JEE Main 4 April 2026 Shift 2 Question Paper

Question 1

For the function $f : [1, \infty) 	o [1, \infty)$ defined by $f(x) = (x-1)^{4} + 1$, among the two statements:
(I) The set $S = \{x \in [1, \infty) : f(x) = f^{-1}(x)\}$ contains exactly two elements, and
(II) The set $S = \{x \in [1, \infty) : f(x) = f^{-1}(x+1)\}$ is an empty set,

Accepted Answer

(A) only (I) is TRUE

Answer

(B) only (II) is TRUE

Answer

(C) both (I) and (II) are TRUE

Answer

(D) neither (I) nor (II) is TRUE

Question 2

Let $S = \{z \in \mathbb{C} : z^{2} + 4z + 16 = 0\}$. Then $\sum_{z \in S} |z + \sqrt{3}i|^{2}$ is equal to:

Accepted Answer

(D) 38

Answer

(A) 42

Answer

(B) 23

Answer

(C) 27

Question 3

If the system of equations:
$x + y + z = 5$
$x + 2y + 3z = 9$
$x + 3y + \lambda z = \mu$
has infinitely many solutions, then the value of $\lambda + \mu$ is:

Accepted Answer

(B) 18

Answer

(A) 16

Answer

(C) 19

Answer

(D) 21

Question 4

If $\alpha = 1$ and $\beta = 1 + i\sqrt{2}$, where $i = \sqrt{-1}$ are two roots of the equation $x^{3} + ax^{2} + bx + c = 0$, $a, b, c \in \mathbb{R}$, then $\int_{-1}^{1}(x^{3} + ax^{2} + bx + c)dx$ is equal to:

Accepted Answer

(C) −8

Answer

(A) −2

Answer

(B) −4

Answer

(D) −10

Question 5

If the quadratic equation $(\lambda + 2)x^{2} - 3\lambda x + 4\lambda = 0$, $\lambda 
eq -2$, has two positive roots, then the number of possible integral values of $\lambda$ is:

Accepted Answer

(B) 2

Answer

(A) 1

Answer

(C) 3

Answer

(D) 4

Question 6

Let $A = \begin{bmatrix} 1 & 2 & 7 \ 4 & -2 & 8 \ 3 & 8 & -7 \end{bmatrix}$ and $\det(A - \alpha I) = 0$, where $\alpha$ is a real number. If the largest possible value of $\alpha$ is $p$, then the circle $(x - p)^{2} + (y - 2p)^{2} = 320$, intersects the co-ordinate axes at

Accepted Answer

(C) 3 points

Answer

(A) 1 point

Answer

(B) 2 points

Answer

(D) 4 points

Question 7

Let $\alpha = \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \ldots \infty$ and $\beta = \frac{1}{3} + \frac{1}{9} + \frac{1}{27} + \ldots \infty$. Then the value of $(0.2)^{\log_{\sqrt{5}}(\alpha)} + (0.04)^{\log_{5}(\beta)}$ is equal to:

Accepted Answer

(C) 8

Answer

(A) 4

Answer

(B) 5

Answer

(D) 25

Question 8

For 10 observations $x_{1}, x_{2}, \ldots, x_{10}$, if $\sum_{i=1}^{10}(x_{i} + 2)^{2} = 180$ and $\sum_{i=1}^{10}(x_{i} - 1)^{2} = 90$, then their standard deviation is:

Accepted Answer

(D) 3

Answer

(A) 2

Answer

(B) $\sqrt{3}$

Answer

(C) $2\sqrt{2}$

Question 9

In the expansion of $\left(9x - \frac{1}{3\sqrt{x}}\right)^{18}$, $x > 0$, if the term independent of $x$ is $(221)k$, then $k$ is equal to:

Accepted Answer

(A) 84

Answer

(B) 78

Answer

(C) 168

Answer

(D) 198

Question 10

Let $P(3\cos\alpha, 2\sin\alpha)$, $\alpha 
eq 0$, be a point on the ellipse $\frac{x^{2}}{9} + \frac{y^{2}}{4} = 1$, $Q$ be a point on the circle $x^{2} + y^{2} - 14x - 14y + 82 = 0$ and $R$ be a point on the line $x + y = 5$ such that the centroid of the triangle $PQR$ is $\left(2 + \cos\alpha, 3 + \frac{2}{3}\sin\alphaight)$. Then the sum of the ordinates of all possible points $R$ is:

Accepted Answer

(D) 8

Answer

(A) 6

Answer

(B) 2

Answer

(C) 4

Question 11

Let $H : \frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ be a hyperbola such that the distance between its foci is 6 and the distance between its directrices is $\frac{8}{3}$. If the line $x = \alpha$ intersects the hyperbola $H$ at the points $A$ and $B$ such that the area of the triangle $AOB$ is $4\sqrt{15}$, where $O$ is the origin, then $\alpha^{2}$ equals

Accepted Answer

(B) 16

Answer

(A) 12

Answer

(C) 24

Answer

(D) 25

Question 12

$\max_{0 \leq x \leq \pi}\left(16\sin\left(\frac{x}{2}\right)\cos^{3}\left(\frac{x}{2}\right)\right)$ is equal to:

Accepted Answer

(B) $3\sqrt{3}$

Answer

(A) $\frac{3\sqrt{3}}{2}$

Answer

(C) $4\sqrt{3}$

Answer

(D) $6\sqrt{3}$

Question 13

The shortest distance between the lines $\vec{r} = \left(\frac{1}{3}\hat{i} + 2\hat{j} + \frac{8}{3}\hat{k}\right) + \lambda(2\hat{i} - 5\hat{j} + 6\hat{k})$ and $\vec{r} = \left(-\frac{2}{3}\hat{i} - \frac{1}{3}\hat{k}\right) + \mu(\hat{j} - \hat{k})$, $\lambda, \mu \in \mathbb{R}$, is:

Accepted Answer

(B) 3

Answer

(A) $\sqrt{5}$

Answer

(C) $2\sqrt{3}$

Answer

(D) $\sqrt{15}$

Question 14

If $\left(2\alpha + 1, \alpha^{2} - 3\alpha, \frac{\alpha - 1}{2}\right)$ is the image of $(\alpha, 2\alpha, 1)$ in the line $\frac{x - 2}{3} = \frac{y - 1}{2} = \frac{z}{1}$, then the possible value(s) of α is (are)

Accepted Answer

(A) Only 3

Answer

(B) Only 3 and −1

Answer

(C) Only 3, $\frac{1}{4}$ and −1

Answer

(D) Only 3 and $\frac{1}{4}$

Question 15

Let $\hat{u}$ and $\hat{v}$ be unit vectors inclined at an acute angle such that $|\hat{u} 	imes \hat{v}| = \frac{\sqrt{3}}{2}$. If $\vec{A} = \lambda\hat{u} + \hat{v} + (\hat{u} 	imes \hat{v})$, then λ is equal to:

Accepted Answer

(A) $\frac{4}{3}(\vec{A} \cdot \hat{u}) - \frac{2}{3}(\vec{A} \cdot \hat{v})$

Answer

(B) $\frac{2}{3}(\vec{A} \cdot \hat{u}) - \frac{1}{3}(\vec{A} \cdot \hat{v})$

Answer

(C) $\frac{4}{3}(\vec{A} \cdot \hat{u}) + \frac{2}{3}(\vec{A} \cdot \hat{v})$

Answer

(D) $(\vec{A} \cdot \hat{u}) - \frac{1}{2}(\vec{A} \cdot \hat{v})$

Question 16

Let for some α ∈ $\mathbb{R}$, $f : \mathbb{R} 	o \mathbb{R}$ be a function satisfying $f(x + y) = f(x) + 2y^{2} + y + \alpha xy$ for all $x, y \in \mathbb{R}$. If $f(0) = -1$ and $f(1) = 2$, then the value of $\sum_{n=1}^{5}(\alpha + f(n))$ is:

Accepted Answer

(B) 140

Answer

(A) 110

Answer

(C) 150

Answer

(D) 170

Question 17

Let $A = \{(a, b, c) : a, b, c 	ext{ are non-negative integers and } a + b + 2c = 22\}$. Then $n(A)$ is equal to:

Accepted Answer

(C) 144

Answer

(A) 121

Answer

(B) 124

Answer

(D) 169

Question 18

The area of the region bounded by the curves $x + 3y^{2} = 0$ and $x + 4y^{2} = 1$ is equal to:

Accepted Answer

(C) $\frac{4}{3}$

Answer

(A) $\frac{1}{3}$

Answer

(B) $\frac{2}{3}$

Answer

(D) $\frac{5}{3}$

Question 19

Let $y = y(x)$ be the solution of the differential equation: $\frac{dy}{dx} + \left(\frac{6x^{2} + (3x^{2} + 2x^{3} + 4)e^{-2x}}{(x^{3} + 2)(2 + e^{-2x})}\right)y = 2 + e^{-2x}$, $x \in (-1, 2)$, satisfying $y(0) = \frac{3}{2}$. If $y(1) = \alpha(2 + e^{-2})$, then α is equal to:

Accepted Answer

(D) $\frac{13}{12}$

Answer

(A) $\frac{13}{8}$

Answer

(B) $\frac{6}{13}$

Answer

(C) $\frac{12}{13}$

Question 20

The integral $\int_{0}^{1}\cot^{-1}(1 + x + x^{2})dx$ is equal to:

Accepted Answer

(D) $2	an^{-1}2 - \frac{1}{2}\log_{e}\left(\frac{5}{4}ight) - \frac{\pi}{2}$

Answer

(A) $2	an^{-1}2 + \frac{1}{2}\log_{e}\left(\frac{5}{4}ight) + \frac{\pi}{2}$

Answer

(B) $2	an^{-1}2 + \frac{1}{2}\log_{e}\left(\frac{5}{4}ight) - \frac{\pi}{2}$

Answer

(C) $2	an^{-1}2 - \frac{1}{2}\log_{e}\left(\frac{5}{4}ight) + \frac{\pi}{2}$

Question 21

From a month of 31 days, 3 different dates are selected at random. If the probability that these dates are in an increasing A.P. is equal to $\frac{a}{b}$, where $a, b \in \mathbb{N}$ and $\gcd(a, b) = 1$, then $a + b$ is equal to ______

Accepted Answer

944

Question 22

Let $f(x) = \begin{cases} e^{x-1}, & x < 0 \ x^{2} - 5x + 6, & x \geq 0 \end{cases}$ and $g(x) = f(|x|) + |f(x)|$. If the number of points where $g$ is not continuous and is not differentiable are α and β respectively, then $\alpha + \beta$ is equal to ______

Accepted Answer

4

Question 23

Let $A, B$ be points on the two half-lines $x - \sqrt{3}|y| = \alpha$, $\alpha > 0$ at a distance of α from their point of intersection $P$. The line segment $AB$ meets the angle bisector of the given half-lines at the point $Q$. If $PQ = \frac{9}{2}$ and $R$ is the radius of the circumcircle of $	riangle PAB$, then $\frac{\alpha^{2}}{R}$ is equal to ______

Accepted Answer

9

Question 24

Let $A, B$ and $C$ be the vertices of a variable right angled triangle inscribed in the parabola $y^{2} = 16x$. Let the vertex $B$ containing the right angle be $(4, 8)$ and the locus of the centroid of $	riangle ABC$ be a conic $C_{o}$. Then three times the length of latus rectum of $C_{o}$ is ______

Accepted Answer

16

Question 25

Let $f$ be a twice differentiable function such that $f(x) = \int_{0}^{x}	an(t - x)dt - \int_{0}^{x}f(t)	an t\,dt$, $x \in \left(-\frac{\pi}{2}, \frac{\pi}{2}ight)$. Then $f''\left(\frac{\pi}{6}ight) + 12f'\left(-\frac{\pi}{6}ight) + f\left(\frac{\pi}{6}ight)$ is equal to ______

