JEE Main 2025 · 03 Apr 2025 · Shift 2

Q1.A magnetic dipole experiences a torque of $80\sqrt{3}\mathrm{Nm}$ when placed in uniform magnetic field in such a way that dipole moment makes angle of $60^{\circ }$ with magnetic field. The potential energy of the dipole is :

Q2.In the resonance experiment, two air columns (closed at one end) of 100 cm and 120 cm long, give 15 beats per second when each one is sounding in the respective fundamental modes. The velocity of sound in the air column is :

Q3.Two cylindrical vessels of equal cross sectional area of $2{\mathrm{m}}^2$ contain water upto height 10 m and 6 m, respectively. If the vessels are connected at their bottom then the work done by the force of gravity is : (Density of water is …

Q4.Width of one of the two slits in a Young's double slit interference experiment is half of the other slit. The ratio of the maximum to the minimum intensity in the interference pattern is :

Q5.An ideal gas exists in a state with pressure ${\mathrm{P}}_0$, volume ${\mathrm{V}}_0$. It is isothermally expanded to 4 times of its initial volume (${\mathrm{V}}_0$), then isobarically compressed to its original volume. Finally the system is heated isochorically to bring …

Q6.Two monochromatic light beams have intensities in the ratio $1:9$. An interference pattern is obtained by these beams. The ratio of the intensities of maximum to minimum is

Q7.Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A : The Bohr model is applicable to hydrogen and hydrogen-like atoms only.

Reason R : The formulation of Bohr model does not include repulsive force between electron …

Q8.Using a battery, a 100 pF capacitor is charged to 60 V and then the battery is removed. After that, a second uncharged capacitor is connected to the first capacitor in parallel. If the final voltage across the second capacitor is 20 V, its capacitance is : (in pF)

Q9.A monochromatic light of frequency $5\times 10^{14}\mathrm{Hz}$ travelling through air, is incident on a medium of refractive index '2'. Wavelength of the refracted light will be :

Q10.Consider two blocks A and B of masses ${\mathrm{m}}_1=10\mathrm{kg}$ and ${\mathrm{m}}_2=5\mathrm{kg}$ that are placed on a frictionless table. The block A moves with a constant speed $v=3\mathrm{m}/\mathrm{s}$ towards the block B kept at rest. A spring with spring …

Q11.A particle is projected with velocity $u$ so that its horizontal range is three times the maximum height attained by it. The horizontal range of the projectile is given as $\frac{n{u}^2}{25g}$, where value of $n$ is :
(Given '$g$' is the acceleration due to gravity).

Q12.A solid steel ball of diameter 3.6 mm acquired terminal velocity $2.45\times 10^{-2}\mathrm{m}/\mathrm{s}$ while falling under gravity through an oil of density $925\mathrm{kg}{\mathrm{m}}^{-3}$. Take density of steel as $7825\mathrm{kg}{\mathrm{m}}^{-3}$ and g as …

Q13.The truth table corresponding to the circuit given below is

Q14.A particle moves along the x-axis and has its displacement $x$ varying with time $t$ according to the equation
$x=c_0(t^2-2)+c(t-2{)}^2$
where $c_0$ and c are constants of appropriate dimensions. Then, which of the following statements is correct?

Q15.An electric bulb rated as $100\text{W}-220\text{V}$ is connected to an ac source of rms voltage 220 V. The peak value of current through the bulb is:

Q16.Pressure of an ideal gas, contained in a closed vessel, is increased by $0.4\%$ when heated by $1^{\circ }\text{C}$. Its initial temperature must be:

Q17.A motor operating on 100 V draws a current of 1 A. If the efficiency of the motor is $91.6\%$, then the loss of power in units of $\text{cal}/\text{s}$ is

Q18.A block of mass 1 kg, moving along x with speed $v_i=10\text{m/s}$ enters a rough region ranging from $x=0.1\text{m}$ to $x=1.9\text{m}$. The retarding force acting on the block in this range is $F_r=-kx\text{N}$, with $k=10\text{N/m}$. Then the final spee …

Q19.Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: If oxygen ion (${\text{O}}^{-2}$) and Hydrogen ion (${\text{H}}^{+}$) enter normal to the magnetic field with equal momentum, then the path of ${\text{O}}^{-2}$ ion …

Q20.Light from a point source in air falls on a spherical glass surface (refractive index, $\mu =1.5$ and radius of curvature $=50\text{cm}$). The image is formed at a distance of 200 cm from the glass surface inside the glass. The magnitude of distance of the light source from …

Q21.The excess pressure inside a soap bubble A in air is half the excess pressure inside another soap bubble B in air. If the volume of the bubble A is $n$ times the volume of the bubble B, then, the value of $n$ is ____.

Q22.Two cells of emf 1 V and 2 V and internal resistance $2\Omega$ and $1\Omega$, respectively, are connected in series with an external resistance of $6\Omega$. The total current in the circuit is $I_1$. Now the same two cells in parallel configuration are connected to …

Q23.An electron in the hydrogen atom initially in the fourth excited state makes a transition to $n^{\text{th}}$ energy state by emitting a photon of energy 2.86 eV. The integer value of n will be ____.

