JEE Main 2025 · April session

JEE Main 8 April 2025, Shift 2

75 questions: 15 numerical-answer and 60 multiple choice. 13 were rated hard and 20 easy. Its hard-question count was the 2nd highest of the 8 2025 shifts Lumi analysed. The biggest chapter was Coordination Compounds, with 3 questions.

Questions: 75; none dropped
Numerical answer: 15; 20% of the shift
Hard: 13; 17% of the shift
Chapters asked: 53; 12 questions with a figure

Key findings · 8 Apr 2025, Shift 2

1
13 hard questions (17%): the 2nd 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 8 of 25 rated hard; Physics had the most easy questions (10 of 25).
3
13 questions tested a new idea, one no earlier year had asked: 20% of the 64 questions tagged to an idea.
4
29 came back from 2024: the same idea had been asked in the 2024 shifts Lumi analysed.
5
18 shared an idea with another 2025 shift (28% of tagged questions). Shifts in the same year can test the same idea in a new setting.
6
Biggest chapters: Electrostatic Potential and Capacitance in Physics (3), Coordination Compounds in Chemistry (3) and Binomial Theorem in Maths (2).

The shift at a glance

Subjects, difficulty and chapters

Physics

25 Q · 5 numerical

Easy 10Medium 12Hard 3

Top chapters

Chemistry

25 Q · 5 numerical

Easy 7Medium 16Hard 2

Top chapters

Maths

25 Q · 5 numerical

Easy 3Medium 14Hard 8

Top chapters

Binomial Theorem2 Q
Complex Numbers and Quadratic Equations2 Q
Conic Sections2 Q
Integrals2 Q
Relations and Functions2 Q
Straight Lines2 Q

Question format

Single correct48 Q
Numerical value15 Q
Other3 Q
Two statements3 Q
Match the list3 Q
Diagram based2 Q
Assertion–reason1 Q

What each question asks you to do

Multi-step30 Q
Calculation18 Q
Application15 Q
Conceptual8 Q
Recall4 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