Accepted Answer

5

Question 26

Match the LIST-I with LIST-II. Choose the correct answer from the options given below:

Accepted Answer

(A) A-III, B-IV, C-I, D-II

Answer

(B) A-I, B-II, C-III, D-IV

Answer

(C) A-IV, B-III, C-I, D-II

Answer

(D) A-I, B-IV, C-III, D-II

Question 27

Two cars $A$ and $B$ are moving in the same direction along a straight line with speeds 100 km/h and 80 km/h, respectively such that car $A$ is moving ahead of car $B$. A person in car $B$ throws a stone with a speed $v$ so that it hits the car $A$ with a speed of 5 m/s. The value of $v$ is ______ km/h.

Accepted Answer

(C) 38

Answer

(A) 18

Answer

(B) 28

Answer

(D) 48

Question 28

At $t = 0$, a body of mass 100 g starts moving under the influence of a force $(5\hat{i} + 10\hat{j})$ N. After 2 s its position is $(2x\hat{i} + 5y\hat{j})$ m. The ratio $x : y$ is ______.

Accepted Answer

(D) 5 : 4

Answer

(A) 1 : 2

Answer

(B) 2 : 5

Answer

(C) 5 : 2

Question 29

If $x$ and $y$ coordinates of a projectile as a function of time $(t)$ are given as $24t$ and $43.6t - 4.9t^{2}$, respectively, then the angle (in degrees) made by the projectile with horizontal when $t = 2$ s is ______.

Accepted Answer

(B) 45

Answer

(A) 60

Answer

(C) 30

Answer

(D) 75

Question 30

The height in terms of radius of the earth $(R)$, at which the acceleration due to gravity becomes $\frac{g}{9}$, where $g$ is acceleration due to gravity on earth's surface, is ______.

Accepted Answer

(C) $2R$

Answer

(A) $\sqrt{3}R$

Answer

(B) $2\sqrt{2}R$

Answer

(D) $\frac{4}{9}R$

Question 31

A metal string $A$ is suspended from a rigid support and its free end is attached to a block of mass $M$. Second block having mass $2M$ is suspended at the bottom of the first block using a string $B$. The area of cross sections of strings $A$ and $B$ are same. The ratio of lengths of strings of $A$ to $B$ is 2 and the ratio of their Young's moduli $(Y_{A}/Y_{B})$ is 0.5. The ratio of elongations in $A$ to $B$ is ______.

Accepted Answer

(D) 6

Answer

(A) 1

Answer

(B) 4

Answer

(C) 8

Question 32

A water spray gun is attached to a hose of cross sectional area 30 cm$^{2}$. The gun comprises of 10 perforations each of cross sectional area 15 mm$^{2}$. If the water flows in the hose with the speed of 50 cm/s, calculate the speed at which the water flows out from each perforation. (Neglect any edge effects)

Accepted Answer

(B) 10 m/s

Answer

(A) 100 m/s

Answer

(C) 1000 m/s

Answer

(D) $15 	imes 10^{2}$ m/s

Question 33

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: If the average kinetic energy of $H_{2}$ and $O_{2}$ molecules, kept in two different sized containers are same, then their temperatures will be same.
Reason R: The r.m.s. speed of $H_{2}$ and $O_{2}$ molecules are same at same temperature.
Choose the correct answer from the options given below

Accepted Answer

(C) A is true but R is false

Answer

(A) Both A and R are true and R is the correct explanation of A

Answer

(B) Both A and R are true but R is NOT the correct explanation of A

Answer

(D) A is false but R is true

Question 34

The temperature of a metal strip having coefficient of linear expansion $\alpha$ is increased from $T_{1}$ to $T_{2}$ resulting in increase of its length by $\Delta L_{1}$. The temperature is further increased from $T_{2}$ to $T_{3}$ such that the increase in its length is $\Delta L_{2}$. Given $T_{3} + T_{1} = 2T_{2}$ and $T_{2} - T_{1} = \Delta T$, the value of $\Delta L_{2}$ is ______.

