JEE Main 2025 (22 Jan Shift 2)

65 Questions • 75 Minutes • 2025

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A small rigid spherical ball of mass M is dropped in a long vertical tube containing glycerine. The velocity of the ball becomes constant after some time. If the density of glycerine is half of the density of the ball, then the viscous force acting on the ball will be (consider g as acceleration due to gravity)

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The torque due to the force $(2\hat i+\hat j+2\hat k)$ about the origin, acting on a particle whose position vector is $(\hat i+\hat j+\hat k)$, would be

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A transparent film of refractive index, 2.0 is coated on a glass slab of refractive index, 1.45. What is the minimum thickness of transparent film to be coated for the maximum transmission of Green light of wavelength 550 nm. [Assume that the light is incident nearly perpendicular to the glass surface.]

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Given are statements for certain thermodynamic variables, (A) Internal energy, volume (V) and mass (M) are extensive variables. (B) Pressure (P), temperature (T) and density ($\rho$) are intensive variables. (C) Volume (V), temperature (T) and density ($\rho$) are intensive variables. (D) Mass (M), temperature (T) and internal energy are extensive variables. Choose the correct answer from the options given below :

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An electron projected perpendicular to a uniform magnetic field $B$ moves in a circle. If Bohr's quantization is applicable, then the radius of the electronic orbit in the first excited state is :

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Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : In Young's double slit experiment, the fringes produced by red light are closer as compared to those produced by blue light. Reason (R): The fringe width is directly proportional to the wavelength of light. In the light of the above statements, choose the correct answer from the options given below :

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A rectangular metallic loop is moving out of a uniform magnetic field region to a field free region with a constant speed. When the loop is partially inside the magnetic field, the plot of magnitude of induced emf ($\varepsilon$) with time ($t$) is given by

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A ball of mass 100 g is projected with velocity 20 m/s at $60^\circ$ with horizontal. The decrease in kinetic energy of the ball during the motion from point of projection to highest point is

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Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : A simple pendulum is taken to a planet of mass and radius, 4 times and 2 times, respectively, than the Earth. The time period of the pendulum remains same on earth and the planet. Reason (R): The mass of the pendulum remains unchanged at Earth and the other planet. In the light of the above statements, choose the correct answer from the options given below :

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A series LCR circuit is connected to an alternating source of emf $E$. The current amplitude at resonant frequency is $I_0$. If the value of resistance $R$ becomes twice of its initial value then amplitude of current at resonance will be

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Which one of the following is the correct dimensional formula for the capacitance in F ? M, L, T and C stand for unit of mass, length, time and charge,

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A light source of wavelength $\lambda$ illuminates a metal surface and electrons are ejected with maximum kinetic energy of 2 eV. If the same surface is illuminated by a light source of wavelength $\frac\lambda2$, then the maximum kinetic energy of ejected electrons will be (The work function of metal is 1 eV)

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The maximum percentage error in the measurement of density of a wire is [Given, mass of wire $=(0.60\pm0.003)$ g, radius of wire $=(0.50\pm0.01)$ cm, length of wire $=(10.00\pm0.05)$ cm]

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For a diatomic gas, if $\gamma_1=\left(\frac{C_p}{C_v}\right)$ for rigid molecules and $\gamma_2=\left(\frac{C_p}{C_v}\right)$ for another diatomic molecules, but also having vibrational modes. Then, which one of the following options is correct ? ($C_p$ and $C_v$ are specific heats of the gas at constant pressure and volume)

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A force $\vec F=2\hat i+b\hat j+\hat k$ is applied on a particle and it undergoes a displacement $\hat i-2\hat j-\hat k$. What will be the value of $b$, if work done on the particle is zero.

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Given below are two statements : Statement (I) : Nitrogen, sulphur, halogen and phosphorus present in an organic compound are detected by Lassaigne's Test. Statement (II) : The elements present in the compound are converted from covalent form into ionic form by fusing the compound with Magnesium in Lassaigne's test. In the light of the above statements, choose the correct answer from the options given below :

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Density of 3 M NaCl solution is 1.25 g/mL. The molality of the solution is :

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The correct order of the following complexes in terms of their crystal field stabilization energies is :

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Given below are two statements : Statement (I) : Corrosion is an electrochemical phenomenon in which pure metal acts as an anode and impure metal as a cathode. Statement (II) : The rate of corrosion is more in alkaline medium than in acidic medium. In the light of the above statements, choose the correct answer from the options given below :

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RBr —(i) Mg, dry ether; (ii) H₂O→ 2-Methylbutane The maximum number of RBr producing 2-methylbutane by above sequence of reactions is ________ - (Consider the structural isomers only)

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Paper Info

Exam: JEE
Year: 2025
Questions: 65
Duration: 75 mins

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