JEE Main 8 April 2026 Shift 2 Question Paper

Question 1

Consider the relation R on the set $\{-2, -1, 0, 1, 2\}$ defined by $(a, b) \in R$ if and only if $1 + ab > 0$. Then, among the statements:
I. The number of elements in R is 17
II. R is an equivalence relation

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

The number of values of $z \in \mathbb{C}$, satisfying the equations $|z - (4 + 8i)| = \sqrt{10}$ and $|z - (3 + 5i)| + |z - (5 + 11i)| = 4\sqrt{5}$, is:

Accepted Answer

(B) 2

Answer

(A) 0

Answer

(C) 1

Answer

(D) 4

Question 3

If the system of linear equations:
$x + y + z = 6$,
$x + 2y + 5z = 10$,
$2x + 3y + \lambda z = \mu$
has infinitely many solutions, then the value of $\lambda + \mu$ equals:

Accepted Answer

(C) 22

Answer

(A) 12

Answer

(B) 16

Answer

(D) 28

Question 4

Let $A = \begin{bmatrix} \alpha & 1 & 2 \ 2 & 3 & 0 \ 0 & 4 & 5 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & 0 & 0 \ 0 & -5\alpha & 0 \ 0 & 4\alpha & -2\alpha \end{bmatrix} + \mathrm{adj}(A)$. If $\det(B) = 66$, then $\det(\mathrm{adj}(A))$ equals:

Accepted Answer

(C) 441

Answer

(A) 289

Answer

(B) 361

Answer

(D) 529

Question 5

Let $\alpha = 3 + 4 + 8 + 9 + 13 + 14 + \ldots$ upto 40 terms. If $(	an \beta)^{\frac{\alpha}{1020}}$ is a root of the equation $x^2 + x - 2 = 0$, $\beta \in \left(0, \frac{\pi}{2}ight)$, then $\sin^2 \beta + 3\cos^2 \beta$ is equal to:

Accepted Answer

(A) 2

Answer

(B) $\frac{7}{4}$

Answer

(C) $\frac{5}{2}$

Answer

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

Question 6

A candidate has to go to the examination centre to appear in an examination. The candidate uses only one means of transportation for the entire distance out of bus, scooter and car. The probabilities of the candidate going by bus, scooter and car, respectively, are $\frac{2}{5}$, $\frac{1}{5}$ and $\frac{2}{5}$. The probabilities that the candidate reaches late at the examination centre are $\frac{1}{5}$, $\frac{1}{3}$ and $\frac{1}{4}$ if the candidate uses bus, scooter and car, respectively. Given that the candidate reached late at the examination centre, the probability that the candidate travelled by bus is:

Accepted Answer

(B) $\frac{12}{37}$

Answer

(A) $\frac{11}{37}$

Answer

(C) $\frac{13}{37}$

Answer

(D) $\frac{14}{37}$

Question 7

A set of four observations has mean 1 and variance 13. Another set of six observations has mean 2 and variance 1. Then, the variance of all these 10 observations is equal to:

Accepted Answer

(C) 6.04

Answer

(A) 5.96

Answer

(B) 6.14

Answer

(D) 6.24

Question 8

If $26\left(\frac{2^3}{3}\binom{12}{2} + \frac{2^5}{5}\binom{12}{4} + \frac{2^7}{7}\binom{12}{6} + \ldots + \frac{2^{13}}{13}\binom{12}{12}\right) = 3^{13} - \alpha$, then $\alpha$ is equal to:

Accepted Answer

(C) 51

Answer

(A) 45

Answer

(B) 48

Answer

(D) 54

Question 9

A person has three different bags and four different books. The number of ways, in which he can put these books in the bags so that no bag is empty, is:

Accepted Answer

(B) 36

Answer

(A) 18

Answer

(C) 39

Answer

(D) 72

Question 10

If a straight line drawn through the point of intersection of the lines $4x + 3y - 1 = 0$ and $3x + 4y - 1 = 0$, meets the co-ordinate axes at the points P and Q, then the locus of the mid point of PQ is:

