JEE Main 2026 · April session

JEE Main 2 April 2026, Shift 1

75 questions: 15 numerical-answer and 60 multiple choice. 13 were rated hard and 20 easy. Its hard-question count was the joint 3rd highest of the 9 2026 shifts Lumi analysed. The biggest chapter was Organic Chemistry: Some Basic Principles and Techniques, with 3 questions.

Questions: 75; none dropped
Numerical answer: 15; 20% of the shift
Hard: 13; 17% of the shift
Chapters asked: 54; 7 questions with a figure

Key findings · 2 Apr 2026, Shift 1

1
13 hard questions (17%): the joint 3rd highest count of the 9 2026 shifts Lumi analysed. Across those shifts the hard share ran from 8% to 19%.
2
Maths was the hardest section, with 9 of 25 rated hard; Physics had the most easy questions (12 of 25).
3
13 questions tested a new idea, one no earlier year had asked: 19% of the 67 questions tagged to an idea.
4
17 came back from 2025: the same idea had been asked in the 2025 shifts Lumi analysed.
5
13 shared an idea with another 2026 shift (19% 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 (2), Organic Chemistry: Some Basic Principles and Techniques in Chemistry (3) and Complex Numbers and Quadratic Equations in Maths (2).

The shift at a glance

Subjects, difficulty and chapters

Physics

25 Q · 5 numerical

Easy 12Medium 13Hard 0

Top chapters

Chemistry

25 Q · 5 numerical

Easy 6Medium 15Hard 4

Top chapters

Maths

25 Q · 5 numerical

Easy 2Medium 14Hard 9

Top chapters

Complex Numbers and Quadratic Equations2 Q
Conic Sections2 Q
Differential Equations2 Q
Integrals2 Q
Sequences and Series2 Q
Three Dimensional Geometry2 Q

Question format

Single correct48 Q
Numerical value15 Q
Two statements5 Q
Match the list3 Q
Other2 Q
Diagram based2 Q

What each question asks you to do

Multi-step30 Q
Calculation25 Q
Application8 Q
Conceptual7 Q
Recall4 Q
Diagram reading1 Q

Most common: Multi-step.

Against the other 2026 shifts

This shift next to the 8 other 2026 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	27%	17%	20%	19%	40%
2 Apr, Shift 2	75	17%	8%	20%	25%	47%
4 Apr, Shift 1	74	26%	18%	20%	23%	43%
4 Apr, Shift 2	75	31%	19%	20%	6%	40%
5 Apr, Shift 1	75	31%	9%	20%	12%	40%
5 Apr, Shift 2	75	31%	19%	20%	14%	36%
6 Apr, Shift 1	75	24%	16%	20%	23%	45%
6 Apr, Shift 2	75	28%	16%	20%	20%	49%
8 Apr, Shift 2	75	24%	17%	20%	21%	53%

