JEE Main 2026 · April session

JEE Main 5 April 2026, Shift 2

75 questions: 15 numerical-answer and 60 multiple choice. 14 were rated hard and 23 easy. Its hard-question count was the joint highest of the 9 2026 shifts Lumi analysed. The biggest chapter was Conic Sections, with 3 questions.

Questions: 75; none dropped
Numerical answer: 15; 20% of the shift
Hard: 14; 19% of the shift
Chapters asked: 55; 6 questions with a figure

Key findings · 5 Apr 2026, Shift 2

1
14 hard questions (19%): the joint 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 10 of 25 rated hard; Physics had the most easy questions (13 of 25).
3
9 questions tested a new idea, one no earlier year had asked: 14% of the 63 questions tagged to an idea.
4
18 came back from 2025: the same idea had been asked in the 2025 shifts Lumi analysed.
5
20 shared an idea with another 2026 shift (32% of tagged questions). Shifts in the same year can test the same idea in a new setting.
6
Biggest chapters: Current Electricity in Physics (2), Aldehydes, Ketones and Carboxylic Acids in Chemistry (2) and Conic Sections in Maths (3).

The shift at a glance

Subjects, difficulty and chapters

Physics

25 Q · 5 numerical

Easy 13Medium 9Hard 3

Top chapters

Chemistry

25 Q · 5 numerical

Easy 6Medium 18Hard 1

Top chapters

Maths

25 Q · 5 numerical

Easy 4Medium 11Hard 10

Top chapters

Question format

Single correct46 Q
Numerical value15 Q
Two statements6 Q
Match the list3 Q
Diagram based2 Q
Other2 Q
Assertion–reason1 Q

What each question asks you to do

Multi-step27 Q
Calculation22 Q
Conceptual11 Q
Application9 Q
Recall4 Q
Data or graph2 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