Accepted Answer

(B) $x + y - 14xy = 0$

Answer

(A) $x + y - 7 = 0$

Answer

(C) $2x + y + 14xy = 0$

Answer

(D) $x + 2y - 14xy = 0$

Question 11

Let O be the vertex of the parabola $y^2 = 4x$ and its chords OP and OQ are perpendicular to each other. If the locus of the mid-point of the line segment PQ is a conic C, then the length of its latus rectum is:

Accepted Answer

(B) 2

Answer

(A) 1

Answer

(C) 4

Answer

(D) 8

Question 12

Let $\alpha = 3\sin^{-1}\left(\frac{6}{11}\right)$ and $\beta = 3\cos^{-1}\left(\frac{4}{9}\right)$, where inverse trigonometric functions take only the principal values.
Given below are two statements:
Statement I: $\cos(\alpha + \beta) > 0$.
Statement II: $\cos(\alpha) < 0$.
In the light of the above statements, choose the correct answer from the options given below:

Accepted Answer

(A) Both Statement I and Statement II are true

Answer

(B) Both Statement I and Statement II are false

Answer

(C) Statement I is true but Statement II is false

Answer

(D) Statement I is false but Statement II is true

Question 13

For the function $f(x) = e^{\sin|x|} - |x|$, $x \in \mathbb{R}$, consider the following statements:
Statement I: $f$ is differentiable for all $x \in \mathbb{R}$.
Statement II: $f$ is increasing in $\left(-\pi, -\frac{\pi}{2}\right)$.
In the light of the above statements, choose the correct answer from the options given below:

Accepted Answer

(A) Both Statement I and Statement II are true

Answer

(B) Both Statement I and Statement II are false

Answer

(C) Statement I is true but Statement II is false

Answer

(D) Statement I is false but Statement II is true

Question 14

Let $\vec{a} = 4\hat{i} - \hat{j} + 3\hat{k}$, $\vec{b} = 10\hat{i} + 2\hat{j} - \hat{k}$ and a vector $\vec{c}$ be such that $2(\vec{a} 	imes \vec{b}) + 3(\vec{b} 	imes \vec{c}) = \vec{0}$. If $\vec{a} \cdot \vec{c} = 15$, then $\vec{c} \cdot (\hat{i} + \hat{j} - 3\hat{k})$ is equal to:

Accepted Answer

(B) $-5$

Answer

(A) $-6$

Answer

(C) $-4$

Answer

(D) $-3$

Question 15

Let the foot of perpendicular from the point $(\lambda, 2, 3)$ on the line $\dfrac{x-4}{1} = \dfrac{y-9}{2} = \dfrac{z-5}{1}$ be the point $(1, \mu, 2)$. Then the distance between the lines $\dfrac{x-1}{2} = \dfrac{y-2}{3} = \dfrac{z+4}{6}$ and $\dfrac{x-\lambda}{2} = \dfrac{y-\mu}{3} = \dfrac{z+5}{6}$ is equal to:

Accepted Answer

(C) $\dfrac{\sqrt{146}}{7}$

Answer

(A) $\dfrac{12}{7}$

Answer

(B) $\dfrac{\sqrt{145}}{7}$

Answer

(D) $\dfrac{\sqrt{143}}{7}$

Question 16

The value of the integral $\displaystyle\int_{0}^{2} \dfrac{\sqrt{x(x^2+x+1)}}{(\sqrt{x+1})(\sqrt{x^4+x^2+1})}\,dx$ is equal to:

Accepted Answer

(C) $\dfrac{2}{3}\log_e(3 + 2\sqrt{2})$

Answer

(A) $\dfrac{1}{3}\log_e(3 - 2\sqrt{2})$

Answer

(B) $\dfrac{2}{3}\log_e(4 + \sqrt{2})$

Answer

(D) $\dfrac{1}{3}\log_e(1 + 6\sqrt{2})$

Question 17

Let $y = y(x)$ be the solution of the differential equation $x\sqrt{1-x^2}\,dy + \left(y\sqrt{1-x^2} - x\cos^{-1}xight)dx = 0$, $x \in (0,1)$, $\displaystyle\lim_{x 	o 1^-} y(x) = 1$. Then $y\left(\dfrac{1}{2}ight)$ equals:

Accepted Answer

(A) $3 - \dfrac{\pi}{\sqrt{3}}$

Answer

(B) $4 - \sqrt{3}\pi$

Answer

(C) $4 - \dfrac{2\pi}{\sqrt{3}}$

Answer

(D) $3 - \dfrac{\pi}{2\sqrt{3}}$

Question 18

Let $f : (1, \infty) 	o \mathbb{R}$ be a function defined as $f(x) = \dfrac{x-1}{x+1}$. Let $f^{i+1}(x) = f(f^{i}(x))$, $i = 1, 2, \ldots, 25$, where $f^{1}(x) = f(x)$. If $g(x) + f^{26}(x) = 0$, $x \in (1, \infty)$, then the area of the region bounded by the curves $y = g(x)$, $2y = 2x - 3$, $y = 0$ and $x = 4$ is:

Accepted Answer

(A) $\dfrac{1}{8} + \log_e 2$

Answer

(B) $\dfrac{1}{4} + \log_e 2$

Answer

(C) $\dfrac{5}{6} + 3\log_e 2$

Answer

(D) $\dfrac{5}{6} + \log_e 2$

Question 19

Let $f(x) = \begin{cases} \dfrac{1}{3}, & x \le \pi/2 \ \dfrac{b(1 - \sin x)}{(\pi - 2x)^2}, & x > \pi/2 \end{cases}$. If $f$ is continuous at $x = \pi/2$, then the value of $\displaystyle\int_{0}^{3b-6} |x^2 + 2x - 3|\,dx$ is:

Accepted Answer

(D) $4$

Answer

(A) $5$

Answer

(B) $2$

Answer

(C) $3$

Question 20

Let $\dfrac{x^2}{f(a^2 + 7a + 3)} + \dfrac{y^2}{f(3a + 15)} = 1$ represent an ellipse with major axis along $y$-axis, where $f$ is a strictly decreasing positive function on $\mathbb{R}$. If the set of all possible values of $a$ is $\mathbb{R} - [\alpha, \beta]$, then $\alpha^2 + \beta^2$ is equal to:

Accepted Answer

(B) $40$

Answer

(A) $28$

Answer

(C) $61$

Answer

(D) $24$

Question 21

The sum of squares of all the real solutions of the equation $\log_{(x+1)}(2x^2 + 5x + 3) = 4 - \log_{(2x+3)}(x^2 + 2x + 1)$ is equal to ________.

Accepted Answer

2

Question 22

If $\displaystyle\int_{\pi/6}^{\pi/4} \left(\cot\left(x - \dfrac{\pi}{3}\right)\cot\left(x + \dfrac{\pi}{3}\right) + 1\right)dx = \alpha \log_e(\sqrt{3} - 1)$, then $9\alpha^2$ is equal to ________.

Accepted Answer

12

Question 23

Let a line $L_1$ pass through the origin and be perpendicular to the lines $L_2 : \vec{r} = (3 + t)\hat{i} + (2t - 1)\hat{j} + (2t + 4)\hat{k}$ and $L_3 : \vec{r} = (3 + 2s)\hat{i} + (3 + 2s)\hat{j} + (2 + s)\hat{k}$, $t, s \in \mathbb{R}$. If $(a, b, c)$, $a \in \mathbb{Z}$, is the point on $L_3$ at a distance of $\sqrt{17}$ from the point of intersection of $L_1$ and $L_2$, then $(a + b + c)^2$ is equal to ________.

