{x}{4}\right)$$ cm, where magnitude of value of x is ________.

Four capacitors each of capacitance $$16 \mu F$$ are connected as shown in the figure. The capacitance between points A and B is ________ $$\mu F$$.

Conductor wire ABCDE with each arm 10 cm in length is placed in magnetic field of $$\dfrac{1}{\sqrt{2}}$$ Tesla, perpendicular to its plane. When conductor is pulled towards right with constant velocity of 10 cm/s, induced emf between points A and E is ________ mV.