10 easy12 medium3 hard

Chemistry25 questions

7 easy16 medium2 hard

Maths25 questions

3 easy14 medium8 hard

Q1
Let $A = \{0, 1, 2, 3, 4, 5\}$ . Let $R$ be a relation on $A$ defined by $(x, y) \in R$ if and only if $\max\{x, y\} \in \{3, 4\}$ . Then among the statements $(S_1)$ : The number of elements in $R$ is 18, and $(S_2)$ : The relation $R$ is symmetric but neither…
Relations and Functions Sets and Relations Relation Types
MediumOtherIdea asked in 5 yearsAsked the year before
Q2
The sum of the squares of the roots of $|x-2|^2 + |x-2| - 2 = 0$ and the squares of the roots of $x^2 - 2|x-3| - 5 = 0$ , is
Complex Numbers and Quadratic Equations Quadratic Roots Roots of Modulus Quadratics
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q3
Let $A = \left\{\theta \in [0, 2\pi] : 1 + 10\,\mathrm{Re}\left(\frac{2\cos\theta + i\sin\theta}{\cos\theta - 3i\sin\theta}\right) = 0\right\}$ . Then $\sum_{\theta \in A} \theta^2$ is equal to
Complex Numbers and Quadratic Equations General Solutions Cosine General Solution
HardSingle correctNew idea
Q4
Let $A = \begin{bmatrix} 2 & 2+p & 2+p+q \\ 4 & 6+2p & 8+3p+2q \\ 6 & 12+3p & 20+6p+3q \end{bmatrix}$ . If $\det(\mathrm{adj}(\mathrm{adj}(3A))) = 2^m \cdot 3^n$ , $m, n \in \mathbb{N}$ , then $m + n$ is equal to
Determinants Matrix Inverse Inverse Relation to Double Adjoint
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q5
Let $\alpha$ be a solution of $x^2 + x + 1 = 0$ , and for some $a$ and $b$ in $\mathbb{R}$ , $\begin{bmatrix} 4 & a & b \end{bmatrix}\begin{bmatrix} 1 & 16 & 13 \\ -1 & -1 & 2 \\ -2 & -14 & -8 \end{bmatrix} = \begin{bmatrix} 0 & 0 & 0 \end{bmatrix}$ . If…
Matrices Roots of Unity Periodicity of Omega Powers
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q6
If $\frac{1}{1^4} + \frac{1}{2^4} + \frac{1}{3^4} + \ldots \infty = \frac{\pi^4}{90}$ , $\frac{1}{1^4} + \frac{1}{3^4} + \frac{1}{5^4} + \ldots \infty = \alpha$ , $\frac{1}{2^4} + \frac{1}{4^4} + \frac{1}{6^4} + \ldots \infty = \beta$ , then…
Sequences and Series
EasySingle correct
Q7
There are 12 points in a plane, no three of which are in the same straight line, except 5 points which are collinear. Then the total number of triangles that can be formed with the vertices at any three of these 12 points is
Permutations and Combinations Triangles from Points with Collinearity
EasySingle correctIdea asked in 3 yearsAsked the year before
Q8
The number of integral terms in the expansion of $\left(5^{\frac{1}{2}} + 7^{\frac{1}{8}}\right)^{1016}$ is
Binomial Theorem
MediumSingle correct
Q9
If $A$ and $B$ are two events such that $P(A) = 0.7$ , $P(B) = 0.4$ and $P(A \cap \overline{B}) = 0.5$ , where $\overline{B}$ denotes the complement of $B$ , then $P\left(B \mid (A \cup \overline{B})\right)$ is equal to
Probability Conditional Probability Conditioning on a Union of Events
MediumSingle correctNew idea
Q10
A line passing through the point $P(a, 0)$ makes an acute angle $\alpha$ with the positive $x$ -axis. Let this line be rotated about the point $P$ through an angle $\frac{\alpha}{2}$ in the clock-wise direction. If in the new position, the slope of the line…
Straight Lines
HardSingle correct
Q11
Let $a$ be the length of a side of a square OABC with O being the origin. Its side OA makes an acute angle $\alpha$ with the positive $x$ -axis and the equations of its diagonals are $(\sqrt{3}+1)x + (\sqrt{3}-1)y = 0$ and…
Straight Lines Straight Line Distance Square Area from Vertex and Diagonal
MediumSingle correctIdea asked in 2 years
Q12
Let the ellipse $3x^2 + py^2 = 4$ pass through the centre $C$ of the circle $x^2 + y^2 - 2x - 4y - 11 = 0$ of radius $r$ . Let $f_1, f_2$ be the focal distances of the point $C$ on the ellipse. Then $6f_1f_2 - r$ is equal to
Conic Sections Ellipse Eccentricity Product of Focal Distances
MediumSingle correctNew idea
Q13
