JEE Main 2025 · April session

JEE Main 7 April 2025, Shift 2

75 questions: 15 numerical-answer and 60 multiple choice. 9 were rated hard and 18 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: 56; 9 questions with a figure

Key findings · 7 Apr 2025, Shift 2

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 8 of 25 rated hard; Physics had the most easy questions (13 of 25).
3
15 questions tested a new idea, one no earlier year had asked: 25% of the 61 questions tagged to an idea.
4
30 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 (30% 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), Coordination Compounds in Chemistry (3) and Conic Sections in Maths (4).

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 5Medium 19Hard 1

Top chapters

Coordination Compounds3 Q
Solutions3 Q
Aldehydes, Ketones and Carboxylic Acids2 Q
Amines2 Q
Haloalkanes and Haloarenes2 Q
Alcohols, Phenols and Ethers1 Q

Maths

25 Q · 5 numerical

Easy 0Medium 17Hard 8

Top chapters

Question format

Single correct41 Q
Numerical value15 Q
Match the list5 Q
Assertion–reason5 Q
Other4 Q
Two statements3 Q
Diagram based2 Q

What each question asks you to do

Multi-step34 Q
Conceptual16 Q
Calculation13 Q
Recall6 Q
Application5 Q
Diagram reading1 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

5 easy19 medium1 hard

Maths25 questions

0 easy17 medium8 hard

Q1
Let $A=\{(\alpha,\beta)\in\mathbf{R}\times\mathbf{R}: |\alpha-1|\le 4 \text{ and } |\beta-5|\le 6\}$ and $B=\{(\alpha,\beta)\in\mathbf{R}\times\mathbf{R}: 16(\alpha-2)^2+9(\beta-6)^2\le 144\}$ . Then
Conic Sections
MediumSingle correct
Q2
If the range of the function $f(x)=\frac{5-x}{x^2-3x+2}$ , $x\ne 1,2$ , is $(-\infty,\alpha]\cup[\beta,\infty)$ , then $\alpha^2+\beta^2$ is equal to :
Relations and Functions Quadratic Roots Range of Rational Quadratic Functions
MediumSingle correctNew idea
Q3
The number of real roots of the equation $x|x-2|+3|x-3|+1=0$ is :
Complex Numbers and Quadratic Equations
MediumSingle correct
Q4
If the locus of $z\in\mathbf{C}$ , such that $\mathrm{Re}\left(\frac{z-1}{2z+i}\right)+\mathrm{Re}\left(\frac{\bar z-1}{2\bar z-i}\right)=2$ , is a circle of radius $r$ and center $(a,b)$ , then $\frac{15ab}{r^2}$ is equal to :
Complex Numbers and Quadratic Equations
HardSingle correct
Q5
Let the system of equations $x+5y-z=1$ $4x+3y-3z=7$ $24x+y+\lambda z=\mu$ $\lambda,\mu\in\mathbf{R}$ , have infinitely many solutions. Then the number of the solutions of this system, if $x,y,z$ are integers and satisfy $7\le x+y+z\le 77$ , is :
Determinants Cramer's Rule Evaluating Parameters for Consistency
HardSingle correctIdea asked in 6 yearsAsked the year before
Q6
Let $a_n$ be the $n^{\mathrm{th}}$ term of an A.P. If $S_n=a_1+a_2+a_3+\ldots+a_n=700$ , $a_6=7$ and $S_7=7$ , then $a_n$ is equal to :
Sequences and Series AP and GP AP Sum of n terms
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q7
If the sum of the second, fourth and sixth terms of a G.P. of positive terms is 21 and the sum of its eighth, tenth and twelfth terms is 15309, then the sum of its first nine terms is :
Sequences and Series AP and GP GP General Term
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q8
Let $p$ be the number of all triangles that can be formed by joining the vertices of a regular polygon $P$ of $n$ sides and $q$ be the number of all quadrilaterals that can be formed by joining the vertices of $P$ . If $p+q=126$ , then the eccentricity of the…
Permutations and Combinations Number of Triangles from Points
MediumSingle correctIdea asked in 3 years
Q9
Let a random variable $X$ take values $0, 1, 2, 3$ with $P(X=0)=P(X=1)=p$ , $P(X=2)=P(X=3)$ and $E(X^2)=2E(X)$ . Then the value of $8p-1$ is :
Probability
MediumSingle correct
Q10
A bag contains 19 unbiased coins and one coin with head on both sides. One coin drawn at random is tossed and head turns up. If the probability that the drawn coin was unbiased, is $\frac{m}{n}$ , $\gcd(m,n)=1$ , then $n^2-m^2$ is equal to :
Probability Bayes' Theorem Biased vs Unbiased Instrument Selection
MediumSingle correctNew idea
Q11
If the orthocenter of the triangle formed by the lines $y=x+1$ , $y=4x-8$ and $y=mx+c$ is at $(3,-1)$ , then $m-c$ is :
Straight Lines
MediumSingle correct
Q12
Let the length of a latus rectum of an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ be 10. If its eccentricity is the minimum value of the function $f(t)=t^2+t+\frac{11}{12}$ , $t\in\mathbf{R}$ , then $a^2+b^2$ is equal to :
