JEE Main 2025 · April session

JEE Main 2 April 2025, Shift 2

75 questions: 15 numerical-answer and 60 multiple choice. 6 were rated hard and 23 easy. Its hard-question count was the joint 7th highest of the 8 2025 shifts Lumi analysed. The biggest chapter was Organic Chemistry: Some Basic Principles and Techniques, with 4 questions.

Questions: 75; none dropped
Numerical answer: 15; 20% of the shift
Hard: 6; 8% of the shift
Chapters asked: 56; 15 questions with a figure

Key findings · 2 Apr 2025, Shift 2

1
6 hard questions (8%): the joint 7th highest count of the 8 2025 shifts Lumi analysed. Across those shifts the hard share ran from 8% to 20%.
2
Maths was the hardest section, with 4 of 25 rated hard; Physics had the most easy questions (13 of 25).
3
14 questions tested a new idea, one no earlier year had asked: 22% of the 64 questions tagged to an idea.
4
31 came back from 2024: the same idea had been asked in the 2024 shifts Lumi analysed.
5
14 shared an idea with another 2025 shift (22% of tagged questions). Shifts in the same year can test the same idea in a new setting.
6
Biggest chapters: Ray Optics and Optical Instruments in Physics (3), Organic Chemistry: Some Basic Principles and Techniques in Chemistry (4) and Integrals in Maths (3).

The shift at a glance

Subjects, difficulty and chapters

Physics

25 Q · 5 numerical

Easy 13Medium 12Hard 0

Top chapters

Chemistry

25 Q · 5 numerical

Easy 6Medium 17Hard 2

Top chapters

Maths

25 Q · 5 numerical

Easy 4Medium 17Hard 4

Top chapters

Question format

Single correct46 Q
Numerical value15 Q
Diagram based5 Q
Other4 Q
Match the list3 Q
Assertion–reason1 Q
Two statements1 Q

What each question asks you to do

Multi-step25 Q
Calculation17 Q
Application16 Q
Conceptual8 Q
Recall5 Q
Diagram reading2 Q
Data or graph2 Q

Most common: Multi-step.

Against the other 2025 shifts

This shift next to the 7 other 2025 shifts Lumi analysed

Shares are of each shift’s scored questions. The highlighted row is this shift.

Shift	Questions	Easy	Hard	Numerical	New ideas	Multi-step
2 Apr, Shift 1	75	21%	12%	20%	21%	44%
2 Apr, Shift 2	75	31%	8%	20%	22%	33%
3 Apr, Shift 1	74	28%	14%	20%	25%	38%
3 Apr, Shift 2	75	29%	8%	20%	31%	36%
4 Apr, Shift 2	75	24%	20%	20%	21%	45%
7 Apr, Shift 1	75	32%	12%	20%	18%	43%
7 Apr, Shift 2	75	24%	12%	20%	25%	45%
8 Apr, Shift 2	75	27%	17%	20%	20%	40%

New ideas: share of a shift’s questions testing an idea no earlier year had asked. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.

Drill down

What this shift asked, and its history

Every chapter this shift asked, with all its topics and ideas. Counts and squares cover every analysed shift from 2017 to 2026; rows this shift did not ask are faded, and each row lists this shift’s questions with the most recent from other shifts.

subjectAskedShareYears’17’20’21’22’23’24’25’26

Open25 this shift3092 · 33%33%8/830299720720358540200225
Open25 this shift3084 · 33%33%8/830298716720359538199224
Open25 this shift3065 · 33%33%8/829299715710354533200225

Squares are the 8 years with analysed shifts, 2017 to 2026. A number is the questions that year when there is more than one; the shade is scaled to one shift, so a year with more analysed shifts (1 to 24 a year) does not look darker. Share is of the level above.

Every question

All 75 questions of this shift

The opening words of each question, with its chapter, topic, idea and how hard it was. Open one for the full text, options and the official answer. “New idea” means no earlier year had tested it.

