JEE Mains 2026 Session 2 Question Paper Solutions OUT - Download PDF

JEE Main 2026 April Session Question Paper PDF

Given below is the link to download official the JEE Main question paper 2026 along with the solutions in the PDF format. It will help students understand the exam pattern and type of questions asked in the JEE Mains April session question paper.

Memory-Based JEE Main 2026 April Session Question Paper PDF

Given below is the link to download the Memory-based questions of JEE Mains 2026 along with the solutions in the PDF format.

How to Download JEE Main 2026 April Question Paper: Free PDF

Students can refer to the steps given below to download the JEE Main 2026 Question Paper. These steps will help students easily download the JEE Main paper for practice and analysis.

• Click on the JEE Main 2026 shift-wise question paper link provided in the table in the above section.

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• Log in using your registered email ID and password.

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JEE Main 2026 Shift-wise Answer Key PDF

The answer key of the memory-based JEE Main 2026 question paper is released by Careers 360. Students can refer to the JEE Main 2026 shift-wise answer key that is available here for the 2nd April Shift 1 and Shift 2. Using this answer key, students can cross-check their answers and estimate their expected scores.

JEE Mains 2026 Session 2 Memory-Based Questions with Solutions

The memory-based questions of JEE Main 2026, along with solutions, are updated here for 2nd April Shift 1 and Shift 2. Students can use these questions to check their answers, estimate their marks, and gain a clear understanding of the paper pattern and important topics.

JEE Mains 2026 April 2 Shift 1: Memory-Based Questions

JEE Mains 2026 April 2 Shift 1 Maths Question Paper

Question 1:
If $y=f(x)$ is the solution of the differential equation $(1+\sin x) \frac{d y}{d x}+\cos x=0$, such that $f(0)=0$, then $f\left(\frac{\pi}{2}\right)$ is equal to:
(1) $\ln 2$
(2) $-\ln 2$
(3) $\ln 3$
(4) $\ln 4$

Question 2:
If eccentricity of an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$, which passes through point $(3,4)$ is $\frac{\sqrt{5}}{3}$, then length of latus rectum of ellipse is:
(1) $\frac{4 \sqrt{5}}{3}$
(2) $\frac{8 \sqrt{5}}{3}$
(3) $\frac{4 \sqrt{7}}{3}$
(4) $\frac{8 \sqrt{7}}{3}$

JEE Mains 2026 April 2 Shift 1 Physics Question Paper

Question1: The dimension of $\frac{1}{2} \varepsilon_0 E^2$ is
1) $\mathrm{MLT}^{-2}$
2) $\mathrm{MLL}^{-1} \mathrm{~T}^{-2}$
3) $\mathrm{MLT}^{-1}$
4) $M L^{-1} T^{-1}$

Question 2: A wooden cubic block of relative density. 0.4 is floating in water. Side of cubic block is 10 cm .
When a coin is placed on the block the dips 0.3 cm in equilibrium. Weight of coin is
1) 0.2 N
2) 30 N
3) 0.3 N
4) 3 N

JEE Mains 2026 April 2 Shift 1 Chemistry Question Paper

Question 1: The correct increasing order of bond length among the following is
$1 \mathrm{O}_2^{+}, \mathrm{O}_2, \mathrm{O}_2^{-}, \mathrm{O}_2^{2-}$
$2 \mathrm{O}_2^{+}, \mathrm{O}_2, \mathrm{O}_2^{2-}, \mathrm{O}_2^{-}$
$30_2^{2-}, 0_2^{-}, 0_2, 0_2^{+}$
$4 \mathrm{O}_2^{-}, \mathrm{O}_2^{2-}, \mathrm{O}_2^{+}, \mathrm{O}_2$

Question 2: For first order reaction, rate constant at $27^{\circ} \mathrm{C}$ and $\mathrm{t}^{\circ} \mathrm{C}$ is $1.5 \times 10^3$ and $4.5 \times 10^3$ respectively. If the activation enesgy of reaction is 60 kJ then find temperature $t$.

JEE Mains 2026 April 2 Shift 2: Memory-Based Questions

JEE Mains 2026 April 2 Shift 2 Maths Question Paper

Question 1
Evaluate the sum $\frac{1^3}{1}+\frac{1^3+2^3}{1+3}+\frac{1^3+2^3+3^3}{1+3+5}+\cdots$ up to 8 terms.
(1) 71
(2) 70
(3) 73
(4) 72

Question 2:
$f(x)$ is 5 degree polynomial has extremes at $x= \pm 1$ and $\lim _{x \rightarrow 0} \frac{f(x)}{x^3}=5$, then $f(2)-f(-2)$ is:

JEE Mains 2026 April 2 Shift 2 Physics Question Paper

Q1. In an equilateral prism, the path of a ray is shown. Determine the refractive index.