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

12 easy13 medium0 hard

Chemistry25 questions

6 easy15 medium4 hard

Maths25 questions

2 easy14 medium9 hard

Q1
Let $\alpha, \alpha+2, \alpha \in \mathbb{Z}$ , be the roots of the quadratic equation $x(x+2)+(x+1)(x+3)+(x+2)(x+4)+\ldots+(x+n-1)(x+n+1)=4n$ for some $n \in \mathbb{N}$ . Then $n+\alpha$ is equal to :
Complex Numbers and Quadratic Equations Quadratic Roots Root-Coefficient Relation
HardSingle correctIdea asked in 6 yearsAsked the year before
Q2
Let $x$ and $y$ be real numbers such that $50\left(\frac{2x}{1+3i}-\frac{y}{1-2i}\right)=31+17i$ , $i=\sqrt{-1}$ . Then the value of $10(x-3y)$ is :
Complex Numbers and Quadratic Equations
EasySingle correct
Q3
Let $\alpha, \beta \in \mathbf{R}$ be such that the system of linear equations $x+2y+z=5$ $2x+y+\alpha z=5$ $8x+4y+\beta z=18$ has no solution. Then $\frac{\beta}{\alpha}$ is equal to :
Determinants Cramer's Rule Condition for No Solution
MediumSingle correctIdea asked in 6 years
Q4
Let $A=\begin{bmatrix}1&2\\1&\alpha\end{bmatrix}$ and $B=\begin{bmatrix}3&3\\\beta&2\end{bmatrix}$ . If $A^2-4A+I=O$ and $B^2-5B-6I=O$ , then among the two statements : (S1): $[(B-A)(B+A)]^T=\begin{bmatrix}13&15\\7&10\end{bmatrix}$ and (S2):…
Matrices Matrix Multiplication Cayley-Hamilton Theorem Application
HardOtherIdea asked in 5 yearsAsked the year before
Q5
Let $A$ be the set of first $101$ terms of an A.P., whose first term is $1$ and the common difference is $5$ and let $B$ be the set of first $71$ terms of an A.P., whose first term is $9$ and the common difference is $7$ . Then the number of elements in…
Sequences and Series AP and GP Counting Common Terms of Finite APs
MediumSingle correctIdea asked in 3 years
Q6
The number of seven-digit numbers, that can be formed by using the digits $1, 2, 3, 5$ and $7$ such that each digit is used at least once, is :
Permutations and Combinations Number of Surjective (Onto) Functions
MediumSingle correctIdea asked in 4 years
Q7
The number of elements in the set $S=\left\{(r,k) : k \in \mathbf{Z} \text{ and } {}^{36}C_{r+1}=\frac{6\left({}^{35}C_r\right)}{\left(k^2-3\right)}\right\}$ , is :
Binomial Theorem Binomial Coefficients Absorption Identity
MediumSingle correctNew idea
Q8
If the mean of the data | Class | 5-10 | 10-15 | 15-20 | 20-25 | 25-30 | 30-35 | | Frequency | 2 | $k$ | 28 | 54 | $k+1$ | 5 | is $21$ , then $k$ is one of the roots of the equation :
Statistics Variance and SD Mean of Discrete Data
MediumSingle correctIdea asked in 4 years
Q9
Let the mid points of the sides of a triangle ABC be $\left(\frac{5}{2}, 7\right)$ , $\left(\frac{5}{2}, 3\right)$ and $(4, 5)$ . If its incentre is $(h, k)$ , then $3h+k$ is equal to :
Straight Lines Straight Line Distance Incenter via Equidistance
MediumSingle correctIdea asked in 3 years
Q10
Let an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ , $a<b$ , pass through the point $(4, 3)$ and have eccentricity $\frac{\sqrt5}{3}$ . Then the length of its latus rectum is :
Conic Sections Ellipse Eccentricity Vertical Ellipse Latus Rectum
MediumSingle correctNew idea
Q11
If $\sin\left(\frac{\pi}{18}\right)\sin\left(\frac{5\pi}{18}\right)\sin\left(\frac{7\pi}{18}\right)=K$ , then the value of $\sin\left(\frac{10K\pi}{3}\right)$ is :
Trigonometric Functions Trigonometric Identities Sine Product Identity with 60 Degrees
MediumSingle correctIdea asked in 2 years
Q12
Let $S=\{x \in [-\pi, \pi] : \sin x(\sin x+\cos x)=a, a \in \mathbb{Z}\}$ . Then $n(S)$ is equal to :
Trigonometric Functions General Solutions Boundedness and Range Analysis
HardSingle correctIdea asked in 2 years
Q13
