JEE Main 2026 · April session

JEE Main 6 April 2026, Shift 1

75 questions: 15 numerical-answer and 60 multiple choice. 12 were rated hard and 18 easy. Its hard-question count was the joint 6th highest of the 9 2026 shifts Lumi analysed. The biggest chapter was Conic Sections, with 5 questions.

Questions: 75; none dropped
Numerical answer: 15; 20% of the shift
Hard: 12; 16% of the shift
Chapters asked: 53; 9 questions with a figure

Key findings · 6 Apr 2026, Shift 1

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 7 of 25 rated hard; Physics had the most easy questions (8 of 25).
3
14 questions tested a new idea, one no earlier year had asked: 23% of the 61 questions tagged to an idea.
4
19 came back from 2025: the same idea had been asked in the 2025 shifts Lumi analysed.
5
16 shared an idea with another 2026 shift (26% of tagged questions). Shifts in the same year can test the same idea in a new setting.
6
Biggest chapters: Alternating Current in Physics (2), Amines in Chemistry (3) and Conic Sections in Maths (5).

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 8Medium 14Hard 3

Top chapters

Maths

25 Q · 5 numerical

Easy 2Medium 16Hard 7

Top chapters

Question format

Single correct49 Q
Numerical value15 Q
Match the list4 Q
Two statements4 Q
Other3 Q

What each question asks you to do

Multi-step34 Q
Calculation26 Q
Conceptual7 Q
Application5 Q
Recall3 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