Q24.A physical quantity C is related to four other quantities $p,q,r$ and $s$ as follows
$C=\frac{p{q}^2}{r^3\sqrt{s}}$
The percentage errors in the measurement of $p,q,r$ and $s$ are $1\%,2\%,3\%$ and $2\%$ respectively.
The percentage error in the measurement …

Q1.40 mL of a mixture of ${\mathrm{CH}}_3\mathrm{COOH}$ and HCl (aqueous solution) is titrated against 0.1 M NaOH solution conductometrically. Which of the following statement is correct?

Q2.10 mL of 2 M NaOH solution is added to 20 mL of 1 M HCl solution kept in a beaker. Now, 10 mL of this mixture is poured into a volumetric flask of 100 mL containing 2 moles of HCl and made the volume upto the mark with distilled water. The solution in this flask is :

Q3.Fat soluble vitamins are :
A. Vitamin ${\mathrm{B}}_1$
B. Vitamin C
C. Vitamin E
D. Vitamin ${\mathrm{B}}_{12}$
E. Vitamin K

Choose the correct answer from the options given below:

Q4.For electron in '2s' and '2p' orbitals, the orbital angular momentum values, respectively are :

Q5.Compounds that should not be used as primary standards in titrimetric analysis are :
A. ${\mathrm{Na}}_2{\mathrm{Cr}}_2{\mathrm{O}}_7$
B. Oxalic acid
C. NaOH
D. ${\mathrm{FeSO}}_4\cdot 6{\mathrm{H}}_2\mathrm{O}$
E. Sodium tetraborate

Choose the most appropriate answer from the …

Q6.In the following series of reactions identify the major products A & B respectively.

Bromobenzene

Q7.The standard cell potential $({\mathrm{E}}_{\text{cell}}^{\ominus })$ of a fuel cell based on the oxidation of methanol in air that has been used to power television relay station is measured as 1.21 V. The standard half cell reduction potential for ${\mathrm{O}}_2$ …

Q8.Identify the diamagnetic octahedral complex ions from below ;
A. $[\mathrm{Mn}(\mathrm{CN}{)}_6{]}^{3-}$
B. $[\mathrm{Co}({\mathrm{NH}}_3{)}_6{]}^{3+}$
C. $[\mathrm{Fe}(\mathrm{CN}{)}_6{]}^{4-}$
D. $[\mathrm{Co}({\mathrm{H}}_2\mathrm{O}{)}_3{\mathrm{F}}_3]$

Choose the correct answer …

Q9.In Dumas' method for estimation of nitrogen 0.4 g of an organic compound gave 60 mL of nitrogen collected at 300 K temperature and 715 mm Hg pressure. The percentage composition of nitrogen in the compound is
(Given : Aqueous tension at …

Q10.Mass of magnesium required to produce 220 mL of hydrogen gas at STP on reaction with excess of dil. HCl is
Given : Molar mass of Mg is $24\mathrm{g}{\mathrm{mol}}^{-1}$.

Q1.Let $\mathrm{f}:\mathrm{R}\to \mathrm{R}$ be a function defined by $\mathrm{f}(\mathrm{x})=\Vert |\mathrm{x}+2|-2|\mathrm{x}\Vert |$. If m is the number of points of local minima and $n$ is the number of points of local maxima of f , then $\mathrm{m}+\mathrm{n}$ is

Q2.Each of the angles $\beta$ and $\gamma$ that a given line makes with the positive y - and z -axes, respectively, is half of the angle that this line makes with the positive $x$-axes. Then the sum of all possible values of the angle $\beta$ is

Q3.If the four distinct points $(4,6),(-1,5),(0,0)$ and $(\mathrm{k},3\mathrm{k})$ lie on a circle of radius r , then $10\mathrm{k}+{\mathrm{r}}^2$ is equal to

Q4.Let the Mean and Variance of five observations ${\mathrm{x}}_1=1,{\mathrm{x}}_2=3,{\mathrm{x}}_3=\mathrm{a},{\mathrm{x}}_4=7$ and ${\mathrm{x}}_5=\mathrm{b},\mathrm{a}>\mathrm{b}$, be 5 and 10 respectively. Then the Variance of the observations …

Q5.Consider the lines $\mathrm{x}(3\lambda +1)+\mathrm{y}(7\lambda +2)=17\lambda +5$, $\lambda$ being a parameter, all passing through a point P . One of these lines (say L ) is farthest from the origin. If the distance of L from the point $(3,6)$ is d , then the value of …

Q6.Let $\mathrm{A}=\{-2,-1,0,1,2,3\}$. let R be a relation on A defined by xRy if and only if $\mathrm{y}=\max \{\mathrm{x},1\}$. Let $l$ be the number of elements in R . Let m and n be the minimum number of elements required to be added in R to make it reflexive and symmetri …

Q7.let the equation $x(x+2)(12-k)=2$ have equal roots. Then the distance of the point $\left(\mathrm{k},\frac{\mathrm{k}}{2}\right)$ from the line $3x+4y+5=0$ is