The value of $\cot^{-1}\left(\frac{\sqrt{1+\tan^2(2)}-1}{\tan(2)}\right) - \cot^{-1}\left(\frac{\sqrt{1+\tan^2\left(\frac{1}{2}\right)}+1}{\tan\left(\frac{1}{2}\right)}\right)$ is equal to
Inverse Trigonometric Functions Inverse Trig Identities Inverse Trig Simplification via tan(θ)
HardSingle correctIdea asked in 2 years
Q14
Let $\vec{a} = \hat{i} + 2\hat{j} + \hat{k}$ and $\vec{b} = 2\hat{i} + \hat{j} - \hat{k}$ . Let $\hat{c}$ be a unit vector in the plane of the vectors $\vec{a}$ and $\vec{b}$ and be perpendicular to $\vec{a}$ . Then such a vector $\hat{c}$ is :
Vector Algebra Dot Product Orthogonal Resolution of a Vector
MediumSingle correctNew idea
Q15
Let the values of $\lambda$ for which the shortest distance between the lines $\frac{x-1}{2} = \frac{y-2}{3} = \frac{z-3}{4}$ and $\frac{x-\lambda}{3} = \frac{y-4}{4} = \frac{z-5}{5}$ is $\frac{1}{\sqrt{6}}$ be $\lambda_1$ and $\lambda_2$ . Then the radius of…
Three Dimensional Geometry Skew Lines Finding an Unknown Parameter from Shortest Distance
HardSingle correctIdea asked in 3 yearsAsked the year before
Q16
Given below are two statements: Statement I : $\lim_{x \to 0}\left(\frac{\tan^{-1}x + \log_e\sqrt{\frac{1+x}{1-x}} - 2x}{x^5}\right) = \frac{2}{5}$ Statement II : $\lim_{x \to 1}\left(x^{\frac{2}{1-x}}\right) = \frac{1}{e^2}$ In the light of the above…
Limits and Derivatives L'Hopital's Rule Choosing Series Expansion over L'Hopital
MediumTwo statementsIdea asked in 7 yearsAsked the year before
Q17
Let the function $f(x) = \frac{x}{3} + \frac{3}{x} + 3$ , $x \neq 0$ be strictly increasing in $(-\infty, \alpha_1) \cup (\alpha_2, \infty)$ and strictly decreasing in $(\alpha_3, \alpha_4) \cup (\alpha_4, \alpha_5)$ . Then $\sum_{i=1}^{5} \alpha_i^2$ is equal…
Application of Derivatives Monotonicity Finding Intervals
EasySingle correctIdea asked in 5 yearsAsked the year before
Q18
Let $f(x)$ be a positive function and $I_1 = \int_{-\frac{1}{2}}^{1} 2x\, f\big(2x(1-2x)\big)\,dx$ and $I_2 = \int_{-1}^{2} f\big(x(1-x)\big)\,dx$ . Then the value of $\frac{I_2}{I_1}$ is equal to __________
Integrals Definite Integral Properties King's Property
HardSingle correctIdea asked in 6 yearsAsked the year before
Q19
The integral $\int_{-1}^{\frac{3}{2}} \left(\left|\pi^2 x \sin(\pi x)\right|\right) dx$ is equal to :
Integrals Definite Integral Properties Modulus Function Interval Splitting
MediumSingle correctIdea asked in 3 years
Q20
Let $f(x) = x - 1$ and $g(x) = e^x$ for $x \in \mathbb{R}$ . If $\frac{dy}{dx} = \left(e^{-2\sqrt{x}}\, g\big(f(f(x))\big) - \frac{y}{\sqrt{x}}\right)$ , $y(0) = 0$ , then $y(1)$ is
Differential Equations Linear Differential Equations Standard Linear Form Identification
HardSingle correctIdea asked in 3 years
Q21
Let the domain of the function $f(x) = \cos^{-1}\left(\frac{4x+5}{3x-7}\right)$ be $[\alpha, \beta]$ and the domain of $g(x) = \log_2(2 - 6\log_{27}(2x+5))$ be $(\gamma, \delta)$ . Then $|7(\alpha + \beta) + 4(\gamma + \delta)|$ is equal to __________
Relations and Functions Functions and Domain Inverse Trig Function Domain
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q22
The product of the last two digits of $(1919)^{1919}$ is __________
Binomial Theorem
MediumNumerical value
Q23
Let $r$ be the radius of the circle, which touches $x$ -axis at point $(a, 0)$ , $a < 0$ and the parabola $y^2 = 9x$ at the point $(4, 6)$ . Then $r$ is equal to __________
Conic Sections
HardNumerical value
Q24
Let the area of the triangle formed by the lines $x + 2 = y - 1 = z$ , $\frac{x-3}{5} = \frac{y}{-1} = \frac{z-1}{1}$ and $\frac{x}{-3} = \frac{y-3}{3} = \frac{z-2}{1}$ be $A$ . Then $A^2$ is equal to __________
Three Dimensional Geometry
HardNumerical value
Q25
Let the area of the bounded region $\{(x, y) : 0 \le 9x \le y^2, y \ge 3x - 6\}$ be $A$ . Then $6A$ is equal to __________
Application of Integrals Area Under Curves Area of Inequalities
MediumNumerical valueIdea asked in 8 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.