JEE Main 2025 · April session

JEE Main 3 April 2025, Shift 2

75 questions: 15 numerical-answer and 60 multiple choice. 6 were rated hard and 22 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: 49; 8 questions with a figure

Key findings · 3 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
19 questions tested a new idea, one no earlier year had asked: 31% of the 61 questions tagged to an idea.
4
29 came back from 2024: the same idea had been asked in the 2024 shifts Lumi analysed.
5
15 shared an idea with another 2025 shift (25% of tagged questions). Shifts in the same year can test the same idea in a new setting.
6
Biggest chapters: Mechanical Properties of Fluids in Physics (3), Organic Chemistry: Some Basic Principles and Techniques in Chemistry (4) and Conic Sections 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 3Medium 18Hard 4

Top chapters

Question format

Single correct42 Q
Numerical value15 Q
Diagram based5 Q
Other5 Q
Two statements4 Q
Match the list2 Q
Assertion–reason2 Q

What each question asks you to do

Multi-step27 Q
Calculation25 Q
Application8 Q
Conceptual8 Q
Recall5 Q
Diagram reading1 Q
Data or graph1 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

Chemistry25 questions

6 easy17 medium2 hard

Maths25 questions

3 easy18 medium4 hard

Q1
Let $A = \{-2, -1, 0, 1, 2, 3\}$ . Let R be a relation on $A$ defined by $xRy$ if and only if $y = \max\{x, 1\}$ . 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…
Relations and Functions Sets and Relations Counting Reflexive and Symmetric Relations
MediumSingle correctIdea asked in 2 years
Q2
If the domain of the function $f(x) = \log_7 (1 - \log_4 (x^2 - 9x + 18))$ is $(\alpha, \beta) \cup (\gamma, \delta)$ , then $\alpha + \beta + \gamma + \delta$ is equal to
Relations and Functions Functions and Domain Domain of Nested Logarithms
MediumSingle correctNew idea
Q3
Let $f$ be a function such that $f(x) + 3f\left(\frac{24}{x}\right) = 4x,\ x \neq 0$ . Then $f(3) + f(8)$ is equal to
Relations and Functions
EasySingle correct
Q4
Let the equation $x(x + 2)(12 - k) = 2$ have equal roots. Then the distance of the point $\left(k, \frac{k}{2}\right)$ from the line $3x + 4y + 5 = 0$ is
Complex Numbers and Quadratic Equations Quadratic Roots Root-Coefficient Relation
EasySingle correctIdea asked in 6 yearsAsked the year before
Q5
If $z_1, z_2, z_3 \in \mathbb{C}$ are the vertices of an equilateral triangle, whose centroid is $z_0$ , then $\sum_{k=1}^{3} (z_k - z_0)^2$ is equal to
Complex Numbers and Quadratic Equations Roots of Unity Equilateral Triangle Condition via Omega
MediumSingle correctIdea asked in 2 years
Q6
The sum $1 + \frac{1+3}{2!} + \frac{1+3+5}{3!} + \frac{1+3+5+7}{4!} + \ldots$ upto $\infty$ terms, is equal to
Sequences and Series
MediumSingle correct
Q7
Line $\mathrm{L_1}$ of slope 2 and line $\mathrm{L_2}$ of slope $\frac{1}{2}$ intersect at the origin O. In the first quadrant, $\mathrm{P_1, P_2, \ldots, P_{12}}$ are 12 points on line $\mathrm{L_1}$ and $\mathrm{Q_1, Q_2, \ldots, Q_9}$ are 9 points on line…
Permutations and Combinations Triangles from Points with Collinearity
EasySingle correctIdea asked in 3 yearsAsked the year before
Q8
If the probability that the random variable $X$ takes the value $x$ is given by $P(X = x) = k(x + 1)3^{-x},\ x = 0, 1, 2, 3\ldots$ , where $k$ is a constant, then $P(X \geq 3)$ is equal to
Probability Arithmetico-Geometric Series Sum of Infinite AGP
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q9
Let the Mean and Variance of five observations $x_1 = 1, x_2 = 3, x_3 = a, x_4 = 7$ and $x_5 = b,\ a > b$ , be 5 and 10 respectively. Then the Variance of the observations $n + x_n,\ n = 1, 2, \ldots, 5$ is
Statistics Variance and SD Finding Unknown Observations from Mean and Variance
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q10
