JEE Main 2025 (23 Jan Shift 1)

67 Questions • 75 Minutes • 2025

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A spherical surface of radius of curvature $R$, separates air from glass (refractive index $=1.5$). The centre of curvature is in the glass medium. A point object ' $O$ ' placed in air on the optic axis of the surface, so that its real image is formed at ' $I$ ' inside glass. The line $OI$ intersects the spherical surface at $P$ and $PO=PI$. The distance $PO$ equals to

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The position of a particle moving on $x$-axis is given by $x(t)=A\sin t+B\cos^2t+Ct^2+D$, where $t$ is time. The dimension of $\frac{ABC}D$ is

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Given a thin convex lens (refractive index $\mu_2$), kept in a liquid (refractive index $\mu_1$, $\mu_1<\mu_2$) having radii of curvatures $|R_1|$ and $|R_2|$. Its second surface is silver polished. Where should an object be placed on the optic axis so that a real and inverted image is formed at the same place?

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Given below are two statements: Statement I: The hot water flows faster than cold water Statement II: Soap water has higher surface tension as compared to fresh water. In the light above statements, choose the correct answer from the options given below

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Consider a circular disc of radius 20 cm with centre located at the origin. A circular hole of radius 5 cm is cut from this disc in such a way that the edge of the hole touches the edge of the disc. The distance of centre of mass of residual or remaining disc from the origin will be

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The electric flux is $\phi=\alpha\sigma+\beta\lambda$ where $\lambda$ and $\sigma$ are linear and surface charge density, respectively. $\left(\frac\alpha\beta\right)$ represents

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A sub-atomic particle of mass $10^{-30}$ kg is moving with a velocity $2.21\times10^6$ m/s. Under the matter wave consideration, the particle will behave closely like ($h=6.63\times10^{-34}$ J.s)

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Consider a moving coil galvanometer (MCG): A. The torsional constant in moving coil galvanometer has dimensions $[ML^2T^{-2}]$ B. Increasing the current sensitivity may not necessarily increase the voltage sensitivity. C. If we increase number of turns (N) to its double (2N), then the voltage sensitivity doubles. D. MCG can be converted into an ammeter by introducing a shunt resistance of large value in parallel with galvanometer. E. Current sensitivity of MCG depends inversely on number of turns of coil. Choose the correct answer from the options given below:

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Match the LIST-I with LIST-II. [table] LIST-I | LIST-II ; A. Pressure varies inversely with volume of an ideal gas. | I. Adiabatic process ; B. Heat absorbed goes partly to increase internal energy and partly to do work. | II. Isochoric process ; C. Heat is neither absorbed nor released by a system. | III. Isothermal process ; D. No work is done on or by a gas. | IV. Isobaric process [/table]

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The electric field of an electromagnetic wave in free space is $\vec E=57\cos\left[7.5\times10^6t-5\times10^{-3}(3x+4y)\right](4\hat i-3\hat j)\,N/C$. The associated magnetic field in Tesla is

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A gun fires a lead bullet of temperature 300 K into a wooden block. The bullet having melting temperature of 600 K penetrates into the block and melts down. If the total heat required for the process is 625 J, then the mass of the bullet is ______ grams. (Latent heat of fusion of lead $=2.5\times10^4\,\mathrm{J\,kg^{-1}}$ and specific heat capacity of lead $=125\,\mathrm{J\,kg^{-1}K^{-1}}$)

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What is the lateral shift of a ray refracted through a parallel-sided glass slab of thickness ' $h$ ' in terms of the angle of incidence ' $i$ ' and angle of refraction ' $r$ ', if the glass slab is placed in air medium?

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A radioactive nucleus $n_2$ has 3 times the decay constant as compared to the decay constant of another radioactive nucleus $n_1$. If initial number of both nuclei are the same, what is the ratio of number of nuclei of $n_2$ to the number of nuclei of $n_1$, after one half-life of $n_1$ ?

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A light hollow cube of side length 10 cm and mass 10 g, is floating in water. It is pushed down and released to execute simple harmonic oscillations. The time period of oscillations is $y\pi\times10^{-2}$ s, where the value of $y$ is (Acceleration due to gravity, $g=10\ \mathrm{m/s^2}$, density of water $=10^3\ \mathrm{kg/m^3}$)

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Regarding self-inductance: A. The self-inductance of the coil depends on its geometry. B. Self-inductance does not depend on the permeability of the medium. C. Self-induced e.m.f. opposes any change in the current in a circuit. D. Self-inductance is electromagnetic analogue of mass in mechanics. E. Work needs to be done against self-induced e.m.f. in establishing the current. Choose the correct answer from the options given below:

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A solid sphere of mass ' $m$ ' and radius ' $r$ ' is allowed to roll without slipping from the highest point of an inclined plane of length ' $L$ ' and makes an angle $30^\circ$ with the horizontal. The speed of the particle at the bottom of the plane is $v_1$. If the angle of inclination is increased to $45^\circ$ while keeping $L$ constant. Then the new speed of the sphere at the bottom of the plane is $v_2$. The ratio $v_1^2:v_2^2$ is

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Given below are two statements: Statement I: Fructose does not contain an aldehydic group but still reduces Tollen's reagent Statement II: In the presence of base, fructose undergoes rearrangement to give glucose. In the light of the above statements, choose the correct answer from the options given below

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The complex that shows Facial - Meridional isomerism is:

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$\mathrm{FeO_4^{2-}}\xrightarrow{+2.0\,V}\mathrm{Fe^{3+}}\xrightarrow{0.8\,V}\mathrm{Fe^{2+}}\xrightarrow{-0.5\,V}\mathrm{Fe^0}$ In the above diagram, the standard electrode potentials are given in volts (over the arrow). The value of $E^\circ_{\mathrm{FeO_4^{2-}/Fe^{2+}}}$ is

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The element that does not belong to the same period of the remaining elements (modern periodic table) is:

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Paper Info

Exam: JEE
Year: 2025
Questions: 67
Duration: 75 mins

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