Accepted Answer

(D) $\Delta L_{1}[1 + \alpha\Delta T]$

Answer

(A) $\Delta L_{1}[1 + 2\alpha^{2}(\Delta T)^{2}]$

Answer

(B) $\Delta L_{1}[1 + \alpha^{2}(\Delta T)^{2}]$

Answer

(C) $\Delta L_{1}[1 + 2\alpha\Delta T]$

Question 35

A uniform disc of radius $R$ and mass $M$ is free to oscillate about the axis $A$ as shown in the figure. For small oscillations the time period is ______.
($g$ is acceleration due to gravity)

Accepted Answer

(A) $2\pi\sqrt{\frac{5R}{4g}}$

Answer

(B) $2\pi\sqrt{\frac{2R}{3g}}$

Answer

(C) $2\pi\sqrt{\frac{3R}{2g}}$

Answer

(D) $2\pi\sqrt{\frac{3R}{g}}$

Question 36

A rigid dipole undergoes a simple harmonic motion about its centre in the presence of an electric field $\vec{E}_{1} = E_{0}\hat{x}$. If another electric field $\vec{E}_{2} = 2E_{0}(\hat{y} + \hat{z})$ is introduced to the system, what will be the percentage change in the frequency of the oscillation (approximate)?

Accepted Answer

(A) 73%

Answer

(B) 63%

Answer

(C) 83%

Answer

(D) 53%

Question 37

From the circuit given below, the capacitance between terminals $A$ and $B$ shown in the circuit is ______ μF.
(take $C_{1} = C_{2} = C_{3} = 1$ μF and $C_{4} = 2$ μF.)

Accepted Answer

(A) 2

Answer

(B) 7/2

Answer

(C) 7/3

Answer

(D) 5/2

Question 38

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: In electrostatics, a conductor does not store any net charge inside.
Reason R: Inside the capacitor (with no dielectric medium), the free charge carriers, if placed between the plates of capacitor, experience force and drift.
Choose the correct answer from the options given below

Accepted Answer

(B) Both A and R are true but R is NOT the correct explanation of A

Answer

(A) Both A and R are true and R is the correct explanation of A

Answer

(C) A is true but R is false

Answer

(D) A is false but R is true

Question 39

A solenoid has a core made of material with relative permeability 400. The magnetic field produced in the interior of solenoid is 1.0 T. The magnetic intensity in SI units is α × $10^{5}$. The value of α is ______.
(Free space permeability $\mu_{0} = 4\pi 	imes 10^{-7}$ SI units.)

Accepted Answer

(B) $\frac{1}{16\pi}$

Answer

(A) $\frac{25}{\pi}$

Answer

(C) $\frac{1}{\pi}$

Answer

(D) $\frac{1}{4\pi}$

Question 40

A magnetic field vector in an electromagnetic wave is represented by $\vec{B} = B_{0}\sin\left(2\pi vt - \frac{2\pi x}{\lambda}\right)\hat{j}$. Its associated electric field vector is ______.

Accepted Answer

(A) $\vec{E} = -v\lambda B_{0}\sin\left(2\pi vt - \frac{2\pi x}{\lambda}\right)\hat{k}$

Answer

(B) $\vec{E} = -v\lambda B_{0}\sin\left(2\pi vt - \frac{2\pi x}{\lambda}\right)\hat{i}$

Answer

(C) $\vec{E} = v\lambda B_{0}\sin\left(2\pi vt - \frac{2\pi x}{\lambda}\right)\hat{k}$

Answer

(D) $\vec{E} = v\lambda B_{0}\sin\left(2\pi vt - \frac{2\pi x}{\lambda}\right)\hat{i}$

Question 41

A convex lens is made from glass material having refractive index of 1.4 with same radius of curvature on both sides. The ratio of its focal length and radius of curvature is ______.