Consider the lines $x(3\lambda + 1) + y(7\lambda + 2) = 17\lambda + 5$ , $\lambda$ 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…
Straight Lines Straight Line Distance Extremum Distance to a Family of Lines
MediumSingle correctNew idea
Q11
If the four distinct points $(4, 6), (-1, 5), (0, 0)$ and $(k, 3k)$ lie on a circle of radius $r$ , then $10k + r^2$ is equal to
Conic Sections
MediumSingle correct
Q12
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…
Conic Sections Ellipse Eccentricity Center to Focus Distance
HardSingle correctNew idea
Q13
The number of solutions of the equation $\left(4 - \sqrt{3}\right)\sin x - 2\sqrt{3}\cos^2 x = -\frac{4}{1+\sqrt{3}},\ x \in \left[-2\pi, \frac{5\pi}{2}\right]$ is
Trigonometric Functions General Solutions Quadratic Substitution in Trigonometry
HardSingle correctIdea asked in 5 yearsAsked the year before
Q14
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
Three Dimensional Geometry Lines in 3D Direction Cosines Squares Identity
MediumSingle correctNew idea
Q15
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
Three Dimensional Geometry Lines in 3D Distance Measured Parallel to Another Line
MediumSingle correctNew idea
Q16
Let $f: \mathrm{R} \to \mathrm{R}$ be a function defined by $f(x) = \left||x+2| - 2|x|\right|$ . If $m$ is the number of points of local minima and $n$ is the number of points of local maxima of $f$ , then $m + n$ is
Application of Derivatives Maxima and Minima Extrema at Non-Differentiable Points
MediumSingle correctNew idea
Q17
The shortest distance between the curves $y^2 = 8x$ and $x^2 + y^2 + 12y + 35 = 0$ is:
Application of Derivatives Maxima and Minima Shortest Distance Between Curves
MediumSingle correctIdea asked in 3 years
Q18
The integral $\int_0^{\pi} \frac{8x\,dx}{4\cos^2 x + \sin^2 x}$ is equal to
Integrals Definite Integral Properties King's Property
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q19
The area of the region $\left\{(x, y) : |x - y| \leq y \leq 4\sqrt{x}\right\}$ is
Application of Integrals Area Under Curves Area of Inequalities
MediumSingle correctIdea asked in 8 yearsAsked the year before
Q20
Let $y = y(x)$ be the solution of the differential equation $\frac{dy}{dx} + 3\left(\tan^2 x\right)y + 3y = \sec^2 x,\ y(0) = \frac{1}{3} + e^3$ . Then $y\left(\frac{\pi}{4}\right)$ is equal to
Differential Equations Linear Differential Equations Integrating Factors with Trigonometric Functions
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q21
Let $(1 + x + x^2)^{10} = a_0 + a_1 x + a_2 x^2 + \ldots + a_{20} x^{20}$ . If $(a_1 + a_3 + a_5 + \ldots + a_{19}) - 11a_2 = 121k$ , then $k$ is equal to ____________.
Binomial Theorem Binomial Coefficients Sum of Even and Odd Coefficients
HardNumerical valueIdea asked in 3 years
Q22
Let I be the identity matrix of order $3 \times 3$ and for the matrix $A = \begin{bmatrix} \lambda & 2 & 3 \\ 4 & 5 & 6 \\ 7 & -1 & 2 \end{bmatrix}$ , $|A| = -1$ . Let $B$ be the inverse of the matrix $\mathrm{adj}\left(A\,\mathrm{adj}\left(A^2\right)\right)$ .…
Determinants Matrix Inverse Commutativity of Adjoint and Inverse
HardNumerical valueNew idea
Q23
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 __________.
Conic Sections
MediumNumerical value
Q24
Let $\vec{a} = \hat{i} + 2\hat{j} + \hat{k}, \vec{b} = 3\hat{i} - 3\hat{j} + 3\hat{k}, \vec{c} = 2\hat{i} - \hat{j} + 2\hat{k}$ and $\vec{d}$ be a vector such that $\vec{b} \times \vec{d} = \vec{c} \times \vec{d}$ and $\vec{a} \cdot \vec{d} = 4$ . Then…
Vector Algebra Cross Product Simultaneous Cross and Dot Equations
MediumNumerical valueIdea asked in 5 yearsAsked the year before
Q25
If $\lim_{x \to 0}\left(\frac{\tan x}{x}\right)^{\frac{1}{x^2}} = p$ , then $96 \log_e p$ is equal to ___________.
Limits and Derivatives L'Hopital's Rule Indeterminate Power Forms
MediumNumerical valueIdea asked in 3 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.