Accepted Answer

4

Question 24

Consider the circle $C : x^2 + y^2 - 6x - 8y - 11 = 0$. Let a variable chord AB of the circle C subtend a right angle at the origin. If the locus of the foot of the perpendicular drawn from the origin on the chord AB is the circle $x^2 + y^2 - \alpha x - \beta y - \gamma = 0$, then $\alpha + \beta + 2\gamma$ is equal to ________.

Accepted Answer

18

Question 25

Let $f$ be a polynomial function such that $\log_2(f(x)) = \left(\log_2\left(2 + \dfrac{2}{3} + \dfrac{2}{9} + \ldots \infty\right)\right) \cdot \log_3\left(1 + \dfrac{f(x)}{f(1/x)}\right)$, $x > 0$ and $f(6) = 37$. Then $\displaystyle\sum_{n=1}^{10} f(n)$ is equal to ________.

Accepted Answer

395

Question 26

A new unit $(\alpha)$ of length is chosen such that it is equal to the speed of light in vacuum. What is the distance between Venus and Earth in terms of $\alpha$ units if light takes 6 min. 40 s to cover this distance?

Accepted Answer

(B) $400\,\alpha$

Answer

(A) $200\,\alpha$

Answer

(C) $300\,\alpha$

Answer

(D) $500\,\alpha$

Question 27

Consider the equation $H = \dfrac{x^p \epsilon^q E^r}{t^s}$, where $H$ = magnetic field; $E$ = electric field, $\epsilon$ = permittivity, $x$ = distance, $t$ = time. The values of $p, q, r$ and $s$ respectively are:

Accepted Answer

(A) $1, 1, 1, 1$

Answer

(B) $-1, 1, 2, 1$

Answer

(C) $1, -1, -2, 1$

Answer

(D) $-1, -2, -2, 1$

Question 28

A car moving with a speed of 54 km/h takes a turn of radius 20 m. A simple pendulum is suspended from the ceiling of the car. Determine the angle made by the string of the pendulum with the vertical during the turning. (Take $g = 10$ m/s$^2$)

Accepted Answer

(C) $	an^{-1}(1.125)$

Answer

(A) $	an^{-1}(0.5)$

Answer

(B) $	an^{-1}(0.75)$

Answer

(D) $	an^{-1}(0.25)$

Question 29

A gas balloon is going up with a constant velocity of 10 m/s. When this balloon reached a height of 75 m, a stone is dropped from it and balloon keeps moving up with the same velocity. The height of the balloon when the stone hits the ground is ________ m. (Take $g = 10$ m/s$^2$)

Accepted Answer

(D) 125

Answer

(A) 85

Answer

(B) 150

Answer

(C) 129

Question 30

A thin biconvex lens is prepared from the glass $(\mu = 1.5)$ both curved surfaces of which have equal radii of 20 cm each. Left side surface of the lens is silvered from outside to make it reflecting. To have the position of image and object at the same place, the object should be placed, from the lens at a distance of ________ cm.

Accepted Answer

(A) 10

Answer

(B) 12.5

Answer

(C) 13

Answer

(D) 13.5

Question 31

Two identical bodies, projected with the same speed at two different angles cover the same horizontal range $R$. If the time of flight of these bodies are 5 s and 10 s, respectively, then the value of $R$ is ________ m. (Take $g = 10$ m/s$^2$)

Accepted Answer

(A) 250

Answer

(B) 25

Answer

(C) 500

Answer

(D) 125

Question 32

A solid cylinder having radius $R$ and length $L$ is slipping on a rough horizontal plane. At time $t = 0$ the cylinder has a translational velocity $v_0 = 49$ m/s, perpendicular to its axis and a rotational velocity $v_0/4R$ about the centre. The time taken by the cylinder to start rolling is ________ seconds. (coefficient of kinetic friction $\mu_K = 0.25$ and $g = 9.8$ m/s$^2$)

Accepted Answer

(B) 5

Answer

(A) 15

Answer

(C) 10

Answer

(D) 7.5

Question 33

A liquid of density 600 kg/m$^3$ flowing steadily in a tube of varying cross-section. The cross-section at a point $A$ is 1.0 cm$^2$ and that at $B$ is 20 mm$^2$. Both the points $A$ and $B$ are in same horizontal plane, the speed of the liquid at $A$ is 10 cm/s. The difference in pressures at $A$ and $B$ points is ________ Pa.