If the point of intersection of the lines $\frac{x+1}{3}=\frac{y+a}{5}=\frac{z+b+1}{7}$ and $\frac{x-2}{1}=\frac{y-b}{4}=\frac{z-2a}{7}$ lies on $xy$ -plane, then the value of $a+b$ is :
Three Dimensional Geometry Lines in 3D Point of Intersection Calculation
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q14
If $\vec a$ and $\vec b$ are two vectors such that $|\vec a|=2$ and $|\vec b|=3$ , then the maximum value of $3\left|3\vec a+2\vec b\right|+4\left|3\vec a-2\vec b\right|$ is :
Vector Algebra Dot Product Parallelogram Law Identity
HardSingle correctNew idea
Q15
Let a line L passing through the point $(1, 1, 1)$ be perpendicular to both the vectors $2\hat i+2\hat j+\hat k$ and $\hat i+2\hat j+2\hat k$ . If $P(a, b, c)$ is the foot of perpendicular from the origin on the line L, then the value of $34(a+b+c)$ is :
Three Dimensional Geometry Lines in 3D Line Perpendicular to Two Given Lines
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q16
If $\lim_{x\to2}\frac{\sin\left(x^3-5x^2+ax+b\right)}{\left(\sqrt{x-1}-1\right)\log_e(x-1)}=m$ , then $a+b+m$ is equal to :
Continuity and Differentiability L'Hopital's Rule Determining Unknown Constants from Finite Limits
HardSingle correctIdea asked in 4 yearsAsked the year before
Q17
If the curve $y=f(x)$ passes through the point $(1, e)$ and satisfies the differential equation $dy=y(2+\log_e x)\,dx$ , $x>0$ , then $f(e)$ is equal to :
Differential Equations Variable Separable Form Direct Integration
EasySingle correctIdea asked in 3 years
Q18
The number of critical points of the function $f(x)=\begin{cases}\left|\frac{\sin x}{x}\right|, & x\neq0\\ 1, & x=0\end{cases}$ in the interval $(-2\pi, 2\pi)$ is equal to :
Application of Derivatives Maxima and Minima Critical vs Stationary Points
HardSingle correctIdea asked in 3 years
Q19
Let $[\cdot]$ denote the greatest integer function. Then the value of $\int_0^3\left(\frac{e^x+e^{-x}}{[x]!}\right)dx$ is :
Integrals Definite Integral Properties Greatest Integer Function Integrals
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q20
Let $y=y(x)$ be the solution curve of the differential equation $(1+\sin x)\frac{dy}{dx}+(y+1)\cos x=0$ , $y(0)=0$ . If the curve $y=y(x)$ passes through the point $\left(\alpha, \frac{-1}{2}\right)$ , then a value of $\alpha$ is :
Differential Equations Linear Differential Equations Integrating Factors with Trigonometric Functions
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q21
If the domain of the function $f(x)=\sqrt{\log_{(0.6)}\left(\left|\frac{2x-5}{x^2-4}\right|\right)}$ is $(-\infty, a] \cup \{b\} \cup [c, d) \cup (e, \infty)$ , then the value of $a+b+c+d+e$ is __________.
Relations and Functions Functions and Domain Domain via Logarithmic Inequalities
HardNumerical valueIdea asked in 2 years
Q22
If $\sum_{k=1}^{n}a_k=6n^3$ , then $\sum_{k=1}^{6}\left(\frac{a_{k+1}-a_k}{36}\right)^2$ is equal to __________.
Sequences and Series
MediumNumerical value
Q23
Let $a, b, c \in \{1, 2, 3, 4\}$ . If the probability, that $ax^2+2\sqrt2\,bx+c>0$ for all $x \in \mathbf{R}$ , is $\frac{m}{n}$ , $\gcd(m, n)=1$ , then $m+n$ is equal to __________.
Probability Quadratic Roots Always Positive Condition
MediumNumerical valueIdea asked in 2 years
Q24
Let a circle C have its centre in the first quadrant, intersect the coordinate axes at exactly three points and cut off equal intercepts from the coordinate axes. If the length of the chord of C on the line $x+y=1$ is $\sqrt{14}$ , then the square of the…
Conic Sections
HardNumerical value
Q25
If $\alpha=\int_0^{2\sqrt3}\log_2\left(x^2+4\right)dx+\int_2^4\sqrt{2^x-4}\,dx$ , then $\alpha^2$ is equal to __________.
Integrals Definite Integral Properties Integral of Inverse Functions
HardNumerical valueNew idea

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 2026 shifts.