JEE Main 2026 · April session

JEE Main 5 April 2026, Shift 1

75 questions: 15 numerical-answer and 60 multiple choice. 7 were rated hard and 23 easy. Its hard-question count was the 8th highest of the 9 2026 shifts Lumi analysed. The biggest chapter was Mechanical Properties of Solids, with 3 questions.

Questions: 75; none dropped
Numerical answer: 15; 20% of the shift
Hard: 7; 9% of the shift
Chapters asked: 54; 13 questions with a figure

Key findings · 5 Apr 2026, Shift 1

1
7 hard questions (9%): the 8th 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 4 of 25 rated hard; Chemistry had the most easy questions (10 of 25).
3
8 questions tested a new idea, one no earlier year had asked: 12% of the 68 questions tagged to an idea.
4
23 came back from 2025: the same idea had been asked in the 2025 shifts Lumi analysed.
5
23 shared an idea with another 2026 shift (34% of tagged questions). Shifts in the same year can test the same idea in a new setting.
6
Biggest chapters: Mechanical Properties of Solids in Physics (3), Alcohols, Phenols and Ethers in Chemistry (2) and Conic Sections in Maths (2).

The shift at a glance

Subjects, difficulty and chapters

Physics

25 Q · 5 numerical

Easy 8Medium 15Hard 2

Top chapters

Chemistry

25 Q · 5 numerical

Easy 10Medium 14Hard 1

Top chapters

Maths

25 Q · 5 numerical

Easy 5Medium 16Hard 4

Top chapters

Question format

Single correct40 Q
Numerical value15 Q
Other11 Q
Two statements5 Q
Diagram based4 Q

What each question asks you to do

Multi-step30 Q
Calculation21 Q
Application9 Q
Conceptual8 Q
Recall6 Q
Data or graph1 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