Accepted Answer

(D) 72

Answer

(A) 18

Answer

(B) 144

Answer

(C) 36

Question 34

A spherical liquid drop of radius $R$ acquires the terminal velocity $v_1$ when falls through a gas of viscosity $\eta$. Now the drop is broken into 64 identical droplets and each droplet acquires terminal velocity $v_2$ falling through the same gas. The ratio of terminal velocities $v_1/v_2$ is ________.

Accepted Answer

(D) 16

Answer

(A) 4

Answer

(B) 0.25

Answer

(C) 32

Question 35

Initial pressure and volume of a monoatomic ideal gas are $P$ and $V$. The change in internal energy of this gas in adiabatic expansion to volume $V_{final} = 27V$ is ________ J.

Accepted Answer

(C) $-\dfrac{4}{3}PV$

Answer

(A) $-2PV(3\sqrt{3}-1)$

Answer

(B) $\dfrac{4}{3}PV$

Answer

(D) $\dfrac{3}{4}PV$

Question 36

The frequency of oscillation of a mass $m$ suspended by a spring is $v_1$. If the length of the spring is cut to half, the same mass oscillates with frequency $v_2$. The value of $v_2/v_1$ is ________.

Accepted Answer

(C) $\sqrt{2}$

Answer

(A) 1

Answer

(B) 2

Answer

(D) $\sqrt{3}$

Question 37

A monochromatic source of light operating at 15 kW emits $2.5 	imes 10^{22}$ photons/s. The region of an electromagnetic spectrum to which the emitted electromagnetic radiation belongs to ________. (Take $h = 6.6 	imes 10^{-34}$ J·s and $c = 3 	imes 10^{8}$ m/s).

Accepted Answer

(D) Ultraviolet

Answer

(A) Microwave

Answer

(B) Infrared

Answer

(C) Visible

Question 38

A current carrying circular loop of radius 2 cm with unit normal $\hat{n} = \dfrac{\hat{k}+\hat{i}}{\sqrt{2}}$ is placed in a magnetic field, $\vec{B} = B_0(3\hat{i}+2\hat{k})$. If $B_0 = 4	imes 10^{-3}$ T and current $I = 100\sqrt{2}$ A, the torque experienced by the loop is ________ Wb·A. ($\pi = 3.14$)

Accepted Answer

(D) $5024	imes 10^{-7}\,\hat{j}$

Answer

(A) $16	imes 10^{-5}\,\hat{k}$

Answer

(B) $5024	imes 10^{-7}\,\hat{k}$

Answer

(C) $5024	imes 10^{-7}\,\hat{i}$

Question 39

A 30 cm long solenoid has 10 turns per cm and area of 5 cm$^2$. The current through the solenoid coil varies from 2 A to 4 A in 3.14 s. The e.m.f. induced in the coil is $\alpha 	imes 10^{-5}$ V. The value of $\alpha$ is ________.

Accepted Answer

(B) 12

Answer

(A) 60

Answer

(C) 120

Answer

(D) 34

Question 40

Two point charges $q_1 = 3\,\mu C$ and $q_2 = -4\,\mu C$ are placed at points $(2\hat{i}+3\hat{j}+3\hat{k})$ and $(\hat{i}+\hat{j}+\hat{k})$ respectively. Force on charge $q_2$ is ________ N. $\left(	ext{Take } \dfrac{1}{4\pi\epsilon_0} = 9	imes 10^{9}	ext{ SI Units}ight)$

Accepted Answer

(B) $(4\hat{i}+8\hat{j}+8\hat{k})	imes 10^{-3}$

Answer

(A) $(12\hat{i}+24\hat{j}+24\hat{k})	imes 10^{-3}$

Answer

(C) $(3\hat{i}+6\hat{j}+6\hat{k})	imes 10^{-3}$

Answer

(D) $(-4\hat{i}-8\hat{j}-8\hat{k})	imes 10^{-3}$

Question 41

Light ray incident along a vector $\vec{AO}$ ($\vec{AO} = 2\hat{i} - 3\hat{j}$) emerges out along vector $\vec{OB}$ ($\vec{OB} = C\hat{i} - 4\hat{j}$) as shown in the figure below. The value of $C$ is ________.

