JEE Main 22 January 2026 Shift 1 Question Paper

Question 1

Let $\overrightarrow{AB} = 2\hat{i} + 4\hat{j} - 5k$ and $\overrightarrow{AD} = \hat{i} + 2\hat{j} + \lambda k$, $\lambda \in \mathbb{R}$. Let the projection of the vector $\vec{v} = \hat{i} + \hat{j} + \hat{k}$ on the diagonal $\overrightarrow{AC}$ of the parallelogram ABCD be of length one unit. If α, β, where α > β, be the roots of the equation $\lambda^2 x^2 - 6\lambda x + 5 = 0$, then 2α − β is equal to

Accepted Answer

(C) 3

Answer

(A) 1

Answer

(B) 4

Answer

(D) 6

Question 2

Let the relation R on the set M = {1, 2, 3,.......16} be given by
$R = \{(x,y) : 4y = 5x - 3,\ x, y \in M\}$.
Then the minimum number of elements required to be added in R, in order to make the relation symmetric, is equal to

Accepted Answer

(B) 2

Answer

(A) 1

Answer

(C) 4

Answer

(D) 3

Question 3

Let the line x = −1 divide the area of the region $\left\{(x,y) : 1 + x^2 \le y \le 3 - x\right\}$ in the ratio m : n, gcd (m, n) = 1. Then m + n is equal to

Accepted Answer

(D) 27

Answer

(A) 25

Answer

(B) 28

Answer

(C) 26

Question 4

Two distinct numbers a and b are selected at random from 1, 2, 3,......, 50. The probability, that their product ab is divisible by 3, is

Accepted Answer

(B) $\frac{664}{1225}$

Answer

(A) $\frac{561}{1225}$

Answer

(C) $\frac{272}{1225}$

Answer

(D) $\frac{8}{25}$

Question 5

Let $f(x) = x^{2025} - x^{2000}$, $x \in [0, 1]$ and the minimum value of the function f(x) in the interval [0, 1] be $(80)^{80} (n)^{-81}$. Then n is equal to

Accepted Answer

(A) −81

Answer

(B) −40

Answer

(C) −41

Answer

(D) −80

Question 6

Let P(α, β, γ) be the point on the line $\frac{x-1}{2} = \frac{y+1}{-3} = z$ at a distance $4\sqrt{14}$ from the point (1, −1, 0) and nearer to the origin. Then the shortest distance, between the lines $\frac{x-\alpha}{1} = \frac{y-\beta}{2} = \frac{z-\gamma}{3}$ and $\frac{x+5}{2} = \frac{y-10}{1} = \frac{z-3}{1}$ , is equal to

Accepted Answer

(B) $4\sqrt{\frac{7}{5}}$

Answer

(A) $7\sqrt{\frac{5}{4}}$

Answer

(C) $4\sqrt{\frac{5}{7}}$

Answer

(D) $2\sqrt{\frac{7}{4}}$

Question 7

If a random variable x has the probability distribution
x : 0, 1, 2, 3, 4, 5, 6, 7
p(x) : 0, 2k, k, 3k, $2k^2$, 2k, $k^2 + k$, $7k^2$
then $P(3 < x \le 6)$ is equal to

Accepted Answer

(D) 0.33

Answer

(A) 0.34

Answer

(B) 0.22

Answer

(C) 0.64

Question 8

The number of distinct real solutions of the equation $x|x + 4| + 3|x + 2| + 10 = 0$ is

Accepted Answer

(B) 1

Answer

(A) 3

Answer

(C) 0

Answer

(D) 2

Question 9

Let $f : [1, \infty) \rightarrow \mathbb{R}$ be a differentiable function, If $6\int_1^x f(t)\,dt = 3xf(x) + x^3 - 4$ for all $x \ge 1$, then the value of f(2) − f(3) is

Accepted Answer

(D) 3

Answer

(A) −4

Answer

(B) −3

Answer

(C) 4

Question 10

If the line αx + 2y = 1, where α ∈ ℝ, does not meet the hyperbola $x^2 - 9y^2 = 9$, then a possible value of α is :

Accepted Answer

(B) 0.8

Answer

(A) 0.6

Answer

(C) 0.5

Answer

(D) 0.7

Question 11

If the image of the point P (1, 2 , a) in the line $\frac{x-6}{3} = \frac{y-7}{2} = \frac{7-z}{2}$ is Q(5, b, c), then $a^2 + b^2 + c^2$ is equal to

