JEE Main 2025 (24 Jan Shift 2)

63 Questions • 75 Minutes • 2025

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Which of the following figure represents the relation between Celsius and Fahrenheit temperatures ?

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The position vector of a moving body at any instant of time is given as $\vec r=\left(5t^2\hat i-5t\hat j\right)$ m. The magnitude and direction of velocity at $t=2$ s is,

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Young's double slit interference apparatus is immersed in a liquid of refractive index $1.44$. It has slit separation of $1.5$ mm. The slits are illuminated by a parallel beam of light whose wavelength in air is $690$ nm. The fringe-width on a screen placed behind the plane of slits at a distance of $0.72$ m, will be :

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A long straight wire of a circular cross-section with radius $a$ carries a steady current $I$. The current I is uniformly distributed across this cross-section. The plot of magnitude of magnetic field B with distance $r$ from the centre of the wire is given by

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In photoelectric effect, the stopping potential $(V_0)$ v/s frequency $(\nu)$ curve is plotted. ( h is the Planck's constant and $\phi_0$ is work function of metal ) (A) $V_0$ v/s $\nu$ is linear. (B) The slope of $V_0$ v/s $\nu$ curve $=\frac{\phi_0}h$ (C) h constant is related to the slope of $V_0$ v/s $\nu$ line. (D) The value of electric charge of electron is not required to determine $h$ using $V_0$ v/s $\nu$ curve. (E) The work function can be estimated without knowing the value of $h$. Choose the correct answer from the options given below :

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A solid sphere and a hollow sphere of the same mass and of same radius are rolled on an inclined plane. Let the time taken to reach the bottom by the solid sphere and the hollow sphere be $t_1$ and $t_2$, respectively, then

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A small uncharged conducting sphere is placed in contact with an identical sphere but having $4\times10^{-8}$ C charge and then removed to a distance such that the force of repulsion between them is $9\times10^{-3}$ N. The distance between them is (Take $\frac1{4\pi\epsilon_0}$ as $9\times10^9$ in SI units)

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A particle oscillates along the $x$-axis according to the law, $x(t)=x_0\sin^2\left(\frac t2\right)$ where $x_0=1$ m. The kinetic energy (K) of the particle as a function of $x$ is correctly represented by the graph

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A photograph of a landscape is captured by a drone camera at a height of $18$ km. The size of the camera film is $2\text{ cm}\times2\text{ cm}$ and the area of the landscape photographed is $400\text{ km}^2$. The focal length of the lens in the drone camera is :

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Arrange the following in the ascending order of wavelength $(\lambda)$ : (A) Microwaves $(\lambda_1)$ (B) Ultraviolet rays $(\lambda_2)$ (C) Infrared rays $(\lambda_3)$ (D) X-rays $(\lambda_4)$ Choose the most appropriate answer from the options given below :

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The energy $E$ and momentum $p$ of a moving body of mass $m$ are related by some equation. Given that $c$ represents the speed of light, identify the correct equation

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The temperature of a body in air falls from $40^\circ$C to $24^\circ$C in 4 minutes. The temperature of the air is $16^\circ$C. The temperature of the body in the next 4 minutes will be:

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A solid sphere is rolling without slipping on a horizontal plane. The ratio of the linear kinetic energy of the centre of mass of the sphere and rotational kinetic energy 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 an insulated container, a gas is adiabatically shrunk to half of its initial volume. The temperature of the gas decreases. Reason (R): Free expansion of an ideal gas is an irreversible and an adiabatic process. In the light of the above statements, choose the correct answer from the options given below :

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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) : An electron in a certain region of uniform magnetic field is moving with constant velocity in a straight line path. Reason (R): The magnetic field in that region is along the direction of velocity of the electron. In the light of the above statements, choose the correct answer from the options given below :

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For hydrogen atom, the orbital/s with lowest energy is/are : (A) $4s$ (B) $3p_x$ (C) $3d_{x^2-y^2}$ (D) $3d_{z^2}$ (E) $4p_z$ Choose the correct answer from the options given below :

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Match List - I with List - II. [table] List I (Transition metal ion) | List II (Spin only magnetic moment, B.M.) ; (A) $Ti^{3+}$ | (I) 3.87 ; (B) $V^{2+}$ | (II) 0.00 ; (C) $Ni^{2+}$ | (III) 1.73 ; (D) $Sc^{3+}$ | (IV) 2.84 [/table] Choose the correct answer from the options given below :

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Given below are two statements : Statement (I): Experimentally determined oxygen-oxygen bond lengths in the $O_3$ are found to be same and the bond length is greater than that of a $O=O$ (double bond) but less than that of a single $(O-O)$ bond. Statement (II) : The strong lone pair-lone pair repulsion between oxygen atoms is solely responsible for the fact that the bond length in ozone is smaller than that of a double bond $(O=O)$ but more than that of a single $(O-O)$ bond. In the light of the above statements, choose the correct answer from the options given below :

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When Ethane-1,2-diamine is added progressively to an aqueous solution of Nickel (II) chloride, the sequence of colour change observed will be :

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Given below are two statements : Statement (I) : The first ionization energy of Pb is greater than that of Sn. Statement (II) : The first ionization energy of Ge is greater than that of Si. In the light of the above statements, choose the correct answer from the options given below :

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Paper Info

Exam: JEE
Year: 2025
Questions: 63
Duration: 75 mins

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