NTA JEE Main 2025 April 4th Shift 1

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.