8 easy15 medium2 hard

Chemistry25 questions

10 easy14 medium1 hard

Maths25 questions

5 easy16 medium4 hard

Q1
Let $a, b \in \mathbb{C}$ . Let $\alpha, \beta$ be the roots of the equation $x^2 + ax + b = 0$ . If $\beta - \alpha = \sqrt{11}$ and $\beta^2 - \alpha^2 = 3i\sqrt{11}$ , then $(\beta^3 - \alpha^3)^2$ is equal to:
Complex Numbers and Quadratic Equations Quadratic Roots Root-Coefficient Relation
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q2
Let the sum of the first $n$ terms of an A.P. be $3n^2 + 5n$ . Then the sum of squares of the first 10 terms of the A.P. is:
Sequences and Series AP and GP AP Recognition from Quadratic Sum
EasySingle correctIdea asked in 2 years
Q3
Let A be a $3 \times 3$ matrix such that $A^T\begin{bmatrix}1\\0\\1\end{bmatrix}=\begin{bmatrix}5\\2\\2\end{bmatrix}$ , $A^T\begin{bmatrix}0\\0\\1\end{bmatrix}=\begin{bmatrix}3\\1\\1\end{bmatrix}$ ,…
Determinants Matrix Inverse Trap involving |adj(A)| vs |A^-1|
HardSingle correctIdea asked in 6 yearsAsked the year before
Q4
Consider the system of linear equations in $x, y, z$ : $x + 2y + tz = 0$ , $6x + y + 5tz = 0$ , $3x + t^2y + f(t)\,z = 0$ , where $f: \mathbb{R} \to \mathbb{R}$ is a differentiable function. If this system has infinitely many solutions for all…
Determinants Cramer's Rule Parameter Evaluation in Homogeneous Systems
MediumSingle correctIdea asked in 5 years
Q5
$\sum_{n=1}^{10}\left(\frac{528}{n(n+1)(n+2)}\right)$ is equal to:
Sequences and Series AP and GP Method of Differences for Telescoping Series
EasySingle correctIdea asked in 6 yearsAsked the year before
Q6
Let $\tan A$ , $\tan B$ , where $A, B \in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$ , be the roots of the quadratic equation $x^2 - 2x - 5 = 0$ . Then $20\sin^2\left(\frac{A+B}{2}\right)$ is equal to:
Trigonometric Functions Trigonometric Identities Compound Angle Formulas
MediumSingle correctIdea asked in 5 years
Q7
A letter is known to have arrived by post either from KANPUR or from ANANTPUR. On the envelope just two consecutive letters AN are visible. The probability, that the letter came from ANANTPUR, is:
Probability Conditional Probability Bayes' Theorem with Partial String Evidence
MediumSingle correctNew idea
Q8
The mean deviation about the mean for the data | $x_i$ | 5 | 7 | 9 | 10 | 12 | 15 | | $f_i$ | 8 | 6 | 2 | 2 | 2 | 6 | is equal to:
Statistics
EasySingle correct · figure
Q9
Let a focus of the ellipse $E: \frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ be $S(4, 0)$ and its eccentricity be $\frac{4}{5}$ . If the point $P(3, \alpha)$ lies on E and O is the origin, then the area of $\Delta POS$ is equal to:
Conic Sections Ellipse Eccentricity Eccentricity calculation
EasySingle correctIdea asked in 6 years
Q10
Let P be a moving point on the circle $x^2 + y^2 - 6x - 8y + 21 = 0$ . Then, the maximum distance of P from the vertex of the parabola $x^2 + 6x + y + 13 = 0$ is equal to:
Conic Sections General Conic Section Vertex of Parabola from General Equation
MediumSingle correctNew idea
Q11
In an equilateral triangle PQR, let the vertex P be at $(3, 5)$ and the side QR be along the line $x + y = 4$ . If the orthocentre of the triangle PQR is $(\alpha, \beta)$ , then $9(\alpha + \beta)$ is equal to:
Straight Lines
MediumSingle correct
Q12
The sum of all the integral values of $p$ such that the equation $3\sin^2 x + 12\cos x - 3 = p$ , $x \in \mathbb{R}$ , has at least one solution, is:
Trigonometric Functions Maxima and Minima Extrema of Trigonometric Compositions
MediumSingle correctIdea asked in 2 years
Q13
The square of the distance of the point $P(5, 6, 7)$ from the line $\frac{x-2}{2}=\frac{y-5}{3}=\frac{z-2}{4}$ is equal to:
Three Dimensional Geometry Lines in 3D Perpendicular Distance from Point to Line
EasySingle correctIdea asked in 6 yearsAsked the year before
Q14
Let $\vec{a} = \sqrt{7}\hat{i} + \hat{j} - \hat{k}$ and $\vec{b} = \hat{j} + 2\hat{k}$ . If $\vec{r}$ is a vector such that $\vec{r} \times \vec{a} + \vec{a} \times \vec{b} = \vec{0}$ and $\vec{r} \cdot \vec{a} = 0$ , then $|3\vec{r}|^2$ is equal to:
Vector Algebra Cross Product Solving Vector Equations with Cross Products
MediumSingle correctIdea asked in 6 years
Q15
The square of the distance of the point of intersection of the lines $\vec{r} = (\hat{i} + \hat{j} - \hat{k}) + \lambda(a\hat{i} - \hat{j})$ , $a \neq 0$ and $\vec{r} = (4\hat{i} - \hat{k}) + \mu(2\hat{i} + a\hat{k})$ from the origin is:
Three Dimensional Geometry Lines in 3D Condition for Intersection of Two Lines
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q16
The area of the region $R = \{(x, y) : xy \leq 27,\ 1 \leq y \leq x^2\}$ is equal to:
Application of Integrals Area Under Curves Area of Inequalities
MediumSingle correctIdea asked in 8 yearsAsked the year before
Q17
The product of all possible values of $\alpha$ , for which $\lim_{x \to 0}\left(\frac{1 - \cos(\alpha x)\cos((\alpha+1)x)\cos((\alpha+2)x)}{\sin^2((\alpha+1)x)}\right) = 2$ , is:
Limits and Derivatives L'Hopital's Rule Simplifying with Standard Limits Before L'Hopital
HardSingle correctIdea asked in 6 yearsAsked the year before
Q18
The value of the integral $\int_0^{\infty} \frac{\log_e(x)}{x^2+4}\,dx$ is:
Integrals Definite Integral Properties Reciprocal Substitution (x = 1/t)
HardSingle correctIdea asked in 2 years
Q19
Let $f: \mathbb{R} \to \mathbb{R}$ be a differentiable function such that $f\left(\frac{x+y}{3}\right) = \frac{f(x)+f(y)}{3}$ for all $x, y \in \mathbb{R}$ , and $f'(0) = 3$ . Then the minimum value of the function $g(x) = 3 + e^x f(x)$ , is:
Continuity and Differentiability Differentiability via Functional Equations
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q20
The value of the integral $\int_{\pi/6}^{\pi/3}\left(\frac{4 - \operatorname{cosec}^2 x}{\cos^4 x}\right)dx$ is:
Integrals Integration by Substitution Even Power of Secant Substitution
MediumSingle correctIdea asked in 2 years
Q21
Let $A = \{1, 2, 3, 4, 5, 6\}$ . The number of one-one functions $f: A \to A$ such that $f(1) \geq 3$ , $f(3) \leq 4$ and $f(2) + f(3) = 5$ , is ________.
Relations and Functions Permutations and Combinations Number of Injective Functions
MediumNumerical valueIdea asked in 4 years
Q22
Two players A and B play a series of games of badminton. The player, who wins 5 games first, wins the series. Assuming that no game ends in a draw, the number of ways, in which player A wins the series is ________.
Permutations and Combinations Combinations of Distinct Objects
MediumNumerical valueIdea asked in 8 yearsAsked the year before
Q23
If the sum of the coefficients of $x^7$ and $x^{14}$ in the expansion of $\left(\frac{1}{x^3} - x^4\right)^n$ , $x \neq 0$ , is zero, then the value of $n$ is ________.
Binomial Theorem Binomial Coefficients Basic nCr Properties
MediumNumerical valueIdea asked in 2 years
Q24
If $\frac{\pi}{4} + \sum_{p=1}^{11} \tan^{-1}\left(\frac{2^{p-1}}{1 + 2^{2p-1}}\right) = \alpha$ , then $\tan\alpha$ is equal to ________.
Inverse Trigonometric Functions Inverse Trig Identities Telescoping Inverse Trig Series
MediumNumerical valueIdea asked in 4 years
Q25
Let $y = y(x)$ be the solution of the differential equation $x\sin\left(\frac{y}{x}\right)dy = \left(y\sin\left(\frac{y}{x}\right) - x\right)dx$ , $y(1) = \frac{\pi}{2}$ , and let $\alpha = \cos\left(\frac{y(e^{12})}{e^{12}}\right)$ . Then the number of…
Differential Equations Homogeneous Equations Substitution y = vx
HardNumerical valueIdea asked in 6 years

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.