A. 1.71
B. 1.52
C. 1.39
D. 1.84

Q2. What is the equivalent gate for the circuit?

A. AND gate
B. OR gate
C. NAND gate
D. NOR gate

JEE Mains 2026 April 2 Shift 2 Chemistry Question Paper

Question 1: Arrange following complexes in increasing order of CFSE ( $\Delta 0$ )
(a) $\left[\mathrm{Co}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{2+}$
(b) $\left[\mathrm{Co}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{3+}$
(c) $\left[\mathrm{Co}(\mathrm{en})_3\right]^{3+}$

$
\begin{array}{ll}
1 & c>a>b \\
2 & c>b>a \\
3 & a>b>c \\
4 & b>a>c
\end{array}
$

JEE Mains 2026 April 4 Shift 1: Memory-Based Questions

JEE Mains 2026 April 4 Shift 1 Physics Questions

Question 1:

The initial radius of a soap bubble is 1 cm . It is slowly inflated to a radius of 2 cm . Calculate the work done in expanding the bubble.

(1) $2.63 \times 10^{-4} \mathrm{~J}$
(2) $1.46 \times 10^{-4} \mathrm{~J}$
(3) $5.27 \times 10^{-4} \mathrm{~J}$
(4) $12.64 \times 10^{-4} \mathrm{~J}$

Question 2:
Nuclei A and B form a nucleus C. BE/N for A, B and C are $\mathbf{3 ~ M e V}, \mathbf{7 ~ M e V}$ and $\mathbf{6 ~ M e V}$. Then energy produced in

$2 A^3+B^4 \rightarrow C^{10}$

1) 8 MeV
2) 12 MeV
3) 14 MeV
4) 10 MeV

JEE Mains 2026 April 4 Shift 1 Chemistry Questions

Question 1:

Total number of lone pairs and $\sigma$ bond pairs formed by central atom ( Xe ) in $\mathrm{XeO}_6^{4-}$

Question 2:

Match the following

JEE Mains 2026 April 4 Shift 1 Maths Questions

Question 1:

Let $A=\{1,2,3,4,5\}$ and $B=\{a, b, c\}$. Then the number of functions which are not onto is/are:

Question 2:

If $z$ be a complex number such that $|z+2|=|z-2|$ and $\arg \left(\frac{z-3}{z+i}\right)=\frac{\pi}{4}$ then the value of $z$ is

(1) $3i$

(2) $-3i$

(3) $2i$

(4) $-2i$

JEE Mains 2026 April 4 Shift 2: Memory-Based Questions

JEE Mains April 4 Shift 2 Questions Chemistry

Question 1:

Match the column

(A) I-b, II-a, III-c, IV-d
(B) I-a, II-b, III-c, IV-d
(C) I-b, II-a, III-d, IV-c
(D) I-c, II-a, III-b, IV-d

Question 2:

Manganese forms oxide and fluoride with highest oxidation state. The difference in the highest oxidation state of Mn in the oxide and fluoride is

$1) \quad 1$

$2) \quad 2$

$3)\quad 3$

$4) \quad 4$

JEE Mains April 4 Shift 2 Questions Maths

Question 1:

If the system of equations

$
\begin{aligned}
& x+y+z=5 \\
& x+2 y+3 z=9 \\
& x+3 y+\lambda z=\mu \text { has infinite number of solutions. Then, the value of } \lambda+\mu \text { is }
\end{aligned}
$

(1) 18

(2) 23

(3) 21

(4) 22

Question 2:

The number of non-negative integer solution of the equation $a+b+2 c=22$, is

(1) 124

(2) 144

(3) 135

(4) 136

Question 3:

Evaluate $(0.2)^{\log _{\sqrt{5}}^\alpha}+(0.04)^{\log _5^\beta}$
if $\alpha=\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\ldots$

$
\beta=\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\ldots
$
(1) 4
(2) 8
(3) 12
(4) 10

JEE Mains April 4 Shift 2 Questions Physics

Question 1:

Two strings with length ( $l_1, l_2$ ), Young's modulii ( $Y_1, Y_2$ ) are elongated under two weights as shown. Find $\Delta l_1 / \Delta l_2$.
a. 3
b. $2 / 3$
c. $4 / 3$
d. $1 / 3$

Question 2:

Consider a ring of radius $R$, rotates about a horizontal axis as shown. Time period of small oscillate
a. $2 \pi \sqrt{\frac{5 R}{g}}$
b. $2 \pi \sqrt{\frac{R}{2 g}}$
c. $2 \pi \sqrt{\frac{3 R}{2 g}}$
d. $2 \pi \sqrt{\frac{R}{g}}$

JEE Mains 2026 April 5 Shift 1: Memory-Based Questions

Physics

Question 1:

Select the quantity with matching dimensions of $\mathrm{ML}^2 \mathrm{~T}^{-4} \mathrm{~A}^{-2}$.
$(1) \frac{R}{\sqrt{L C}}$
(2) $\frac{1}{R} \sqrt{\frac{L}{C}}$
$(3) \frac{R}{L C}$
(4) $\frac{C}{\sqrt{L R}}$

Question 2:

Young's modulus of wire is $Y$. Keeping the material the same, if the radius of the wire is doubled while the length is halved. Then the new value of Young's modulus is
$(1)2 Y$
$(2)4 Y$
$(3) Y$
$(4) Y / 2$

Chemistry

Question 1:

Half life for a first order reaction is 6.93 min . What is the time required (in min) to complete $90 \%$ of reaction? (Mearest integer)

Question 2:

Select the correct statements:

a) Glucose has 2 anomeric forms
b) Both forms have difference in configuration of $C_1$ carton.
c)$\alpha$ form has more m. P ythan $\beta$-form
d) $\quad \theta_{s p}$ of $\alpha$ -form is $19^{\circ}$ and $\beta$ form is 12

Maths

Question 1:

The sum of value $\sum_{n=1}^{10} \frac{528}{n(n+1)(n+2)}$ is equal to:

(1) 220
(2) 65
(3) 130
(4) 260

Question 2:

Consider an equilateral triangle $P Q R$, where $P(3,5)$ and $Q R$ is $x+y=4$. It the orthocentre of $\triangle P Q R$ is $(\alpha, \beta)$, then $9(\alpha+\beta)$ is equal to

(1) 56
(2) 48
(3) 64
(4) 36

JEE Mains 2026 April 5 Shift 2: Memory-Based Questions

Physics

Question 1:

Escape velocity on earth is $v_e=\sqrt{2 g R}$. A planet of half the radius of earth will density equal to that of earth, the escape speed shall be $\frac{v_e}{N}$ then $N$ is

Question 2:

Find dimensions of $\sqrt{\frac{G h}{C^5}}$
1. $\mathrm{ML}^2 \mathrm{~T}^{-1}$
2. $\mathrm{M}^0 \mathrm{~L}^0 \mathrm{~T}^1$
3. $\mathrm{M}^0 \mathrm{LT}^{-1}$
4. $\mathrm{M}^0 \mathrm{~L}^0 \mathrm{~T}^{-1}$

Chemistry

Question 1:

Given below are two statements:
Statement I: Glucose is found to exist in two different anomeric form $\alpha$ and $\beta$
Statement II: In open chain structure $\mathbf{C}_{\mathbf{3}}$, $\mathbf{C}_{\mathbf{4}}$, $\mathbf{C}_{\mathbf{5}}$ of glucose & fructose both have same orientation
In the light of above statements choose the correct option.

1. Both statement I and statement II are correct
2. Statement I is correct but statement II is incorrect

3. Statement I is incorrect but statement II is correct
4. Both statement I and statement II are incorrect

Question 2:

Given below are two statements:
Statement I: The shape of $\mathrm{ICl}_3^{-}$is square planar
Statement II: The shape of $\mathrm{ClBr}_2^{-}$is pyramidal
In the light of above statements choose the correct option.

1. Both statement I and statement II are correct

2. Statement I is correct but statement II is incorrect

3. Statement I is incorrect but statement II is correct

4. Both statement I and statement II are incorrect

Question 3:

RMgX reacts with $H_2 \mathrm{O}$ and release gas which has volume $1.4 \mathrm{dm}^3 / \mathrm{gm}$ at The gas reacts with Na in presence of dry ther to form " $Y$ ". Find molar $\operatorname{mass}$ of x & y.