Subject

Difficulty

Idea

Find

75 of 75 questions

Physics25 questions

13 easy12 medium0 hard

Q26
Match List - I with List - II. List - I (A) Heat capacity of body (B) Specific heat capacity of body (C) Latent heat (D) Thermal conductivity List - II (I) $\mathrm{J\,kg^{-1}}$ (II) $\mathrm{J\,K^{-1}}$ (III) $\mathrm{J\,kg^{-1}\,K^{-1}}$ (IV)…
Thermal Properties of Matter
EasyMatch the list
Q27
Given a charge $q$ , current $I$ and permeability of vacuum $\mu_0$ . Which of the following quantity has the dimension of momentum ?
Units and Measurements Biot-Savart Law Dimensions of Permeability
MediumSingle correctIdea asked in 2 years
Q28
The moment of inertia of a circular ring of mass $M$ and diameter $r$ about a tangential axis lying in the plane of the ring is :
System of Particles and Rotational Motion Moment of Inertia MOI of a Ring About Tangents
EasySingle correctNew idea
Q29
A body of mass 1 kg is suspended with the help of two strings making angles as shown in figure. Magnitudes of tensions $T_1$ and $T_2$ , respectively, are (in N) : (Take acceleration due to gravity $10\ \mathrm{m/s^2}$ )
Laws of Motion Newton's Laws of Motion Equilibrium of a String Junction (Knot)
EasySingle correct · figureIdea asked in 2 years
Q30
A sportsman runs around a circular track of radius $r$ such that he traverses the path ABAB. The distance travelled and displacement, respectively, are
Motion in a Straight Line Kinematics in 1D Distance and Displacement Distinction
EasySingle correct · figureIdea asked in 3 yearsAsked the year before
Q31
Two water drops each of radius $r$ coalesce to form a bigger drop. If $T$ is the surface tension, the surface energy released in this process is :
Mechanical Properties of Fluids Surface Tension Splitting and Coalescence
EasySingle correctIdea asked in 5 yearsAsked the year before
Q32
Identify the characteristics of an adiabatic process in a monoatomic gas. (A) Internal energy is constant. (B) Work done in the process is equal to the change in internal energy. (C) The product of temperature and volume is a constant. (D) The product of…
Thermodynamics Thermodynamic Processes Adiabatic Process Analysis
MediumOtherIdea asked in 7 yearsAsked the year before
Q33
An electron with mass $m$ with an initial velocity $(t=0)$ $\vec{v} = v_0\hat{i}$ $(v_0 > 0)$ enters a magnetic field $\vec{B} = B_0\hat{j}$ . If the initial de-Broglie wavelength at $t = 0$ is $\lambda_0$ then its value after time $t$ would be :
Dual Nature of Radiation and Matter Matter Waves Wavelength in a Uniform Magnetic Field
MediumSingle correctNew idea
Q34
A sinusoidal wave of wavelength 7.5 cm travels a distance of 1.2 cm along the $x$ -direction in 0.3 sec. The crest P is at $x = 0$ at $t = 0$ sec and maximum displacement of the wave is 2 cm. Which equation correctly represents this wave ?
Waves
MediumSingle correct
Q35
If $\mu_0$ and $\epsilon_0$ are the permeability and permittivity of free space, respectively, then the dimension of $\left(\frac{1}{\mu_0\epsilon_0}\right)$ is :
Units and Measurements Coulomb's Law Dimensional Analysis of Permittivity
EasySingle correctIdea asked in 3 yearsAsked the year before
Q36
Two identical objects are placed in front of convex mirror and concave mirror having same radii of curvature of 12 cm, at same distance of 18 cm from the respective mirrors. The ratio of sizes of the images formed by convex mirror and by concave mirror is :
Ray Optics and Optical Instruments Spherical Mirrors Linear Magnification
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q37
A bi-convex lens has radius of curvature of both the surfaces same as $1/6$ cm. If this lens is required to be replaced by another convex lens having different radii of curvatures on both sides $(R_1 \neq R_2)$ , without any change in lens power then possible…
Ray Optics and Optical Instruments Lens Maker's Formula Lens Maker's Equation
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q38
Energy released when two deuterons ( $_1\mathrm{H}^2$ ) fuse to form a helium nucleus ( $_2\mathrm{He}^4$ ) is : (Given : Binding energy per nucleon of $_1\mathrm{H}^2 = 1.1$ MeV and binding energy per nucleon of $_2\mathrm{He}^4 = 7.0$ MeV)