13 easy9 medium3 hard

Chemistry25 questions

6 easy18 medium1 hard

Maths25 questions

4 easy11 medium10 hard

Q1
Let $\alpha, \beta$ be the roots of the equation $x^2-x+p=0$ and $\gamma, \delta$ be the roots the equation $x^2-4x+q=0$ ; $p, q \in \mathbf{Z}$ . If $\alpha, \beta, \gamma, \delta$ are in G.P., then $|p+q|$ equals :
Complex Numbers and Quadratic Equations Quadratic Roots Root-Coefficient Relation
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q2
Let $z_1, z_2 \in \mathbb{C}$ be the distinct solutions of the equation $z^2+4z-(1+12i)=0$ . Then $|z_1|^2+|z_2|^2$ is equal to :
Complex Numbers and Quadratic Equations Quadratic Roots Root-Coefficient Relation
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q3
If $f: \mathbf{N} \to \mathbf{Z}$ is defined by $f(n)=\begin{vmatrix} n & -1 & -5 \\ -2n^2 & 3(2k+1) & 2k+1 \\ -3n^3 & 3k(2k+1) & 3k(k+2)+1 \end{vmatrix}$ , $k \in \mathbf{N}$ , and $\sum_{n=1}^{k} f(n)=98$ , then k is equal to :
Determinants
HardSingle correct
Q4
Let M be a $3\times 3$ matrix such that $M\begin{pmatrix}1\\0\\0\end{pmatrix}=\begin{pmatrix}1\\2\\3\end{pmatrix}$ , $M\begin{pmatrix}0\\1\\0\end{pmatrix}=\begin{pmatrix}0\\1\\2\end{pmatrix}$ and…
Matrices Matrix Inverse Solving Matrix Equations
MediumSingle correctIdea asked in 2 years
Q5
If the sum of the first 10 terms of the series $\frac{1}{1+1^4\times 4}+\frac{2}{1+2^4\times 4}+\frac{3}{1+3^4\times 4}+\frac{4}{1+4^4\times 4}+\dots\dots$ is $\frac{m}{n}$ , $\gcd(m, n)=1$ , then $m+n$ is equal to :
Sequences and Series AP and GP Method of Differences (Vn Method)
HardSingle correctIdea asked in 5 yearsAsked the year before
Q6
Let $A_1, A_2, A_3, \dots\dots, A_{39}$ be 39 arithmetic means between the numbers 59 and 159. Then the mean of $A_{25}, A_{28}, A_{31}$ and $A_{36}$ is equal to :
Sequences and Series AP and GP AP General Term
EasySingle correctIdea asked in 4 years
Q7
The coefficient of $x^2$ in the expansion of $\left(2x^2+\frac{1}{x}\right)^{10}$ , $x \neq 0$ , is :
Binomial Theorem
EasySingle correct
Q8
The probabilities that players A and B of a team are selected for the captaincy for a tournament are 0.6 and 0.4, respectively. If A is selected the captain, the probability that the team wins the tournament is 0.8 and if B is selected the captain, the…
Probability Conditional Probability Law of Total Probability
EasySingle correctNew idea
Q9
A box contains 5 blue, 6 yellow and 4 red balls. The number of ways, of drawing 8 balls containing at least two balls of each colour, is :
Permutations and Combinations Combinations of Distinct Objects
MediumSingle correctIdea asked in 8 yearsAsked the year before
Q10
A variable X takes values $0, 0, 2, 6, 12, 20, \dots, n(n-1)$ with frequencies ${}^nC_0, {}^nC_1, {}^nC_2, {}^nC_3, {}^nC_4, {}^nC_5, \dots, {}^nC_n$ , respectively. If the mean of this data is 60, then its median is :
Statistics
HardSingle correct
Q11
Let the point P be the vertex of the parabola $y=x^2-6x+12$ . If a line passing through the point P intersects the circle $x^2+y^2-2x-4y+3=0$ at the points R and S, then the maximum value of $(PR+PS)^2$ is :
Conic Sections Power of a Point Secant-Tangent Power Theorem
HardSingle correctIdea asked in 2 years
Q12
Let the directrix of the parabola $P: y^2=8x$ , cut x-axis at the point A. Let $B(\alpha, \beta)$ , $\alpha>1$ , be a point on P such that the slope of AB is $3/5$ . If BC is a focal chord of P, then six times the area of $\Delta ABC$ is :
Conic Sections Parabola Focal Chords Parameter relation t1*t2 = -1
MediumSingle correctIdea asked in 2 years
Q13
Let the eccentricity e of a hyperbola satisfy the equation $6e^2-11e+3=0$ . If the foci of the hyperbola are $(3, 5)$ and $(3, -4)$ , then the length of its latus rectum is :
Conic Sections
MediumSingle correct
Q14