Accepted Answer

(C) 298

Answer

(A) 293

Answer

(B) 264

Answer

(D) 283

Question 12

Let the set of all values of r, for which the circles $(x + 1)^2 + (y + 4)^2 = r^2$ and $x^2 + y^2 - 4x - 2y - 4 = 0$ intersect at two distinct points be the interval (α, β). Then αβ is equal to

Accepted Answer

(A) 25

Answer

(B) 20

Answer

(C) 21

Answer

(D) 24

Question 13

If $A = \begin{bmatrix} 2 & 3 \ 3 & 5 \end{bmatrix}$, then the determinant of the matrix $(A^{2025} - 3A^{2024} + A^{2023})$ is

Accepted Answer

(D) 16

Answer

(A) 28

Answer

(B) 12

Answer

(C) 24

Question 14

The value of $\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\left(\frac{1}{[x]+4}\right)dx$, where $[\bullet]$ denotes the greatest integer function, is

Accepted Answer

(C) $\frac{7}{60}(3\pi - 1)$

Answer

(A) $\frac{1}{60}(21\pi - 1)$

Answer

(B) $\frac{1}{60}(\pi - 7)$

Answer

(D) $\frac{7}{60}(\pi - 3)$

Question 15

If the chord joining the points $P_{1}(x_{1}, y_{1})$ and $P_{2}(x_{2}, y_{2})$ on the parabola $y^{2} = 12x$ subtends a right angle at the vertex of the parabola, then $x_{1}x_{2} - y_{1}y_{2}$ is equal to

Accepted Answer

(A) 288

Answer

(B) 280

Answer

(C) 284

Answer

(D) 292

Question 16

The number of solutions of $	an^{-1} 4x + 	an^{-1}6x = \frac{\pi}{6}$, where $-\frac{1}{2\sqrt{6}} < x < \frac{1}{2\sqrt{6}}$ is equal to

Accepted Answer

(C) 1

Answer

(A) 3

Answer

(B) 0

Answer

(D) 2

Question 17

Let the solution curve of the differential equation $xdy - ydx = \sqrt{x^{2} + y^{2}}\,dx$, $x > 0$, $y(1) = 0$, be $y = y(x)$. Then $y(3)$ is equal to

Accepted Answer

(A) 4

Answer

(B) 6

Answer

(C) 1

Answer

(D) 2

Question 18

If the sum of the first four terms of an A.P. is 6 and the sum of its first six terms is 4, then the sum of its first twelve terms is

Accepted Answer

(D) –22

Answer

(A) –20

Answer

(B) –24

Answer

(C) –26

Question 19

Let $\alpha = \frac{-1+i\sqrt{3}}{2}$ and $\beta = \frac{-1-i\sqrt{3}}{2}$, $i = \sqrt{-1}$. If $(7 - 7\alpha + 9\beta)^{20} + (9 + 7\alpha - 7\beta)^{20} + (-7 + 9\alpha + 7\beta)^{20} + (14 + 7\alpha + 7\beta)^{20} = m^{10}$, then m is _________.

Accepted Answer

49

Question 20

Let A be a $3 	imes 3$ matrix such that $A + A^{T} = O$. If $A\begin{bmatrix}1\-1\0\end{bmatrix} = \begin{bmatrix}3\3\2\end{bmatrix}$, $A^{2}\begin{bmatrix}1\-1\0\end{bmatrix} = \begin{bmatrix}-3\19\-24\end{bmatrix}$ and $\det(	ext{adj}(2	ext{adj}(A + I))) = (2)^{\alpha}.(3)^{\beta}.(11)^{\gamma}$, $\alpha$, $\beta$, $\gamma$ are non-negative integers, then $\alpha + \beta + \gamma$ is equal to ______

Accepted Answer

18

Question 21

If $\int (\sin x)^{\frac{-11}{2}} (\cos x)^{\frac{-5}{2}} dx = -\frac{p_{1}}{q_{1}}(\cot x)^{\frac{9}{2}} - \frac{p_{2}}{q_{2}}(\cot x)^{\frac{5}{2}} - \frac{p_{3}}{q_{3}}(\cot x)^{\frac{1}{2}} + \frac{p_{4}}{q_{4}}(\cot x)^{\frac{-3}{2}} + C$, where $p_{i}$ and $q_{i}$ are positive integers with $\gcd(p_{i}, q_{i}) = 1$ for $i = 1, 2, 3, 4$ and C is the constant of integration, then $\frac{15p_{1}p_{2}p_{3}p_{4}}{q_{1}q_{2}q_{3}q_{4}}$ is equal to _______.