Conic Sections Ellipse Eccentricity Length of Latus Rectum
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q13
Let $e_1$ and $e_2$ be the eccentricities of the ellipse $\frac{x^2}{b^2}+\frac{y^2}{25}=1$ and the hyperbola $\frac{x^2}{16}-\frac{y^2}{b^2}=1$ , respectively. If $b<5$ and $e_1e_2=1$ , then the eccentricity of the ellipse having its axes along the coordinate…
Conic Sections Ellipse Eccentricity Coordinates of foci
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q14
The number of solutions of the equation $\cos 2\theta\cos\frac{\theta}{2}+\cos\frac{5\theta}{2}=2\cos^3\frac{5\theta}{2}$ in $\left[-\frac{\pi}{2},\frac{\pi}{2}\right]$ is :
Trigonometric Functions General Solutions Multiple Angle Equating
HardSingle correctNew idea
Q15
Let $\vec{a}$ and $\vec{b}$ be the vectors of the same magnitude such that $\frac{|\vec{a}+\vec{b}|+|\vec{a}-\vec{b}|}{|\vec{a}+\vec{b}|-|\vec{a}-\vec{b}|}=\sqrt{2}+1$ . Then $\frac{|\vec{a}+\vec{b}|^2}{|\vec{a}|^2}$ is :
Vector Algebra Dot Product Expansion of Sum of Vectors Squared
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q16
If the equation of the line passing through the point $\left(0,-\frac{1}{2},0\right)$ and perpendicular to the lines $\vec{r}=\lambda(\hat{i}+a\hat{j}+b\hat{k})$ and $\vec{r}=(\hat{i}-\hat{j}-6\hat{k})+\mu(-b\hat{i}+a\hat{j}+5\hat{k})$ is…
Three Dimensional Geometry Lines in 3D Line Perpendicular to Two Given Lines
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q17
Consider the lines $L_1: x-1=y-2=z$ and $L_2: x-2=y=z-1$ . Let the feet of the perpendiculars from the point $P(5,1,-3)$ on the lines $L_1$ and $L_2$ be $Q$ and $R$ respectively. If the area of the triangle $PQR$ is $A$ , then $4A^2$ is equal to :
Three Dimensional Geometry Lines in 3D Perpendicular Distance from Point to Line
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q18
Let $f:\mathbf{R}\to\mathbf{R}$ be a polynomial function of degree four having extreme values at $x=4$ and $x=5$ . If $\lim_{x\to 0}\frac{f(x)}{x^2}=5$ , then $f(2)$ is equal to :
Application of Derivatives Maxima and Minima Determining Coefficients from Extrema
MediumSingle correctIdea asked in 3 years
Q19
Let $y=y(x)$ be the solution of the differential equation $(x^2+1)y'-2xy=(x^4+2x^2+1)\cos x$ , $y(0)=1$ . Then $\int_{-3}^{3}y(x)\,dx$ is :
Differential Equations Linear Differential Equations General Solution Formula
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q20
If the area of the region $\{(x,y): 1+x^2\le y\le \min\{x+7,\ 11-3x\}\}$ is $A$ , then $3A$ is equal to
Application of Integrals Area Under Curves Area Involving Max/Min Functions
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q21
The sum of the series $2\times1\times{}^{20}C_4-3\times2\times{}^{20}C_5+4\times3\times{}^{20}C_6-5\times4\times{}^{20}C_7+\ldots+18\times17\times{}^{20}C_{20}$ , is equal to ________.
Binomial Theorem Binomial Coefficients Falling Factorial Polynomial Split
HardNumerical valueNew idea
Q22
Let the lengths of the transverse and conjugate axes of a hyperbola in standard form be $2a$ and $2b$ , respectively, and one focus and the corresponding directrix of this hyperbola be $(-5,0)$ and $5x+9=0$ , respectively. If the product of the focal distances…
Conic Sections
HardNumerical value
Q23
For $t>-1$ , let $\alpha_t$ and $\beta_t$ be the roots of the equation $\left((t+2)^{1/7}-1\right)x^2+\left((t+2)^{1/6}-1\right)x+\left((t+2)^{1/21}-1\right)=0$ . If $\lim_{t\to-1^+}\alpha_t=a$ and $\lim_{t\to-1^+}\beta_t=b$ , then $72(a+b)^2$ is equal to…
Limits and Derivatives L'Hopital's Rule Simplifying with Standard Limits Before L'Hopital
HardNumerical valueIdea asked in 6 yearsAsked the year before
Q24
If $\int\left(\frac{1}{x}+\frac{1}{x^3}\right)\sqrt[23]{3x^{-24}+x^{-26}}\,dx=-\frac{\alpha}{3(\alpha+1)}\left(3x^{\beta}+x^{\gamma}\right)^{\frac{\alpha+1}{\alpha}}+C$ , $x>0$ , $(\alpha,\beta,\gamma\in\mathbf{Z})$ , where $C$ is the constant of integration,…
Integrals Integration by Substitution Factoring Highest Power for Substitution
HardNumerical valueIdea asked in 3 years
Q25
If the function $f(x)=\frac{\tan(\tan x)-\sin(\sin x)}{\tan x-\sin x}$ is continuous at $x=0$ , then $f(0)$ is equal to ________.
Continuity and Differentiability Limits via Series Expansion for Continuity
HardNumerical 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.