Let a triangle PQR be such that P and Q lie on the line $\frac{x+3}{8}=\frac{y-4}{2}=\frac{z+1}{2}$ and are at a distance of 6 units from R $(1, 2, 3)$ . If $(\alpha, \beta, \gamma)$ is the centroid of $\Delta$ PQR, then $\alpha+\beta+\gamma$ is equal to :
Three Dimensional Geometry Lines in 3D Foot of the Perpendicular
MediumSingle correctIdea asked in 6 years
Q15
If the distance of the point $(a, 2, 5)$ from the image of the point $(1, 2, 7)$ in the line $\frac{x}{1}=\frac{y-1}{1}=\frac{z-2}{2}$ is 4, then the sum of all possible values of a is equal to :
Three Dimensional Geometry Lines in 3D Image of a Point in a Line
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q16
Let O be the origin, $\overrightarrow{OP}=\vec{a}$ and $\overrightarrow{OQ}=\vec{b}$ . If R is the point on $\overrightarrow{OP}$ such that $\overrightarrow{OP}=5\,\overrightarrow{OR}$ , and M is the point such that…
Vector Algebra
EasySingle correct
Q17
Let $f(x)=\lim_{y\to 0}\frac{(1-\cos(xy))\tan(xy)}{y^3}$ . Then the number of solutions of the equation $f(x)=\sin x$ , $x \in \mathbf{R}$ is :
Limits and Derivatives L'Hopital's Rule Simplifying with Standard Limits Before L'Hopital
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q18
Let $(2^{1-a}+2^{1+a})$ , $f(a)$ , $(3^a+3^{-a})$ be in A.P. and $\alpha$ be the minimum value of $f(a)$ . Then the value of the integral $\int_{\log_e(\alpha-1)}^{\log_e(\alpha)}\frac{dx}{(e^{2x}-e^{-2x})}$ is :
Integrals Integration by Substitution Exponential Factor Manipulation
HardSingle correctIdea asked in 4 years
Q19
Let $f:[1,\infty)\to\mathbf{R}$ be a differentiable function defined as $f(x)=\int_1^x f(t)\,dt+(1-x)(\log_e x-1)+e$ . Then the value of $f(f(1))$ is :
Differential Equations Leibniz Rule Solving Integral Equations
HardSingle correctIdea asked in 6 yearsAsked the year before
Q20
Let $f(x)$ and $g(x)$ be twice differentiable functions satisfying $f''(x)=g''(x)$ for all $x \in \mathbf{R}$ , $f'(1)=2g'(1)=4$ and $g(2)=3f(2)=9$ . Then $f(25)-g(25)$ is equal to :
Continuity and Differentiability Mean Value Theorem Zero Derivative Implies Constant Function
MediumSingle correctNew idea
Q21
Let $A=\{1, 4, 7\}$ and $B=\{2, 3, 8\}$ . Then the number of elements, in the relation $R=\{((a_1, b_1), (a_2, b_2)) \in ((A\times B)\times(A\times B)) : a_1+b_2 \text{ divides } a_2+b_1\}$ is __________.
Relations and Functions Sets and Relations Divisibility Relation
MediumNumerical valueNew idea
Q22
From the point $(-1, -1)$ , two rays are sent making angles of $45^\circ$ with the line $x+y=0$ . These rays get reflected from the mirror $x+2y=1$ . If the equations of the reflected rays are $ax+by=9$ and $cx+dy=7$ , $a, b, c, d \in \mathbf{Z}$ , then the value…
Straight Lines Straight Line Distance Reflection of a Line in a Line
HardNumerical valueIdea asked in 2 years
Q23
If $S=\left\{\theta \in [-\pi, \pi] : \cos\theta\cos\frac{5\theta}{2}=\cos 7\theta\cos\frac{7\theta}{2}\right\}$ , then n(S) is equal to __________.
Trigonometric Functions General Solutions Product-to-Sum Transformation
HardNumerical valueIdea asked in 2 years
Q24
Let $f:\mathbf{R}\to\mathbf{R}$ be a function such that $f(x)+3f\left(\frac{\pi}{2}-x\right)=\sin x$ , $x \in \mathbf{R}$ . Let the maximum value of $f$ on $\mathbf{R}$ be $\alpha$ . If the area of the region bounded by the curves $g(x)=x^2$ and…
Application of Integrals Area Under Curves Area Between Curves
HardNumerical valueIdea asked in 7 yearsAsked the year before
Q25
Let $y=y(x)$ be the solution of the differential equation $(\tan x)^{1/2}\,dy=\left(\sec^3 x-(\tan x)^{3/2}\,y\right)dx$ , $0<x<\frac{\pi}{2}$ , $y\left(\frac{\pi}{4}\right)=\frac{6\sqrt{2}}{5}$ . If $y\left(\frac{\pi}{3}\right)=\frac{4}{5}\alpha$ , then…
Differential Equations Linear Differential Equations Particular Solution Solving
HardNumerical valueIdea asked in 4 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.