JEE Main 2025 · April session

JEE Main 2 April 2025, Shift 1

75 questions: 15 numerical-answer and 60 multiple choice. 9 were rated hard and 16 easy. Its hard-question count was the joint 4th highest of the 8 2025 shifts Lumi analysed. The biggest chapter was Conic Sections, with 4 questions.

Questions: 75; none dropped
Numerical answer: 15; 20% of the shift
Hard: 9; 12% of the shift
Chapters asked: 53; 15 questions with a figure

Key findings · 2 Apr 2025, Shift 1

1
9 hard questions (12%): the joint 4th 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 5 of 25 rated hard; Physics had the most easy questions (9 of 25).
3
13 questions tested a new idea, one no earlier year had asked: 21% 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
17 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: Electric Charges and Fields in Physics (3), Aldehydes, Ketones and Carboxylic Acids in Chemistry (2) and Conic Sections in Maths (4).

The shift at a glance

Subjects, difficulty and chapters

Physics

25 Q · 5 numerical

Easy 9Medium 15Hard 1

Top chapters

Chemistry

25 Q · 5 numerical

Easy 3Medium 19Hard 3

Top chapters

Maths

25 Q · 5 numerical

Easy 4Medium 16Hard 5

Top chapters

Question format

Single correct50 Q
Numerical value15 Q
Diagram based3 Q
Other3 Q
Two statements3 Q
Match the list1 Q

What each question asks you to do

Multi-step33 Q
Calculation19 Q
Application8 Q
Conceptual8 Q
Recall6 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