Accepted Answer

(A) 1.6

Answer

(B) 0.16

Answer

(C) 11.6

Answer

(D) 16

Question 42

$K_1$ and $K_2$ be the maximum kinetic energies of photoelectrons emitted from a surface of a given material for the light of wavelength $\lambda_1$ and $\lambda_2$, respectively. If $\lambda_1 = 2\lambda_2$ then the work function of material is given by:

Accepted Answer

(D) $K_2 - 2K_1$

Answer

(A) $K_2 + 2K_1$

Answer

(B) $2K_2 - K_1$

Answer

(C) $K_1 - 2K_2$

Question 43

Two radioactive substances A and B of mass numbers 200 and 212 respectively, shows spontaneous $\alpha$-decay with same $Q$ value of 1 MeV. The ratio of energies of $\alpha$-rays produced by A and B is ________.

Accepted Answer

(C) $\dfrac{2597}{2600}$

Answer

(A) $\dfrac{2548}{2650}$

Answer

(B) $\dfrac{2706}{2646}$

Answer

(D) $\dfrac{2862}{2499}$

Question 44

The output $Y$ for the given inputs $A$ and $B$ to the circuit is:

Accepted Answer

(B) (2)

Answer

(A) (1)

Answer

(C) (3)

Answer

(D) (4)

Question 45

A parallel plate capacitor is having separation between plates 0.885 mm. It has a capacitance of $1\,\mu$F when the space between the plates is filled with an insulating material of resistivity $1	imes 10^{13}$ $\Omega$m and resistance $17.7	imes 10^{14}$ $\Omega$. Relative permittivity of the insulating material is $\alpha 	imes 10^{7}$. The value of $\alpha$ is ________. (Take permittivity of free space $= 8.85	imes 10^{-12}$ F/m)

Accepted Answer

2

Question 46

Some distant star is to be observed by some telescope of diameter of objective lens $a$, at an angular resolution of $3.0	imes 10^{-7}$ radian. If the wavelength of light from the star reaching the telescope is 500 nm, the minimum diameter of the objective lens of the telescope is ________ cm. (nearest integer)

Accepted Answer

203

Question 47

A 5 mg particle carrying a charge of $5\pi 	imes 10^{-6}$ C is moving with velocity of $(3\hat{i}+2\hat{k})	imes 10^{-2}$ m/s in a region having magnetic field $\vec{B} = 0.1\hat{k}$ Wb/m$^2$. It moves a distance of $\alpha$ meter along $\hat{k}$ when it completes 5 revolutions. The value of $\alpha$ is ________.

Accepted Answer

2

Question 48

The stored charge in the capacitor in steady state of the following circuit is ________ $\mu$C.

Accepted Answer

200

Question 49

Two masses of 3.4 kg and 2.5 kg are accelerated from an initial speed of 5 m/s and 12 m/s, respectively. The distances traversed by the masses in the 5$^{	ext{th}}$ second are 104 m and 129 m, respectively. The ratio of their momenta after 10 s is $\dfrac{x}{8}$. The value of $x$ is ________.

