JEE Main 2026 · April session

JEE Main 6 April 2026, Shift 2

75 questions: 15 numerical-answer and 60 multiple choice. 12 were rated hard and 21 easy. Its hard-question count was the joint 6th highest of the 9 2026 shifts Lumi analysed. The biggest chapter was Conic Sections, with 4 questions.

Questions: 75; none dropped
Numerical answer: 15; 20% of the shift
Hard: 12; 16% of the shift
Chapters asked: 55; 11 questions with a figure

Key findings · 6 Apr 2026, Shift 2

1
12 hard questions (16%): the joint 6th 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 6 of 25 rated hard; Physics had the most easy questions (10 of 25).
3
13 questions tested a new idea, one no earlier year had asked: 20% of the 64 questions tagged to an idea.
4
22 came back from 2025: the same idea had been asked in the 2025 shifts Lumi analysed.
5
21 shared an idea with another 2026 shift (33% of tagged questions). Shifts in the same year can test the same idea in a new setting.
6
Biggest chapters: Electrostatic Potential and Capacitance in Physics (2), 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 10Medium 13Hard 2

Top chapters

Chemistry

25 Q · 5 numerical

Easy 8Medium 13Hard 4

Top chapters

Maths

25 Q · 5 numerical

Easy 3Medium 16Hard 6

Top chapters

Question format

Single correct44 Q
Numerical value15 Q
Other5 Q
Two statements5 Q
Diagram based4 Q
Match the list2 Q

What each question asks you to do

Multi-step37 Q
Calculation18 Q
Application7 Q
Conceptual6 Q
Recall5 Q
Data or graph1 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