Accepted Answer

16

Question 22

If $\frac{\cos^{2} 48^{\circ} - \sin^{2} 12^{\circ}}{\sin^{2} 24^{\circ} - \sin^{2} 6^{\circ}} = \frac{\alpha + \beta\sqrt{5}}{2}$, where $\alpha$, $\beta \in \mathbb{N}$, then $\alpha + \beta$ is equal to _______.

Accepted Answer

4

Question 23

Let ABC be a triangle. Consider four points $p_{1}$, $p_{2}$, $p_{3}$, $p_{4}$ on the side AB, five points $p_{5}$, $p_{6}$, $p_{7}$, $p_{8}$, $p_{9}$ on the side BC and four points $p_{10}$, $p_{11}$, $p_{12}$, $p_{13}$ on the side AC. None of these points is a vertex of the triangle ABC. Then the total number of pentagons, that can be formed by taking all the vertices from the points $p_{1}$, $p_{2}$, .... $p_{13}$, is _________.

Accepted Answer

660

Question 24

A solid sphere of mass 5 kg and radius 10 cm is kept in contact with another solid sphere of mass 10 kg and radius 20 cm. The moment of inertia of this pair of spheres about the tangent passing through the point of contact is__________kg.m$^{2}$.

Accepted Answer

(D) 0.63

Answer

(A) 0.36

Answer

(B) 0.72

Answer

(C) 0.18

Question 25

7.9 MeV α−particle scatters from a target material of atomic number 79. From the given data the estimated diameter of nuclei of the target material is (approximately)_________m.
[$\frac{1}{4\pi \in_{o}} = 9	imes 10^{9}\,\mathrm{Nm}^{2}/\mathrm{C}^{2}$ and electron charge $=1.6	imes 10^{-19}\mathrm{C}$]

Accepted Answer

(A) $5.76 	imes 10^{-14}$

Answer

(B) $1.44 	imes 10^{-13}$

Answer

(C) $2.88 	imes 10^{-14}$

Answer

(D) $1.69 	imes 10^{-12}$

Question 26

Six point charges are kept 60° apart from each other on the circumference of a circle of radius R as shown in figure. The net electric field at the centre of the circle is _________.
($\in_{o}$ is permittivity of free space)

Accepted Answer

(B) $-\frac{Q}{4\pi \in_{o} R^{2}}\left(\sqrt{3}\,\hat{i}-\hat{j}\right)$

Answer

(A) $-\frac{5Q}{8\pi \in_{o} R^{2}}(\hat{i}+\sqrt{3}\hat{j})$

Answer

(C) $-\left(\frac{5Q}{8\pi \in_{o} R^{2}}\right)\left(\hat{i}-3\hat{j}\right)$

Answer

(D) $\frac{Q}{4\pi \in_{o} R^{2}}\left(\sqrt{3}\,\hat{i}-\hat{j}\right)$

Question 27

XPQY is a vertical smooth long loop having a total resistance R where PX is parallel to QY and separation between them is $l$. A constant magnetic field B perpendicular to the plane of the loop exists in the entire space. A rod CD of length L (L > $l$) and mass m is made to slide down from rest under the gravity as shown in figure. The terminal speed acquired by the rod is_________m/s.
(g = acceleration due to gravity)

Accepted Answer

(D) $\frac{mgR}{B^{2}l^{2}}$

Answer

(A) $\frac{2mgR}{B^{2}l^{2}}$

Answer

(B) $\frac{8mgR}{B^{2}l^{2}}$

Answer

(C) $\frac{2mgR}{B^{2}L^{2}}$

Question 28

The escape velocity from a spherical planet A is 10 km/s. The escape velocity from another planet B whose density and radius are 10% of those of planet A, is_______m/s.