Accepted Answer

9

Question 50

Match List-I (Mass of substance) with List-II (Number of atoms). Choose the correct answer from the options given below:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 51

Given below are two statements:
Given: Molar mass of C, H, O, Cl are 12, 1, 16 and 35.5 g mol$^{-1}$, respectively.
Statement I: In 30% (w/w) solution of methanol in CCl$_4$ (at T K), the mole fraction of CCl$_4$ is equal to 0.33.
Statement II: Mixture of methanol and CCl$_4$ shows positive deviation from Raoult's law.
In the light of the above statements, choose the correct answer from the options given below:

Accepted Answer

(A) Both Statement I and Statement II are true

Answer

(B) Both Statement I and Statement II are false

Answer

(C) Statement I is true but Statement II is false

Answer

(D) Statement I is false but Statement II is true

Question 52

Bromine trifluoride autoionizes to form $BrF_2^{\oplus}$ and $BrF_4^{\ominus}$. The shapes of the cation and anion are respectively ________, and ________.

Accepted Answer

(A) bent, square planar

Answer

(B) linear, square planar

Answer

(C) bent, see-saw

Answer

(D) linear, tetrahedral

Question 53

Consider the following reactions in which all the reactants and products are present in gaseous state
$2xy ightleftharpoons x_2 + y_2$   $K_1 = 2.5 	imes 10^5$
$xy + \frac{1}{2}z_2 ightleftharpoons xyz$   $K_2 = 5 	imes 10^{-3}$
The value of $K_3$ for the equilibrium $\frac{1}{2}x_2 + \frac{1}{2}y_2 + \frac{1}{2}z_2 ightleftharpoons xyz$ is:

Accepted Answer

(C) $1.0 	imes 10^{-5}$

Answer

(A) $2.5 	imes 10^{-3}$

Answer

(B) $2.5 	imes 10^{3}$

Answer

(D) $5 	imes 10^{-3}$

Question 54

Given at 298 K: $E^{\ominus}_{Fe^{2+}/Fe} = X$ Volt; $E^{\ominus}_{Fe^{3+}/Fe} = Y$ Volt. The $E^{\ominus}_{Fe^{3+}/Fe^{2+}}$ in Volt at 298 K is given by:

Accepted Answer

(B) $3Y - 2X$

Answer

(A) $2X - 3Y$

Answer

(C) $3Y + 2X$

Answer

(D) $Y + X$

Question 55

Given below are two statements:
$R = 8.314$ J K$^{-1}$ mol$^{-1}$ and 1 cal $= 4.2$ J
Statement I: When $E_a = 12.6$ kcal/mol, the room temperature rate constant is doubled by a $10\,^{\circ}$C increase in temperature (298 K to 308 K)
Statement II: For a first order reactions A $\rightarrow$ B,
Here $[A]_o$ is the initial concentration of A and $t_{1/2}$ is half life of reaction.
In the light of the above statements, choose the correct answer from the options given below:

Accepted Answer

(C) Statement I is true but Statement II is false

Answer

(A) Both Statement I and Statement II are true

Answer

(B) Both Statement I and Statement II are false

Answer

(D) Statement I is false but Statement II is true

Question 56

Match List-I (Electronic configuration of neutral atom, where $n = 2$) with List-II (1st Ionization Energy / kJ mol$^{-1}$). Choose the correct answer from the options given below:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 57

Find the correct statements related to group 15 hydrides.
A. Reducing nature increases from NH$_3$ to BiH$_3$
B. Tendency to donate lone pair of electrons decreases from NH$_3$ to BiH$_3$
C. The stability of hydrides decreases from NH$_3$ to BiH$_3$
D. HEH bond angle decreases from NH$_3$ to SbH$_3$ (E = Elements of group 15)
Choose the correct answer from the options given below:

Accepted Answer

(C) A, B, C and D

Answer

(A) A and B only

Answer

(B) B and C only

Answer

(D) A, C and D Only

Question 58

Given below are two statements:
Statement I: The number of pairs among $[Ti^{4+}, V^{2+}]$, $[V^{2+}, Mn^{2+}]$, $[Mn^{2+}, Fe^{3+}]$ and $[V^{2+}, Cr^{2+}]$ in which both ions are coloured is 3.
Statement II: The number of pairs among $[La^{3+}, Yb^{2+}]$, $[Lu^{3+}, Ce^{4+}]$ and $[Ac^{3+}, Lr^{3+}]$ ions in which both are diamagnetic is 3.
In the light of the above statements, choose the correct from the options given below:

Accepted Answer

(A) Both Statement I and Statement II are correct

Answer

(B) Both Statement I and Statement II are incorrect

Answer

(C) Statement I is correct but Statement II is incorrect

Answer

(D) Statement I is incorrect but Statement II is correct

Question 59

Given below are two statements for catalytic properties of transition metals.
Statement I: First row transition metals which act as catalyst utilise their 3d electrons only for formation of bonds between reactant molecules and atoms on the surface of catalyst.
Statement II: There is increase in the concentration of reactants on the surface of catalyst which strengthens the bonds in reacting molecules.
In the light of the above statements, choose the correct answer from the options given below:

Accepted Answer

(B) Both Statement I and Statement II are incorrect

Answer

(A) Both Statement I and Statement II are correct

Answer

(C) Statement I is correct but Statement II is incorrect

Answer

(D) Statement I is incorrect but Statement II is correct

Question 60

Given below are two statements:
Statement I: Vapours of the liquid with higher boiling point condense before vapours of the liquid with lower boiling points in fractional distillation.
Statement II: The vapours rising up in the fractionating column become richer in high boiling component of the mixture.
In the light of the above statements, choose the correct answer from the options given below:

Accepted Answer

(C) Statement I is true but Statement II is false

Answer

(A) Both Statement I and Statement II are true

Answer

(B) Both Statement I and Statement II are false

Answer

(D) Statement I is false but Statement II is true

Question 61

The major product of which of the following reaction is not obtained by rearrangement reaction?

Accepted Answer

(B) (2)

Answer

(A) (1)

Answer

(C) (3)

Answer

(D) (4)

Question 62

The total number of aromatic compounds/species from the following is

Accepted Answer

(B) 4

Answer

(A) 6

Answer

(C) 3

Answer

(D) 5

Question 63

n-Butane on monochlorination under photochemical condition gives an optically active compound "P". "P" on further chlorination gives dichloro compounds. The number of dichloro compounds obtained (ignore stereoisomers) is:

Accepted Answer

(B) 4

Answer

(A) 3

Answer

(C) 5

Answer

(D) 6

Question 64

Given below are two statements:
Statement I: Due to increase in van der Waals forces, the order of boiling points is $CH_3CH_2CH_2I > CH_3CH_2I > CH_3I$.
Statement II: As para-dichlorobenzene is more symmetric, its melting point is higher than ortho-dichlorobenzene, however its boiling point is lower than ortho-dichlorobenzene.
In the light of the above statements, choose the correct answer from the options given below:

Accepted Answer

(A) Both Statement I and Statement II are true

Answer

(B) Both Statement I and Statement II are false

Answer

(C) Statement I is true but Statement II is false

Answer

(D) Statement I is false but Statement II is true

List-I (Mass of substance)	List-II (Number of atoms)
A.1.8 mg water	I. $2 \times 10^{-4} \times N_A$
B.9.8 mg sulphuric acid	II. $1.5 \times 10^{-4} \times N_A$
C.1.8 mg carbon	III. $3 \times 10^{-4} \times N_A$
D.5.85 mg salt (NaCl)	IV. $7 \times 10^{-4} \times N_A$

List-I (Electronic configuration of neutral atom, where $n = 2$)	List-II (1st Ionization Energy / kJ mol$^{-1}$)
A. $ns^2$	I.2080
B. $ns^2np^1$	II.899
C. $ns^2np^3$	III.800
D. $ns^2np^6$	IV.1402

JEE Main 8 April 2026 Shift 2 Question Paper with Answers

Physics — JEE Main 8 April 2026 Shift 2

Chemistry — JEE Main 8 April 2026 Shift 2

Mathematics — JEE Main 8 April 2026 Shift 2

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