Accepted Answer

(D) 1.25

Answer

(A) 0.5

Answer

(B) 2.5

Answer

(C) 0.8

Question 42

An unpolarized light of certain intensity passes through a combination of two polarizers whose transmission axes are at 30° and 90°, respectively, with respect to the horizontal axis. A third polarizer with its transmission axis at 60° with the horizontal axis is placed between the two existing polarizers. The ratio of the output intensities with and without the third polarizer is ______.

Accepted Answer

(C) 9/4

Answer

(A) 3/4

Answer

(B) 4/3

Answer

(D) 4/9

Question 43

In Rutherford's alpha-particle scattering experiment, only a few alpha particles rebound back because
A. The size of gold nucleus is very small as compared to the size of gold atom.
B. Alpha particle and gold nucleus have equal charge.
C. The impact parameter is minimum for a few alpha particles.
D. A few alpha particles have very high kinetic energy.
E. Only a few alpha particles undergo head-on collision with the nuclei.
Choose the correct answer from the options given below:

Accepted Answer

(D) A, C, E Only

Answer

(A) A, B Only

Answer

(B) B, E Only

Answer

(C) C, D Only

Question 44

The de Broglie wavelength associated with an electron accelerated through a potential difference V is $\lambda_{e}$ and the de Broglie wavelength associated with a proton accelerated through the same potential difference is $\lambda_{p}$. If their corresponding masses are $m_{e}$ and $m_{p}$, respectively, then the ratio of their de Broglie wavelengths $\left(\frac{\lambda_{e}}{\lambda_{p}}\right)$ is ______.

Accepted Answer

(A) $\sqrt{\frac{m_{p}}{m_{e}}}$

Answer

(B) $\sqrt{\frac{m_{e}}{m_{p}}}$

Answer

(C) $\frac{m_{p}}{m_{e}}$

Answer

(D) $\left(\frac{m_{p}}{m_{e}}\right)^{2}$

Question 45

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: A diode under reverse-biased condition provides very small current which is nearly independent of voltage until a critical limit at which the current increases drastically.
Reason R: Below the critical voltage limit, only majority charge carriers flow which increases drastically above critical voltage.
Choose the correct answer from the options given below

Accepted Answer

(C) A is true but R is false

Answer

(A) Both A and R are true and R is the correct explanation of A

Answer

(B) Both A and R are true but R is NOT the correct explanation of A

Answer

(D) A is false but R is true

Question 46

A diode has Zener voltage of 10 V and maximum power dissipation of 0.5 W, then the minimum resistance to be used in series with this diode for safety when it is connected to a 25 V power supply is ______ Ω.

Accepted Answer

300

Question 47

A gun mounted on the ground fires bullets in all directions with same speed. The farthest distance the bullets could reach is 6.4 m. The speed of the bullets from the gun is ______ m/s.
(take $g = 10$ m/$s^{2}$)

Accepted Answer

8

Question 48

Two identical small bar magnets each of dipole moment $3\sqrt{5}$ J/T are placed at a center to center separation of 10 cm, with their axes perpendicular to each other as shown in figure. The value of magnetic field at the point P midway between the magnets is α × $10^{-3}$ T. The value of α is ______.
($\mu_{0} = 4\pi 	imes 10^{-7}$ Tm/A)

Accepted Answer

12

Question 49

A circular coil of radius 2 cm and 125 turns carries a current of 1 A. The coil is placed in a uniform magnetic field of magnitude 0.4 T. The axis of the coil makes an angle of 30° with the direction of the magnetic field. The torque acting on the coil is α × $10^{-4}$ N.m. The value of α is ______.
($\pi = 3.14$)

Accepted Answer

314

Question 50

In a double slit experiment, when one of the slits is covered by a transparent mica sheet of refractive index 1.56, the central fringe shifts to the position of $7^{th}$ bright fringe, obtained with both slits uncovered. If the light source wavelength is 450 nm, the thickness of mica sheet is α × $10^{-9}$ m. The value of α is ______.