Question 4:

Benzamide, on reaction with Br₂+ NaOH, gives benzenamine (Aniline)
On nitration of aniline, a metaproduct is formed more than its ortho Product

Question 5:

Consider the following equilibrium -

$2 \mathrm{AB} \rightleftharpoons \mathrm{~A}_2+\mathrm{B}_2$
If equilibrium pressure is P and degree of dissociation is $\alpha$, then $\mathrm{K}_{\mathrm{p}}$ is
$1\quad \frac{\alpha^2}{4(1-\alpha)^2}$
$2\quad \frac{\rho . \alpha^2}{4(1-\alpha)}$
$3\quad \frac{\rho . \alpha}{(1-\alpha)}$
$4 \quad \frac{\rho . \alpha}{4(1-\alpha)}$

Mathematics

Question 1:

The coefficient of $x^2$ in the binomial expansion of $\left(2 x^2+\frac{1}{x}\right)^{10}$ is
1. 3260
2. 3360
3. 1760
4. 1890

Question 2:
If it is given that the probability of $A$ becoming captain of the team is 0.8 and $B$ becoming captain is 0.4 . If $A$ becomes captain, then the chances of the team winning the match are 0.6 , and when $B$ becomes captain, then the chances of winning the match are 0.7 . Then the probability that the team wins the match is:
1. 0.76
2. 0.78
3. 0.74
4. 0.84

Question 3:
Let $A=\{2,3\}$ and $B=\{5,6\}$. Then, the number of relations from $A \times B$ to $A \times B$ are
1. $2^{12}$
2. $2^{16}$
3. $2^{10}$
4. $2^{15}$

Question 4:
A bag contains 4 red balls, 6 yellow balls and 5 blue balls. In how many ways we can select 8 balls such that we get at least two balls of each colour, is:

JEE Mains 2026 April 6 Shift 1: Memory-Based Questions

Physics

Question 1: In AC series circuit supply voltage $V_{(\mathrm{rms})}=100$ volts; $R=80 \Omega ; X_L=80 \Omega$ and source frequency is $f=50 \mathrm{~Hz}$. Find the power factor 1) $1 / \sqrt{2}$ 2) $1 / 2$ 3) $\frac{3}{4}$ 4) $\sqrt{3} / 2$

Chemistry

Question 1: Consider the reactions :

Find the no. of moles of benzene formed (if the efficiency of the reaction is 60%)
$1\quad0.05$
$2 \quad 0.06$
$3 \quad 0.03$
$4 \quad 0.04$

Question 2: Match column I & II

Question 3:

Match column I & II

Maths

Question 1:

The value of $1^3-2^3+3^3-4^3+\ldots+15^3$ is equal to:

(1) 1856

(2) 1854

(3) 1786

(4) 1826

Question 2:

$\int_{-\pi / 4}^{\pi / 4} \frac{32 \cos ^4 \theta}{1+e^{\sin \theta}} d \theta$ is equal to
(1) $3 \pi+8$
$(2)3 \pi+4$
$(3)4 \pi+8$
(4) $4 \pi+4$

Question 3:

The value of $\lim _{x \rightarrow 0} \frac{x^2 \sin ^2 x}{x^2-\sin ^2 x}$ is equal to:

JEE Mains 2026 April 6 Shift 2: Memory-Based Questions

Chemistry

Question 1: Highest X - O bond order is, ( X is central atom)
$1 \quad \mathrm{~F}_2 \mathrm{O}$
$2 \quad CO$
$3 \quad \mathrm{H}_2 \mathrm{O}$
$4 \quad \mathrm{CO}_2$

Question 2: The hybridisation states of Ni in the 3 complexes $\mathrm{Ni}(\mathrm{CO})_4\left[\mathrm{Ni}\left(\mathrm{NH}_3\right)_6\right]^{2+}, \&\left[\mathrm{Ni}(\mathrm{CN})_4\right]^{2-}$ are,
$1\quad \mathrm{dsp}^2, \mathrm{sp}^3 \mathrm{~d}^2, \mathrm{sp}^3$
$2 \quad\mathrm{sp}^3, \mathrm{sp}^3 \mathrm{~d}^2, \mathrm{sp}^3$
$3 \quad\mathrm{sp}^3, \mathrm{sp}^3 \mathrm{~d}^2, \mathrm{dsp}^2$
$4 \quad \mathrm{sp}^3, \mathrm{~d}^2 \mathrm{sp}^3, \mathrm{dsp}^2$

Mathematics

Question 1:

The area (in square units) of the region $\left\{(x, y): x^2-8 x \leq y \leq-x\right\}$ is :
$(1) \quad\frac{343}{6}$
$(2) \quad \frac{241}{6}$
$(3) \quad \frac{221}{6}$
$(4)\quad \frac{323}{6}$

Question 2:

Sum of $1+\frac{1}{2}\left(1^2+2^2\right)+\frac{1}{3}\left(1^2+2^2+3^2\right)+\ldots$ up to 10 terms is
$(1)\quad \frac{313}{2}$
$(2)\quad \frac{315}{2}$
$(3)\quad313$
$(4) \quad 315$