Nuclei Nuclear Binding Energy Binding Energy per Nucleon
EasySingle correctIdea asked in 6 yearsAsked the year before
Q39
In the digital circuit shown in the figure, for the given inputs the P and Q values are :
Semiconductor Electronics: Materials, Devices and Simple Circuits Logic Gates Combinational Logic Circuits
MediumDiagram based · figureIdea asked in 7 yearsAsked the year before
Q40
Assuming the validity of Bohr's atomic model for hydrogen like ions the radius of $\mathrm{Li^{++}}$ ion in its ground state is given by $\frac{1}{X}a_0$ , where $X =$ __________. (Where $a_0$ is the first Bohr's radius.)
Atoms Bohr's Atomic Model Bohr Orbit Radius
EasySingle correctIdea asked in 4 yearsAsked the year before
Q41
Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Net dipole moment of a polar linear isotropic dielectric substance is not zero even in the absence of an external electric field.…
Electrostatic Potential and Capacitance Dielectrics Polar vs. Non-Polar Dielectrics
EasyAssertion–reasonIdea asked in 2 years
Q42
Two large plane parallel conducting plates are kept 10 cm apart as shown in figure. The potential difference between them is V. The potential difference between the points A and B (shown in the figure) is :
Electrostatic Potential and Capacitance Electric Potential Equipotential Planes of Uniform Field
MediumDiagram based · figureNew idea
Q43
A solenoid having area $A$ and length $l$ is filled with a material having relative permeability 2. The magnetic energy stored in the solenoid is :
Electromagnetic Induction Inductance Magnetic Energy Density
MediumSingle correctIdea asked in 2 years
Q44
Consider a circular loop that is uniformly charged and has a radius $a\sqrt{2}$ . Find the position along the positive $z$ -axis of the cartesian coordinate system where the electric field is maximum if the ring was assumed to be placed in $xy$ plane at the…
Electric Charges and Fields Electric Field Maximum Axial Field of a Ring
MediumSingle correctNew idea
Q45
In a moving coil galvanometer, two moving coils $M_1$ and $M_2$ have the following particulars : $R_1 = 5\ \Omega$ , $N_1 = 15$ , $A_1 = 3.6\times10^{-3}\ \mathrm{m^2}$ , $B_1 = 0.25$ T $R_2 = 7\ \Omega$ , $N_2 = 21$ , $A_2 = 1.8\times10^{-3}\ \mathrm{m^2}$ ,…
Moving Charges and Magnetism
MediumSingle correct
Q46
A wheel of radius 0.2 m rotates freely about its center when a string that is wrapped over its rim is pulled by force of 10 N as shown in figure. The established torque produces an angular acceleration of $2\ \mathrm{rad/s^2}$ . Moment of intertia of the…
System of Particles and Rotational Motion Torque and Equilibrium Lever Arm Method
EasyNumerical value · figureIdea asked in 2 years
Q47
A satellite of mass 1000 kg is launched to revolve around the earth in an orbit at a height of 270 km from the earth's surface. Kinetic energy of the satellite in this orbit is __________ $\times 10^{10}$ J. (Mass of earth $= 6\times10^{24}$ kg, Radius of…
Gravitation Orbital Mechanics Energy of Orbiting Bodies
MediumNumerical valueIdea asked in 3 yearsAsked the year before
Q48
The length of a light string is 1.4 m when the tension on it is 5 N. If the tension increases to 7 N, the length of the string is 1.56 m. The original length of the string is __________ m.
Mechanical Properties of Solids Elasticity Finding Natural Length from Two Tensions
EasyNumerical valueIdea asked in 3 years
Q49
A ray of light suffers minimum deviation when incident on a prism having angle of the prism equal to $60^\circ$ . The refractive index of the prism material is $\sqrt{2}$ . The angle of incidence (in degrees) is __________.
Ray Optics and Optical Instruments Prism Deviation Prism Refractive Index
EasyNumerical valueIdea asked in 3 years
Q50
The internal energy of air in $4\ \mathrm{m}\times4\ \mathrm{m}\times3\ \mathrm{m}$ sized room at 1 atmospheric pressure will be __________ $\times10^6$ J. (Consider air as diatomic molecule)
Kinetic Theory Kinetic Theory of Gases Law of Equipartition
EasyNumerical valueIdea asked in 4 yearsAsked the year before