8 easy14 medium3 hard

Maths25 questions

2 easy16 medium7 hard

Q1
Let $[\cdot]$ denote the greatest integer function. If the domain of the function $f(x)=\sin^{-1}\left(\frac{x+[x]}{3}\right)$ is $[\alpha, \beta)$ , then $\alpha^2+\beta^2$ is equal to:
Inverse Trigonometric Functions Inverse Trig Domains Inverse Trig with GIF and Fractional Part
MediumSingle correctIdea asked in 2 years
Q2
Let one root of the quadratic equation in $x$ : $(k^2-15k+27)x^2+9(k-1)x+18=0$ be twice the other. Then the length of the latus rectum of the parabola $y^2=6kx$ is equal to:
Conic Sections Quadratic Roots Roots in a Specific Ratio
MediumSingle correctNew idea
Q3
Let $e_1$ and $e_2$ be two distinct roots of the equation $x^2-ax+2=0$ . Let the sets $\{a\in\mathbb{R}: e_1$ and $e_2$ are the eccentricities of hyperbolas $\}=(\alpha,\beta)$ , and $\{a\in\mathbb{R}: e_1$ and $e_2$ are the eccentricities of an ellipse and a…
Conic Sections Location of Roots Both roots greater than k
HardSingle correctNew idea
Q4
Let the set of all values of $k\in\mathbb{R}$ such that the equation $z(\overline{z}+2+i)+k(2+3i)=0$ , $z\in\mathbb{C}$ , has at least one solution, be the interval $[\alpha,\beta]$ . Then $9(\alpha+\beta)$ is equal to:
Complex Numbers and Quadratic Equations
HardSingle correct
Q5
The value of $1^3-2^3+3^3-\ldots+15^3$ is:
Sequences and Series
MediumSingle correct
Q6
The sum of the first ten terms of an A.P. is 160 and the sum of the first two terms of a G.P. is 8. If the first term of the A.P. is equal to the common ratio of the G.P. and the first term of the G.P. is equal to common difference of the A.P., then the sum…
Sequences and Series AP and GP AP Sum of n terms
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q7
The number of 4-letter words, with or without meaning, each consisting of two vowels and two consonants that can be formed from the letters of the word INCONSEQUENTIAL, without repeating any letter, is:
Permutations and Combinations Combinations of Distinct Objects
MediumSingle correctIdea asked in 8 yearsAsked the year before
Q8
If the coefficients of the middle terms in the binomial expansions of $(1+\alpha x)^{26}$ and $(1-\alpha x)^{28}$ , $\alpha\neq 0$ , are equal, then the value of $\alpha$ is:
Binomial Theorem Binomial Coefficients Maximum Binomial Coefficient
EasySingle correctIdea asked in 3 years
Q9
A data consists of 20 observations $x_1, x_2,\ldots, x_{20}$ . If $\sum_{i=1}^{20}(x_i+5)^2=2500$ and $\sum_{i=1}^{20}(x_i-5)^2=100$ , then the ratio of mean to standard deviation of this data is:
Statistics Variance and SD Algebraic Expansion of Squared Deviations
MediumSingle correctNew idea
Q10
A bag contains $(\mathrm{N}+1)$ coins $-$ N fair coins, and one coin with 'Head' on both sides. A coin is selected at random and tossed. If the probability of getting 'Head' is $\frac{9}{16}$ , then N is equal to:
Probability Bayes' Theorem Theorem of Total Probability
EasySingle correctIdea asked in 3 years
Q11
If the eccentricity $e$ of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ , passing through $\left(6,4\sqrt{3}\right)$ , satisfies $15(e^2+1)=34e$ , then the length of the latus rectum of the hyperbola $\frac{x^2}{b^2}-\frac{y^2}{2(a^2+1)}=1$ is:
Conic Sections
MediumSingle correct
Q12
Let chord PQ of length $3\sqrt{13}$ of the parabola $y^2=12x$ be such that the ordinates of points P and Q are in the ratio 1:2. If the chord PQ subtends an angle $\alpha$ at the focus of the parabola, then $\sin\alpha$ is equal to:
Conic Sections
HardSingle correct
Q13
Let $0<\alpha<1$ , $\beta=\frac{1}{3\alpha}$ and $\tan^{-1}(1-\alpha)+\tan^{-1}(1-\beta)=\frac{\pi}{4}$ . Then $6(\alpha+\beta)$ is equal to:
Inverse Trigonometric Functions Inverse Trig Identities Tan-1 Sum and Difference
MediumSingle correctIdea asked in 3 years
Q14
Let $\mathrm{S}=\left\{\theta\in(-2\pi,2\pi):\cos\theta+1=\sqrt{3}\sin\theta\right\}$ . Then $\sum_{\theta\in \mathrm{S}}\theta$ is equal to:
Trigonometric Functions General Solutions Sine General Solution
MediumSingle correctNew idea
Q15
Let the image of the point $\mathrm{P}(1,6,a)$ in the line $\mathrm{L}:\frac{x}{1}=\frac{y-1}{2}=\frac{z-a+1}{b}$ , $b>0$ , be $\left(\frac{a}{3},0,a+c\right)$ . If $\mathrm{S}(\alpha,\beta,\gamma)$ , $\alpha>0$ , is the point on L such that the distance of S…
Three Dimensional Geometry Lines in 3D Image of a Point in a Line
HardSingle correctIdea asked in 6 yearsAsked the year before
Q16
Let a line L be perpendicular to both the lines $\mathrm{L}_1:\frac{x+1}{3}=\frac{y+3}{5}=\frac{z+5}{7}$ and $\mathrm{L}_2:\frac{x-2}{1}=\frac{y-4}{4}=\frac{z-6}{7}$ . If $\theta$ is the acute angle between the lines L and…
Three Dimensional Geometry Angle Between Lines Line Perpendicular to Two Given Lines
MediumSingle correctNew idea
Q17
The value of $\lim_{x\to 0}\left(\frac{x^2\sin^2 x}{x^2-\sin^2 x}\right)$ is:
Limits and Derivatives L'Hopital's Rule Choosing Series Expansion over L'Hopital
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q18
The value of the integral $\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}}\left(\frac{32\cos^4 x}{1+e^{\sin x}}\right)dx$ is:
Integrals Definite Integral Properties Symmetric Limits with Exponential Denominator Trick
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q19
The area of the region $\{(x,y): 0\le y\le 6-x,\ y^2\ge 4x-3,\ x\ge 0\}$ is:
Application of Integrals Area Under Curves Area of Inequalities
MediumSingle correctIdea asked in 8 yearsAsked the year before
Q20
Let $e$ be the base of natural logarithm and let $f:\{1,2,3,4\}\to\{1,e,e^2,e^3\}$ and $g:\{1,e,e^2,e^3\}\to\left\{1,\frac{1}{2},\frac{1}{3},\frac{1}{4}\right\}$ be two bijective functions such that $f$ is strictly decreasing and $g$ is strictly increasing.…
Application of Integrals Area Under Curves Area Between Curves
HardSingle correctIdea asked in 7 yearsAsked the year before
Q21
Let $A=\begin{bmatrix}-1&1&-1\\1&0&1\\0&0&1\end{bmatrix}$ satisfy…
Determinants Matrix Inverse Inverse Relation to Double Adjoint
MediumNumerical valueIdea asked in 6 yearsAsked the year before
Q22
Let the centre of the circle $x^2+y^2+2gx+2fy+25=0$ be in the first quadrant and lie on the line $2x-y=4$ . Let the area of an equilateral triangle inscribed in the circle be $27\sqrt{3}$ . Then the square of the length of the chord of the circle on the line…
Conic Sections Straight Line Distance Chord Length via Perpendicular Distance
MediumNumerical valueNew idea
Q23
If $\vec{a}=\hat{i}+\hat{j}+\hat{k}$ , $\vec{b}=\hat{j}-\hat{k}$ and $\vec{c}$ be three vectors such that $\vec{a}\times\vec{c}=\vec{b}$ and $\vec{a}\cdot\vec{c}=3$ , then $\vec{c}\cdot\left(\vec{a}-2\vec{b}\right)$ is equal to ________.
Vector Algebra Cross Product Solving Vector Equations with Cross Products
MediumNumerical valueIdea asked in 6 years
Q24
For the functions $f(\theta)=\alpha\tan^2\theta+\beta\cot^2\theta$ , and $g(\theta)=\alpha\sin^2\theta+\beta\cos^2\theta$ , $\alpha>\beta>0$ , let $\min_{0<\theta<\frac{\pi}{2}}f(\theta)=\max_{0<\theta<\pi}g(\theta)$ . If the first term of a G.P. is…
Sequences and Series AP and GP GP Sum of n terms
HardNumerical valueIdea asked in 5 yearsAsked the year before
Q25
Let $y=y(x)$ be the solution of the differential equation $\left(x^2-x\sqrt{x^2-1}\right)dy+\left(y\left(x-\sqrt{x^2-1}\right)-x\right)dx=0$ , $x\ge 1$ . If $y(1)=1$ , then the greatest integer less than $y\left(\sqrt{5}\right)$ is ________.
Differential Equations Linear Differential Equations Coefficient Normalization for Standard Form
HardNumerical valueIdea asked in 3 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.