Question 3:

$
\int_{-1}^1 \frac{x^3+|x|+1}{x^2+|x|+1} d x
$

$(1) \quad \ln 3-\frac{\pi}{3 \sqrt{3}}$
$(2 )\quad \ln 3+\frac{\pi}{3 \sqrt{3}}$
$(3) \quad\frac{\pi}{3 \sqrt{3}}$
$(4) \quad\frac{-\pi}{3 \sqrt{3}}$

Physics

Question 1: Minimum deviation for an equilateral prism is $30^{\circ}$, refractive index is
a. $\sqrt{2}$
b. $\sqrt{3 / 2}$
c. 2
d. 4

Question 2: If system given below is released from rest, then find speed of 6 kg block just before hitting ground. $\left(g=10 \mathrm{~m} / \mathrm{s}^2\right)$
a. $6.20 \mathrm{~m} / \mathrm{s}$
b. $7.74 \mathrm{~m} / \mathrm{s}$
c. $4.70 \mathrm{~m} / \mathrm{s}$
d. $5.20 \mathrm{~m} / \mathrm{s}$

JEE Mains 2026 April 8 Shift 2: Memory-Based Questions

Chemistry

Question 1:

Increasing order of bond length from the following

$1\quad \mathrm{O}_2^{+}, \mathrm{O}_2, \mathrm{O}_2^{2-}, \mathrm{O}_2^{-}$
$2\quad \mathrm{O}_2^{-}, \mathrm{O}_2^{2-}, \mathrm{O}_2^{+}, \mathrm{O}_2$
$3\quad \mathrm{O}_2^{+}, \mathrm{O}_2, \mathrm{O}_2^{-}, \mathrm{O}_2^{2-}$
$4 \quad O_2^{2-}, O_2^{-}, O_2, O_2^{+}$

Question 2:

Given $\lambda_1=3000 A$ and $\lambda_2=6000 A$ then find the ratio of $E_1$ and $E_2$

Mathematics

Question 1:
If $\alpha=3+4+8+9+13+\ldots$ upto 40 terms and $(\tan \beta)^{\frac{\alpha}{1020}}$ is the root of the equation $x^2-x-2=0$. Then, the value of $\sin ^2 \beta+3 \cos ^2 \beta$ is:
(1) $\frac{5}{3}$
(2)2
(3) 1
(4) $\frac{1}{2}$

Physics

Question 1:

A balloon is moving with speed $10 \mathrm{~m} / \mathrm{s}$ in upward direction. At height of 75 m a stone is released. Distance travelled by stone in air.
a. 70 m
b. 80 m
c. 85 m
d. 90 m

JEE Mains 2026 April Session YouTube Live Analysis

Careers360 YouTube channel also provides live updates and analysis on YouTube regarding the JEE Mains 2026 question paper. Every day, our expert will go live and give you a detailed explanation of the whole shift. The link for the live session is given below:

6 April Shift 1

6 April Shift 2

JEE Mains 2026 April Session Exam Analysis: Shiftwise

Refer to the table given below to get the analysis of the JEE Mains 2026 April question paper. In this section, students will get the analysis about the difficulty level, types of questions asked, important topics, and overall student reactions. The JEE Mains question paper 2026

helps students understand the paper and the expected difficulty level of the coming shifts and attempts.

JEE Mains 2026 April 2 Shift 1 Analysis

JEE Mains 2026 April 2 Shift 2 Analysis

JEE Mains 2026 April 4 Shift 1 Analysis

JEE Mains 2026 April 4 Shift 2 Analysis

JEE Mains 2026 April 5 Shift 1 Analysis

JEE Mains 2026 April 5 Shift 2 Analysis

JEE Mains 2026 April 6 Shift 1: Analysis

JEE Mains 2026 April 6 Shift 2: Analysis

JEE Mains 2026 April 8 Shift 2: Analysis

JEE Main 2026 January Session Question Papers

Given below the links to download JEE Mains 2026 Session 1 Question Papers. These papers help students understand the exam pattern, difficulty level, and important topics covered across different shifts.

JEE Mains Previous Years Question Paper

Students can refer to the Previous year's JEE Main question papers, including the JEE Main April question paper, to understand the exam pattern and important topics.

JEE Main January Session Exam Analysis

To get an idea about the difficulty level of the exam, types of questions asked and important topics students should refer to the JEE Main 2026 January Session analysis. Students can check the day-wise JEE Main 2026 January sessions analysis from the table given below.