Chemistry25 questions

6 easy17 medium2 hard

Maths25 questions

4 easy17 medium4 hard

Q1
If the domain of the function $f(x) = \frac{1}{\sqrt{10+3x-x^2}} + \frac{1}{\sqrt{x+|x|}}$ is $(a, b)$ , then $(1+a)^2 + b^2$ is equal to :
Relations and Functions Functions and Domain Domain of 1/sqrt(f(x))
EasySingle correctNew idea
Q2
Let $A = \{1, 2, 3, \ldots, 100\}$ and $R$ be a relation on $A$ such that $R = \{(a, b) : a = 2b + 1\}$ . Let $(a_1, a_2), (a_2, a_3), (a_3, a_4), \ldots, (a_k, a_{k+1})$ be a sequence of $k$ elements of $R$ such that the second entry of an ordered pair is…
Relations and Functions
MediumSingle correct
Q3
Let $A$ be a $3\times3$ real matrix such that $A^2(A-2I) - 4(A-I) = O$ , where $I$ and $O$ are the identity and null matrices, respectively. If $A^5 = \alpha A^2 + \beta A + \gamma I$ , where $\alpha, \beta$ , and $\gamma$ are real constants, then…
Matrices Matrix Multiplication Cayley-Hamilton Theorem Application
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q4
If the system of equations $2x + \lambda y + 3z = 5$ $3x + 2y - z = 7$ $4x + 5y + \mu z = 9$ has infinitely many solutions, then $(\lambda^2 + \mu^2)$ is equal to :
Determinants Cramer's Rule Evaluating Parameters for Consistency
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q5
The number of terms of an A.P. is even; the sum of all the odd terms is 24, the sum of all the even terms is 30 and the last term exceeds the first by $\frac{21}{2}$ . Then the number of terms which are integers in the A.P. is :
Sequences and Series AP and GP AP Odd vs Even Index Sums
MediumSingle correctNew idea
Q6
The number of ways, in which the letters A, B, C, D, E can be placed in the 8 boxes of the figure below so that no row remains empty and at most one letter can be placed in a box, is :
Permutations and Combinations Distribution of Distinct Objects into Distinct Boxes
MediumSingle correct · figureIdea asked in 3 years
Q7
If $\sum_{r=0}^{10}\left(\frac{10^{r+1}-1}{10^r}\right)\cdot {}^{11}C_{r+1} = \frac{\alpha^{11}-11^{11}}{10^{10}}$ , then $\alpha$ is equal to :
Binomial Theorem Binomial Coefficients GP-Weighted Coefficient Sums
HardSingle correctNew idea
Q8
If the mean and the variance of 6, 4, a, 8, b, 12, 10, 13 are 9 and 9.25 respectively, then $a+b+ab$ is equal to :
Statistics Variance and SD Finding Unknown Observations from Mean and Variance
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q9
Given three indentical bags each containing 10 balls, whose colours are as follows : Bag I: Red 3, Blue 2, Green 5 Bag II: Red 4, Blue 3, Green 3 Bag III: Red 5, Blue 1, Green 4 A person chooses a bag at random and takes out a ball. If the ball is Red, the…
Probability Bayes' Theorem Bayes' Theorem Application
EasySingle correct · figureIdea asked in 6 yearsAsked the year before
Q10
Let the area of the triangle formed by a straight line $L : x + by + c = 0$ with co-ordinate axes be 48 square units. If the perpendicular drawn from the origin to the line $L$ makes an angle of $45^\circ$ with the positive $x$ -axis, then the value of…
Straight Lines Straight Line Distance Distance from Normal Form
MediumSingle correctNew idea
Q11
Let the point $P$ of the focal chord $PQ$ of the parabola $y^2 = 16x$ be $(1, -4)$ . If the focus of the parabola divides the chord $PQ$ in the ratio $m : n$ , $\gcd(m, n) = 1$ , then $m^2 + n^2$ is equal to :
Conic Sections Parabola Focal Chords Ratio of Y-Coordinates of Extremities
MediumSingle correctNew idea
Q12
If the length of the minor axis of an ellipse is equal to one fourth of the distance between the foci, then the eccentricity of the ellipse is :
Conic Sections Ellipse Eccentricity Distance Between Foci
EasySingle correctIdea asked in 2 years
Q13
If $\theta \in \left[-\frac{7\pi}{6}, \frac{4\pi}{3}\right]$ , then the number of solutions of $\sqrt{3}\,\mathrm{cosec}^2\theta - 2(\sqrt{3}-1)\mathrm{cosec}\,\theta - 4 = 0$ , is equal to :
Trigonometric Functions General Solutions Quadratic Substitution in Trigonometry