Q8.Line $L_1$ of slope 2 and line $L_2$ of slope $\frac{1}{2}$ intersect at the origin O . In the first quadrant, ${\mathrm{P}}_1,{\mathrm{P}}_2,\dots .{\mathrm{P}}_{12}$ are 12 points on line ${\mathrm{L}}_1$ and …

Q9.The integral ${\int }_0^{\pi }\frac{8xdx}{4{\cos }^{2}x+{\sin }^{2}x}$ is equal to

Q10.Let f be a function such that $\mathrm{f}(\mathrm{x})+3\mathrm{f}\left(\frac{24}{\mathrm{x}}\right)=4\mathrm{x},\mathrm{x}\ne 0$. Then $\mathrm{f}(3)+\mathrm{f}(8)$ is equal to

Q11.The area of the region $\{(x,y):|x-y|\le y\le 4\sqrt{x}\}$ is

Q12.If the domain of the function
$\mathrm{f}(\mathrm{x})={\log }_7\left(1-{\log }_4\left({\mathrm{x}}^2-9\mathrm{x}+18\right)\right)$ is $(\alpha ,\beta )\cup (\gamma ,\delta )$, then $\alpha +\beta +\gamma +\delta$ is equal to

Q13.If the probability that the random variable X takes the value x is given by $\mathrm{P}(\mathrm{X}=\mathrm{x})=\mathrm{k}(\mathrm{x}+1)3^{-\mathrm{x}}$, $\mathrm{x}=0,1,2,3\dots \dots$, where k is a constant, then $\mathrm{P}(\mathrm{X}\ge 3)$ is equal to

Q14.Let $y=y(x)$ be the solution of the differential equation $\frac{dy}{dx}+3\left({\tan }^{2}x\right)y+3y={\sec }^{2}x$, $\mathrm{y}(0)=\frac{1}{3}+{\mathrm{e}}^3$. Then $\mathrm{y}\left(\frac{\pi }{4}\right)$ is equal to

Q15.If ${\mathrm{z}}_1,{\mathrm{z}}_2,{\mathrm{z}}_3\in \mathrm{C}$ are the vertices of an equilateral triangle, whose centroid is ${\mathrm{z}}_0$, then ${\sum }_{\mathrm{k}=1}^3{\left({\mathrm{z}}_{\mathrm{k}}-{\mathrm{z}}_0\right)}^2$ is equal to

Q16.The number of solutions of equation $(4-\sqrt{3})\sin x-2\sqrt{3}{\cos }^{2}x=-\frac{4}{1+\sqrt{3}},x\in \left[-2\pi ,\frac{5\pi }{2}\right]$ is

Q17.Let C be the circle of minimum area enclosing the ellipse $E:\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ with eccentricity $\frac{1}{2}$ and foci $(\pm 2,0)$. Let PQR be a variable triangle, whose vertex P is on the circle C and the side QR of length $2a$ is parallel to the majo …

Q18.The shortest distance between the curves ${\mathrm{y}}^2=8\mathrm{x}$ and $x^2+y^2+12y+35=0$ is :

Q19.The distance of the point $(7,10,11)$ from the line $\frac{x-4}{1}=\frac{y-4}{0}=\frac{z-2}{3}$ along the line $\frac{x-9}{2}=\frac{y-13}{3}=\frac{z-17}{6}$ is

Q20.The sum $1+\frac{1+3}{2!}+\frac{1+3+5}{3!}+\frac{1+3+5+7}{4!}+\dots$ upto $\infty$ terms, is equal to

Q21.Let I be the identity matrix of order $3\times 3$ and for the matrix $A=\left[\begin{array}{ccc}\lambda & 2& 3\\ 4& 5& 6\\ 7& -1& 2\end{array}\right],|A|=-1$. Let $B$ be the inverse of the matrix …

Q22.Let ${\left(1+x+x^2\right)}^{10}=a_0+a_{1}x+a_2{x}^2+\dots .+a_{20}{x}^{20}$. If $\left(a_1+a_3+a_5+\dots .+a_{19}\right)-11{\mathrm{a}}_2=121\mathrm{k}$, then k is equal to ______ .

Q23.If $\underset{\mathrm{x}\to 0}{\mathrm{Lim}}{\left(\frac{\tan \mathrm{x}}{\mathrm{x}}\right)}^{\frac{1}{{\mathrm{x}}^2}}=\mathrm{p}$, then $96{\log }_{\mathrm{e}}\mathrm{p}$ is equal to

Q24.Let $\vec{a}=\hat{i}+2\hat{j}+\hat{k},\vec{b}=3\hat{i}-3\hat{j}+3\hat{k}$, $\overrightarrow{\mathrm{c}}=2\hat{\mathrm{i}}-\hat{\mathrm{j}}+2\hat{\mathrm{k}}$ and $\overrightarrow{\mathrm{d}}$ be a vector such that $\vec{b}\times \vec{d}=\vec{c}\times \vec{d}$ and …

Q25.If the equation of the hyperbola with foci $(4,2)$ and $(8,2)$ is $3x^2-y^2-\alpha x+\beta y+\gamma =0$, then $\alpha +\beta +\gamma$ is equal to ____.