Accepted Answer

5625

Question 51

The correct order of total number of atoms present in
(A) 2 moles of cyclohexane
(B) 684 g of sucrose
(C) 90.8 L of dihydrogen at STP
is:

Accepted Answer

(D) $B > A > C$

Answer

(A) $C > A > B$

Answer

(B) $C > B > A$

Answer

(C) $B > C > A$

Question 52

The species having identical radii according to the Bohr's theory are:
A. $H$ (first orbit)
B. $He^{+}$ (first orbit)
C. $He^{+}$ (Second orbit)
D. $Li^{2+}$ (first orbit)
E. $Be^{3+}$ (Second orbit)
Choose the correct answer from the options given below:

Accepted Answer

(B) A and E Only

Answer

(A) A and C Only

Answer

(C) B and E Only

Answer

(D) C and D Only

Question 53

Which of the following pictorial diagram most correctly represents the π* (π-antibonding) molecular orbital between two atoms if the internuclear axis is taken to be in the z-direction ($\xrightarrow{	ext{z-axis}}$)?

Accepted Answer

(C) (3)

Answer

(A) (1)

Answer

(B) (2)

Answer

(D) (4)

Question 54

At 27°C, 0.1 M, 1 L $\mathrm{K_{4}[Fe(CN)_{6}]}$ aqueous solution and 0.1 M, 1 L $\mathrm{FeCl_{3}}$ aqueous solution are placed in a container separated by a semi permeable membrane AB. Assume complete dissociation of both the solutes. Which of the following statement is correct?

Accepted Answer

(C) Solution on side 'y' is hypotonic.

Answer

(A) Blue color is formed on both sides.

Answer

(B) Ionic solutes in aqueous solution can pass through semi-permeable membrane.

Answer

(D) To cause the reverse flow of solvent during osmosis, external pressure (any value) should be applied to side 'x'.

Question 55

20 mL of a solution of acetic acid required 28.4 mL of 0.1 M NaOH for its neutralization. A solution (X) was prepared by mixing 20 mL of the above acetic acid and 14.2 mL of 0.1 M NaOH solution. What is the pH of the solution (X)? ($pK_{a}$ value of acetic acid is 4.75).

Accepted Answer

(B) 4.75

Answer

(A) 7.0

Answer

(C) 3.5

Answer

(D) 4.82

Question 56

Match the LIST-I (Reaction) with LIST-II (Mechanism). Choose the correct answer from the options given below:

Accepted Answer

(C) A-III, B-IV, C-I, D-II

Answer

(A) A-III, B-I, C-II, D-IV

Answer

(B) A-III, B-IV, C-II, D-I

Answer

(D) A-I, B-III, C-IV, D-II

Question 57

The $1^{st}$ ionization enthalpy for Mg is +737 kJ/mol. The most probable estimated value of the $2^{nd}$ ionization enthalpy of Mg is ______.

Accepted Answer

(C) +1450 kJ/mol

Answer

(A) −906 kJ/mol

Answer

(B) −856 kJ/mol

Answer

(D) +590 kJ/mol

Question 58

The electronegativity of a group 13 element 'E' is same as that of Ge (on Pauling scale and upto one decimal point). The CORRECT statements about $E^{3+}$ are
A. It can act as a reducing agent.
B. It can act as an oxidizing agent.
C. $E^{3+}$ is more stable than $E^{+}$.
D. The standard electrode potential value for $E^{3+}/E$ is positive.
Choose the correct answer from the options given below:

Accepted Answer

(C) B and D Only

Answer

(A) A and C Only

Answer

(B) B and C Only

Answer

(D) A and D Only

Question 59

Pairs of elements with the same number of electrons in their respective 4f orbital are
[Atomic number. Eu-63, Gd-64, Dy-66, Ho-67, Tm-69, Yb-70, Lu-71, Hf-72]
A. (Eu and Gd)
B. (Dy and Ho)
C. (Yb and Hf)
D. (Lu and Tm)
Choose the correct answer from the options given below:

Accepted Answer

(D) A and C Only

Answer

(A) B and C Only

Answer

(B) A and B Only

Answer

(C) A and D Only

Question 60

Consider the metal complexes $[Ni(en)_{3}]^{2+}$ (A), $[NiCl_{4}]^{2-}$ (B) and $[Ni(NH_{3})_{6}]^{2+}$ (C). Choose the CORRECT option by considering the number of unpaired electrons present in (A), (B) and (C) respectively and the order of frequency of absorption.