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q14
If the image of the point $P(1, 0, 3)$ in the line joining the points $A(4, 7, 1)$ and $B(3, 5, 3)$ is $Q(\alpha, \beta, \gamma)$ , then $\alpha + \beta + \gamma$ is equal to :
Three Dimensional Geometry Lines in 3D Image of a Point in a Line
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q15
The line $L_1$ is parallel to the vector $\vec{a} = -3\hat{i} + 2\hat{j} + 4\hat{k}$ and passes through the point $(7, 6, 2)$ and the line $L_2$ is parallel to the vector $\vec{b} = 2\hat{i} + \hat{j} + 3\hat{k}$ and passes through the point $(5, 3, 4)$ . The…
Three Dimensional Geometry Skew Lines Vector Shortest Distance Formula
EasySingle correctIdea asked in 5 yearsAsked the year before
Q16
Let $\vec{a} = 2\hat{i} - 3\hat{j} + \hat{k}$ , $\vec{b} = 3\hat{i} + 2\hat{j} + 5\hat{k}$ and a vector $\vec{c}$ be such that $(\vec{a} - \vec{c}) \times \vec{b} = -18\hat{i} - 3\hat{j} + 12\hat{k}$ and $\vec{a}\cdot\vec{c} = 3$ . If…
Vector Algebra Cross Product Simultaneous Cross and Dot Equations
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q17
If $\lim_{x\to0} \frac{\cos(2x) + a\cos(4x) - b}{x^4}$ is finite, then $(a+b)$ is equal to :
Limits and Derivatives L'Hopital's Rule Determining Unknown Constants from Finite Limits
MediumSingle correctIdea asked in 4 years
Q18
$4\int_0^1 \left(\frac{1}{\sqrt{3+x^2}+\sqrt{1+x^2}}\right)\mathrm{d}x - 3\log_e(\sqrt{3})$ is equal to :
Integrals Integration by Parts Roots of Quadratics via Parts
HardSingle correctNew idea
Q19
Let $(a, b)$ be the point of intersection of the curve $x^2 = 2y$ and the straight line $y - 2x - 6 = 0$ in the second quadrant. Then the integral $I = \int_a^b \frac{9x^2}{1+5^x}\,\mathrm{d}x$ is equal to :
Integrals Definite Integral Properties Symmetric Limits with Exponential Denominator Trick
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q20
Let $f : [1, \infty) \to [2, \infty)$ be a differentiable function. If $10\int_1^x f(t)\,\mathrm{d}t = 5xf(x) - x^5 - 9$ for all $x \geq 1$ , then the value of $f(3)$ is :
Integrals Leibniz Rule Solving Integral Equations
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q21
If the set of all $a \in \mathbf{R} - \{1\}$ , for which the roots of the equation $(1-a)x^2 + 2(a-3)x + 9 = 0$ are positive is $(-\infty, -\alpha] \cup [\beta, \gamma)$ , then $2\alpha + \beta + \gamma$ is equal to __________.
Complex Numbers and Quadratic Equations Location of Roots Both Roots Positive
MediumNumerical valueNew ideaIdea asked in 2 years
Q22
If the sum of the first 10 terms of the series $\frac{4\cdot1}{1+4\cdot1^4} + \frac{4\cdot2}{1+4\cdot2^4} + \frac{4\cdot3}{1+4\cdot3^4} + \ldots$ is $\frac{m}{n}$ , where $\gcd(m, n) = 1$ , then $m + n$ is equal to __________.
Sequences and Series AP and GP Method of Differences (Vn Method)
HardNumerical valueIdea asked in 5 yearsAsked the year before
Q23
If $y = \cos\left(\frac{\pi}{3} + \cos^{-1}\frac{x}{2}\right)$ , then $(x-y)^2 + 3y^2$ is equal to __________.
Inverse Trigonometric Functions Inverse Trig Identities Trig of Sum of Inverse Trig Functions
MediumNumerical valueIdea asked in 3 years
Q24
Let $A(4, -2)$ , $B(1, 1)$ and $C(9, -3)$ be the vertices of a triangle $ABC$ . Then the maximum area of the parallelogram $AFDE$ , formed with vertices $D$ , $E$ and $F$ on the sides $BC$ , $CA$ and $AB$ of the triangle $ABC$ respectively, is __________.
Straight Lines
HardNumerical value
Q25
Let $y = y(x)$ be the solution of the differential equation $\frac{\mathrm{d}y}{\mathrm{d}x} + 2y\sec^2 x = 2\sec^2 x + 3\tan x\cdot\sec^2 x$ such that $y(0) = \frac{5}{4}$ . Then $12\left(y\left(\frac{\pi}{4}\right) - e^{-2}\right)$ is equal to __________.
Differential Equations Linear Differential Equations Integrating Factors with Trigonometric Functions
MediumNumerical valueIdea asked in 4 yearsAsked the year before

Questions from the official paper published by NTA, answers from the final key. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026; see the other 2025 shifts.