10 easy13 medium2 hard

Chemistry25 questions

8 easy13 medium4 hard

Maths25 questions

3 easy16 medium6 hard

Q1
Let $f:\mathbf{R}\to\mathbf{R}$ be defined as $f(x)=\frac{2x^2-3x+2}{3x^2+x+3}$ . Then $f$ is :
Relations and Functions
MediumSingle correct
Q2
Consider the quadratic equation $(n^2-2n+2)x^2-3x+(n^2-2n+2)^2=0$ , $n\in\mathbf{R}$ . Let $\alpha$ be the minimum value of the product of its roots and $\beta$ be the maximum value of the sum of its roots. Then the sum of the first six terms of the G.P.,…
Complex Numbers and Quadratic Equations Quadratic Roots Root-Coefficient Relation
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q3
Let $S=\{z\in\mathbb{C}: z^2+\sqrt{6}\,iz-3=0\}$ . Then $\sum_{z\in S} z^8$ is equal to :
Complex Numbers and Quadratic Equations Quadratic Roots Newton's Sums
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q4
The sum of all possible values of $\theta\in[0,2\pi]$ , for which the system of equations : $x\cos 3\theta-8y-12z=0$ $x\cos 2\theta+3y+3z=0$ $x+y+3z=0$ has a non-trivial solution, is equal to :
Determinants Cramer's Rule Homogeneous System Solutions
MediumSingle correctIdea asked in 4 years
Q5
Let $A=\begin{bmatrix}1&0&0\\3&1&0\\9&3&1\end{bmatrix}$ and $B=[b_{ij}]$ , $1\le i,j\le 3$ . If $B=A^{99}-I$ , then the value of $\frac{b_{31}-b_{21}}{b_{32}}$ is :
Matrices Matrix Multiplication Binomial Expansion for Commuting Matrices
MediumSingle correctIdea asked in 3 years
Q6
The sum $1+\frac{1}{2}\left(1^2+2^2\right)+\frac{1}{3}\left(1^2+2^2+3^2\right)+\ldots$ upto 10 terms is equal to :
Sequences and Series
MediumSingle correct
Q7
A building has ground floor and 10 more floors. Nine persons enter in a lift at the ground floor. The lift goes up to the 10 $^{\text{th}}$ floor. The number of ways, in which any 4 persons exit at a floor and the remaining 5 persons exit at a different…
Permutations and Combinations Division of Objects into Groups
MediumSingle correctIdea asked in 3 years
Q8
Let the mean and the variance of seven observations $2, 4, \alpha, 8, \beta, 12, 14$ , $\alpha<\beta$ , be 8 and 16 respectively. Then the quadratic equation whose roots are $3\alpha+2$ and $2\beta+1$ is :
Statistics Variance and SD Finding Unknown Observations from Mean and Variance
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q9
A bag contains 6 blue and 6 green balls. Pairs of balls are drawn without replacement until the bag is empty. The probability that each drawn pair consists of one blue and one green ball is :
Probability Conditional Probability Drawing Without Replacement
MediumSingle correctNew idea
Q10
Let C be a circle having centre in the first quadrant and touching the $x$ -axis at a distance of 3 units from the origin. If the circle C has an intercept of length $6\sqrt{3}$ on $y$ -axis, then the length of the chord of the circle C on the line $x-y=3$ is :
Conic Sections Circle Tangents Family of Circles Touching a Line
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q11
The eccentricity of an ellipse E with centre at the origin O is $\frac{\sqrt{3}}{2}$ and its directrices are $x=\pm\frac{4\sqrt{6}}{3}$ . Let $H:\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ be a hyperbola whose eccentricity is equal to the length of semi-major axis of…
Conic Sections
MediumSingle correct
Q12
Let $x=9$ be a directrix of an ellipse E, whose centre is at the origin and eccentricity is $\frac{1}{3}$ . Let P $(\alpha,0)$ , $\alpha>0$ , be a focus of E and AB be a chord passing through P. Then the locus of the mid point of AB is :
Conic Sections General Conic Section Chord Bisected at a Given Point (T=S1)
MediumSingle correctIdea asked in 3 years
Q13
If $\sin\left(\tan^{-1}\left(x\sqrt{2}\right)\right)=\cot\left(\sin^{-1}\sqrt{1-x^2}\right)$ , $x\in(0,1)$ , then the value of $x$ is :
Inverse Trigonometric Functions Inverse Trig Identities Evaluating Trig of Inverse Trig
MediumSingle correctIdea asked in 2 years
Q14
The shortest distance between the lines $\frac{x-4}{1}=\frac{y-3}{2}=\frac{z-2}{-3}$ and $\frac{x+2}{2}=\frac{y-6}{4}=\frac{z-5}{-5}$ is :
Three Dimensional Geometry Skew Lines Cartesian Shortest Distance
EasySingle correctIdea asked in 6 yearsAsked the year before
Q15
Let $\vec{a}=2\hat{i}+3\hat{j}+3\hat{k}$ and $\vec{b}=6\hat{i}+3\hat{j}+3\hat{k}$ . Then the square of the area of the triangle with adjacent sides determined by the vectors $\left(2\vec{a}+3\vec{b}\right)$ and $\left(\vec{a}-\vec{b}\right)$ is :
Vector Algebra Cross Product Area of Triangles and Parallelograms
EasySingle correctIdea asked in 6 yearsAsked the year before
Q16
Let $\lim_{x\to2}\frac{(\tan(x-2))\left(rx^2+(p-2)x-2p\right)}{(x-2)^2}=5$ for some $r, p\in\mathbf{R}$ . If the set of all possible values of q, such that the roots of the equation $rx^2-px+q=0$ lie in $(0,2)$ , be the interval $(\alpha,\beta]$ , then…
Complex Numbers and Quadratic Equations Location of Roots Both roots in interval
HardSingle correctNew idea
Q17
Let $A=\begin{bmatrix}1&3&-1\\2&1&\alpha\\0&1&-1\end{bmatrix}$ be a singular matrix. Let $f(x)=\int_0^x\left(t^2+2t+3\right)dt$ , $x\in[1,\alpha]$ . If M and m are respectively the maximum and the minimum values of $f$ in $[1,\alpha]$ , then $3(M-m)$ is equal…
Determinants Matrix Inverse Singular and Non-singular Matrices
MediumSingle correctIdea asked in 2 yearsAsked the year before
Q18
Let $f:\mathbf{R}\to\mathbf{R}$ be such that $f(xy)=f(x)f(y)$ , for all $x,y\in\mathbf{R}$ and $f(0)\neq0$ . Let $g:[1,\infty)\to\mathbf{R}$ be a differentiable function such that $x^2g(x)=\int_1^x\left(t^2f(t)-tg(t)\right)dt$ . Then $g(2)$ is equal to :
Differential Equations Linear Differential Equations LDEs Formed via Leibniz Integral Rule
HardSingle correctIdea asked in 3 years
Q19
The area of the region $\{(x,y): x^2-8x\le y\le -x\}$ is :
Application of Integrals Area Under Curves Area Between Curves
EasySingle correctIdea asked in 7 yearsAsked the year before
Q20
The value of the integral $\int_{-1}^{1}\left(\frac{x^3+|x|+1}{x^2+2|x|+1}\right)dx$ is equal to :
Integrals Definite Integral Properties Even and Odd Functions
MediumSingle correctIdea asked in 3 years
Q21
Let $R=\{(x,y)\in\mathbf{N}\times\mathbf{N}:\log_e(x+y)\le2\}$ . Then the minimum number of elements, required to be added in R to make it a transitive relation, is __________.
Relations and Functions Sets and Relations Transitive Closure
HardNumerical valueNew idea
Q22
If $(1-x^3)^{10}=\sum_{r=0}^{10}a_r x^r(1-x)^{30-2r}$ , then $\frac{9a_9}{a_{10}}$ is equal to __________.
Binomial Theorem
HardNumerical value
Q23
Let the line $x-y=4$ intersect the circle C : $(x-4)^2+(y+3)^2=9$ at the points Q and R. If P $(\alpha,\beta)$ is a point on C such that PQ = PR, then $(6\alpha+8\beta)^2$ is equal to __________.
Conic Sections
MediumNumerical value
Q24
Let the image of the point P $(0,-5,0)$ in the line $\frac{x-1}{2}=\frac{y}{1}=\frac{z+1}{-2}$ be the point R and the image of the point Q $\left(0,\frac{-1}{2},0\right)$ in the line $\frac{x-1}{-1}=\frac{y+9}{4}=\frac{z+1}{1}$ be the point S. Then the square…
Three Dimensional Geometry Lines in 3D Image of a Point in a Line
HardNumerical valueIdea asked in 6 yearsAsked the year before
Q25
Let $f(x)=\begin{cases}x^3+8;&x<0,\\x^2-4;&x\ge0,\end{cases}$ and $g(x)=\begin{cases}(x-8)^{1/3};&x<0,\\(x+4)^{1/2};&x\ge0.\end{cases}$ Then the number of points, where the function $g\circ f$ is discontinuous, is __________.
Continuity and Differentiability Continuity and Differentiability of Composite Functions
HardNumerical valueIdea asked in 5 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.