9 easy15 medium1 hard

Chemistry25 questions

3 easy19 medium3 hard

Maths25 questions

4 easy16 medium5 hard

Q1
Let the focal chord PQ of the parabola $y^2=4x$ make an angle of $60^\circ$ with the positive $x$ -axis, where P lies in the first quadrant. If the circle, whose one diameter is PS, S being the focus of the parabola, touches the $y$ -axis at the point…
Conic Sections Parabola Focal Chords Point of Contact of Focal Radius Circle with Vertex Tangent
MediumSingle correctNew idea
Q2
Let $z$ be a complex number such that $|z|=1$ . If $\frac{2+k^2z}{k+\bar{z}}=kz$ , $k\in\mathbf{R}$ , then the maximum distance of $k+ik^2$ from the circle $|z-(1+2i)|=1$ is :
Complex Numbers and Quadratic Equations Complex Numbers - Polar Form Polar Triangle Inequality Extrema
HardSingle correctIdea asked in 5 yearsAsked the year before
Q3
If $\theta\in[-2\pi, 2\pi]$ , then the number of solutions of $2\sqrt{2}\cos^2\theta+(2-\sqrt{6})\cos\theta-\sqrt{3}=0$ , is equal to :
Trigonometric Functions General Solutions Quadratic Substitution in Trigonometry
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q4
If S and S' are the foci of the ellipse $\frac{x^2}{18}+\frac{y^2}{9}=1$ and P be a point on the ellipse, then $\min(\mathrm{SP}\cdot\mathrm{S'P})+\max(\mathrm{SP}\cdot\mathrm{S'P})$ is equal to :
Conic Sections Ellipse Eccentricity Product of Focal Distances
MediumSingle correctNew idea
Q5
Let ABCD be a tetrahedron such that the edges AB, AC and AD are mutually perpendicular. Let the areas of the triangles ABC, ACD and ADB be 5, 6 and 7 square units respectively. Then the area (in square units) of the $\Delta$ BCD is equal to :
Three Dimensional Geometry Cross Product Area of Triangles and Parallelograms
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q6
The largest $n\in\mathbf{N}$ such that $3^n$ divides $50!$ is :
Binomial Theorem Permutations and Combinations Exponent of Prime in n! (Legendre's Formula)
EasySingle correctIdea asked in 2 years
Q7
For $\alpha, \beta, \gamma\in\mathbf{R}$ , if $\lim_{x\to0}\frac{x^2\sin\alpha x+(\gamma-1)e^{x^2}}{\sin2x-\beta x}=3$ , then $\beta+\gamma-\alpha$ is equal to :
Limits and Derivatives L'Hopital's Rule Determining Unknown Constants from Finite Limits
MediumSingle correctIdea asked in 4 years
Q8
If the function $f(x)=2x^3-9ax^2+12a^2x+1$ , where $a>0$ , attains its local maximum and local minimum values at p and q, respectively, such that $p^2=q$ , then $f(3)$ is equal to :
Application of Derivatives Maxima and Minima Finding Parameters from Given Extrema
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q9
The number of sequences of ten terms, whose terms are either 0 or 1 or 2, that contain exactly five 1s and exactly three 2s, is equal to :
Permutations and Combinations
EasySingle correct
Q10
Let one focus of the hyperbola $\mathrm{H}: \frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ be at $(\sqrt{10},0)$ and the corresponding directrix be $x=\frac{9}{\sqrt{10}}$ . If $e$ and $l$ respectively are the eccentricity and the length of the latus rectum of H, then…
Conic Sections
EasySingle correct
Q11
If $\vec{a}$ is a nonzero vector such that its projections on the vectors $2\hat{i}-\hat{j}+2\hat{k}$ , $\hat{i}+2\hat{j}-2\hat{k}$ and $\hat{k}$ are equal, then a unit vector along $\vec{a}$ is :
Vector Algebra Dot Product Scalar and Vector Projection
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q12
Let A be the set of all functions $f:\mathbf{Z}\to\mathbf{Z}$ and R be a relation on A such that $R=\{(f, g): f(0)=g(1)\text{ and }f(1)=g(0)\}$ . Then R is :
Relations and Functions Sets and Relations Equivalence Relations
EasySingle correctIdea asked in 4 yearsAsked the year before
Q13
Let the vertices Q and R of the triangle PQR lie on the line $\frac{x+3}{5}=\frac{y-1}{2}=\frac{z+4}{3}$ , $\mathrm{QR}=5$ and the coordinates of the point P be $(0, 2, 3)$ . If the area of the triangle PQR is $\frac{m}{n}$ then :
Three Dimensional Geometry Lines in 3D Perpendicular Distance from Point to Line
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q14
Let $f:\mathbf{R}\to\mathbf{R}$ be a twice differentiable function such that $(\sin x\cos y)(f(2x+2y)-f(2x-2y))=(\cos x\sin y)(f(2x+2y)+f(2x-2y))$ , for all $x, y\in\mathbf{R}$ . If $f'(0)=\frac{1}{2}$ , then the value of $24f''\left(\frac{5\pi}{3}\right)$ is :
Continuity and Differentiability Differentiability via Functional Equations
HardSingle correctIdea asked in 6 yearsAsked the year before
Q15
Let $a\in\mathbf{R}$ and A be a matrix of order $3\times3$ such that $\det(A)=-4$ and $A+I=\begin{bmatrix}1&a&1\\2&1&0\\a&1&2\end{bmatrix}$ , where I is the identity matrix of order $3\times3$ . If $\det((a+1)\operatorname{adj}((a-1)A))$ is $2^m3^n$ ,…
Determinants Matrix Inverse Trap involving |adj(A)| vs |A^-1|
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q16
The term independent of $x$ in the expansion of $\left(\frac{x+1}{x^{2/3}+1-x^{1/3}}-\frac{x-1}{x-x^{1/2}}\right)^{10}$ , $x>1$ , is :
Binomial Theorem
MediumSingle correct
Q17
Let $P_n=\alpha^n+\beta^n$ , $n\in\mathbf{N}$ . If $P_{10}=123$ , $P_9=76$ , $P_8=47$ and $P_1=1$ , then the quadratic equation having roots $\frac{1}{\alpha}$ and $\frac{1}{\beta}$ is :
Complex Numbers and Quadratic Equations Quadratic Roots Newton's Sums
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q18
Let $A=\begin{bmatrix}\alpha&-1\\6&\beta\end{bmatrix}$ , $\alpha>0$ , such that $\det(A)=0$ and $\alpha+\beta=1$ . If I denotes $2\times2$ identity matrix, then the matrix $(I+A)^8$ is :
Matrices Matrix Multiplication Idempotent and Nilpotent Matrices
MediumSingle correctIdea asked in 2 years
Q19
Let $a_1, a_2, a_3,\ldots$ be in an A.P. such that $\sum_{k=1}^{12}a_{2k-1}=-\frac{72}{5}a_1$ , $a_1\neq0$ . If $\sum_{k=1}^{n}a_k=0$ , then n is :
Sequences and Series AP and GP AP Sum of n terms
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q20
If the system of linear equations $3x+y+\beta z=3$ $2x+\alpha y-z=-3$ $x+2y+z=4$ has infinitely many solutions, then the value of $22\beta-9\alpha$ is :
Determinants Cramer's Rule Condition for Infinite Solutions
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q21
If the area of the region $\left\{(x, y): \left|4-x^2\right|\le y\le x^2,\ y\le4,\ x\ge0\right\}$ is $\left(\frac{80\sqrt{2}}{\alpha}-\beta\right)$ , $\alpha, \beta\in\mathbf{N}$ , then $\alpha+\beta$ is equal to ___________.
Application of Integrals Area Under Curves Area with Modulus
HardNumerical valueIdea asked in 4 yearsAsked the year before
Q22
The absolute difference between the squares of the radii of the two circles passing through the point $(-9, 4)$ and touching the lines $x+y=3$ and $x-y=3$ , is equal to ___________.
Conic Sections Circle Tangents Family of Circles Touching a Line
HardNumerical valueIdea asked in 5 years
Q23
Let $[\cdot]$ denote the greatest integer function. If $\int_0^{e^3}\left[\frac{1}{e^{x-1}}\right]dx=\alpha-\log_e2$ , then $\alpha^3$ is equal to ___________.
Integrals Definite Integral Properties Greatest Integer Function Integrals
MediumNumerical valueIdea asked in 7 yearsAsked the year before
Q24
Let $f:\mathbf{R}\to\mathbf{R}$ be a thrice differentiable odd function satisfying $f'(x)\ge0$ , $f''(x)=f(x)$ , $f(0)=0$ , $f'(0)=3$ . Then $9f(\log_e3)$ is equal to ___________.
Differential Equations
MediumNumerical value
Q25
Three distinct numbers are selected randomly from the set $\{1, 2, 3, \ldots, 40\}$ . If the probability, that the selected numbers are in an increasing G.P., is $\frac{m}{n}$ , $\gcd(m, n)=1$ , then $m+n$ is equal to ___________.
Probability
HardNumerical value

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.