Accepted Answer

(A) $2, 2, 2$ and $(A) > (C) > (B)$

Answer

(B) $0, 2, 0$ and $(A) > (C) > (B)$

Answer

(C) $2, 2, 0$ and $(B) > (C) > (A)$

Answer

(D) $2, 2, 2$ and $(C) > (A) > (B)$

Question 61

Consider the following molecules/species:
$(x)$ tropone, $(y)$ acetone, $(z)$ acetate ion
The correct order of carbon – oxygen double bond length is:

Accepted Answer

(C) $z > x > y$

Answer

(A) $x > y > z$

Answer

(B) $y > z > x$

Answer

(D) $x > z > y$

Question 62

Consider $|x|$ is the difference in oxidation states of Mn in highest manganese fluoride and highest manganese oxide. The ions with $|x|$ number of unpaired electrons from the following are:
A. $Sc^{3+}$
B. $Zn^{2+}$
C. $V^{2+}$
D. $Fe^{2+}$
E. $Co^{2+}$
Choose the correct answer from the options given below:

Accepted Answer

(C) C and E Only

Answer

(A) A and B Only

Answer

(B) C, D and E Only

Answer

(D) B and E Only

Question 63

Consider the given graph showing variation of reactant concentration with time.
Three different reactions were started with identical initial concentration of reactants. Which of the following statement is correct?

Accepted Answer

(B) The rate constant of reaction 3 is larger than the rate constant of reaction 2 if the order of reaction is same for both.

Answer

(A) The order of all the three reactions is same.

Answer

(C) The SI unit of rate constant of reaction 1 is $\mathrm{s^{-1}}$.

Answer

(D) Thermal decomposition of HI on gold surface is an example of reaction 2.

Question 64

Compound (X) [styrene] is subjected to the sequence of reactions as shown above: (i) $\mathrm{Br_{2}/CHCl_{3}}$ (ii) $\mathrm{NaNH_{2}}$ excess (iii) $\mathrm{CH_{3}I}$ (iv) $\mathrm{H_{2}}$, $\mathrm{Na/NH_{3}}$ (l), giving Major Product (Y). Molar mass of the major product (Y) formed is ______ g mol$^{-1}$.
(Given molar mass in g mol$^{-1}$ C:12, H: 1, O: 16)

Accepted Answer

(B) 118

Answer

(A) 90

Answer

(C) 160

Answer

(D) 125

List-I	List-II
A.Planck's constant	I. $ML^{2}T^{-2}$
B.Stopping potential	II. $T^{-1}$
C.Work function	III. $ML^{2}T^{-1}$
D.Threshold frequency	IV. $ML^{2}T^{-3}A^{-1}$

List-I (Reaction)	List-II (Mechanism)
A.Williamson Synthesis	I.Electrophilic addition
B.Friedel Craft Reaction	II.Free radical substitution
C.Bromination of vinyl benzene	III.Nucleophilic substitution
D.Chlorination of toluene in light	IV.Electrophilic substitution

List-I (Compound)	List-II (Test)
A.Cyclohexanol	I.Hinsberg's reagent test
B.Cyclohexylamine	II.Phthalein dye test
C.Cyclohexanecarbaldehyde	III.Lucas test
D.Phenol	IV.Tollen's test

$t$ /min	$[A]$ /M
0	0.6500
$x$	0.0650
20	0.00065

JEE Main 4 April 2026 Shift 2 Question Paper with Answers

Physics — JEE Main 4 April 2026 Shift 2

Chemistry — JEE Main 4 April 2026 Shift 2

Mathematics — JEE Main 4 April 2026 Shift 2

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