Accepted Answer

(C) $100\sqrt{10}$

Answer

(A) 1000

Answer

(B) $200\sqrt{5}$

Answer

(D) $1000\sqrt{2}$

Question 29

A meter bridge with two resistances $R_{1}$ and $R_{2}$ as shown in figure was balanced (null point) at 40 cm from the point P. The null point changed to 50 cm from the point P, when 16 Ω resistance is connected in parallel to $R_{2}$. The values of resistances $R_{1}$ and $R_{2}$ are_______.

Accepted Answer

(C) $R_{2} = 8\Omega, R_{1} = \frac{16}{3}\Omega$

Answer

(A) $R_{2} = 16\Omega, R_{1} = \frac{16}{3}\Omega$

Answer

(B) $R_{2} = 4\Omega, R_{1} = \frac{4}{3}\Omega$

Answer

(D) $R_{2} = 12\Omega, R_{1} = \frac{12}{3}\Omega$

Question 30

A projectile is thrown upward at an angle 60° with the horizontal. The speed of the projectile is 20 m/s when its direction of motion is 45° with the horizontal. The initial speed of the projectile is______m/s.

Accepted Answer

(D) $20\sqrt{2}$

Answer

(A) $40\sqrt{2}$

Answer

(B) 40

Answer

(C) $20\sqrt{3}$

Question 31

Given below are two statements:
Statement I : Pressure of fluid is exerted only on a solid surface in contact as the fluid-pressure does not exist everywhere in a still fluid.
Statement II: Excess potential energy of the molecules on the surface of a liquid, when compared to interior, results in surface tension.
In the light of the above statements, choose the correct answer from the options given below.

Accepted Answer

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

Answer

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

Answer

(B) Both Statement I and Statement II are false

Answer

(C) Both Statement I and Statement II are true

Question 32

Find the correct combination of A, B, C and D inputs which can cause the LED to glow.

Accepted Answer

(D) 1101

Answer

(A) 0100

Answer

(B) 0011

Answer

(C) 1000

Question 33

Net gravitational force at the centre of a square is found to be $F_{1}$ when four particles having mass M, 2M, 3M and 4M are placed at the four corners of the square as shown in figure and it is $F_{2}$ when the positions of 3M and 4M are interchanged. The ratio $\frac{F_{1}}{F_{2}}$ is $\frac{\alpha}{\sqrt{5}}$. The value of α is _____.

Accepted Answer

(A) 2

Answer

(B) 3

Answer

(C) 1

Answer

(D) $2\sqrt{5}$

Question 34

The minimum frequency of photon required to break a particle of mass 15.348 amu into 4α particles is ____ kHz.
[mass of He nucleus = 4.002 amu,
1 amu = $1.66 	imes 10^{-27}$ kg, h = $6.6 	imes 10^{-34}$ J.s and c = $3 	imes 10^{8}$ m/s]

Accepted Answer

(D) $14.94 	imes 10^{19}$

Answer

(A) $9 	imes 10^{19}$

Answer

(B) $9 	imes 10^{20}$

Answer

(C) $14.94 	imes 10^{20}$

Question 35

A cylindrical tube $AB$ of length $l$, closed at both ends contains an ideal gas of 1 mol having molecular weight $M$. The tube is rotated in a horizontal plane with constant angular velocity $\omega$ about an axis perpendicular to $AB$ and passing through the edge at end A, as shown in the figure. If $P_{A}$ and $P_{B}$ are the pressures at $A$ and $B$ respectively, then (Consider the temperature is same at all points in the tube)

Accepted Answer

(A) $P_{B} = P_{A} \exp (M\omega^{2}l^{2} / 2RT)$

Answer

(B) $P_{B} = P_{A}$

Answer

(C) $P_{B} = P_{A} \exp (M\omega^{2}l^{2} / 3RT)$

Answer

(D) $P_{B} = P_{A} \exp (M\omega^{2}l^{2} / RT)$

Question 36

Rods x and y of equal dimensions but of different materials are joined as shown in figure. Temperatures of end points $A$ and $F$ are maintained at 100 °C and 40 °C respectively. Given the thermal conductivity of rod x is three times of that of rod y, the temperature at junction points $B$ and $E$ are (close to) :

Accepted Answer

(A) 89 °C and 73 °C respectively

Answer

(B) 80 °C and 60 °C respectively

Answer

(C) 80 °C and 70 °C respectively

Answer

(D) 60 °C and 45 °C respectively

Question 37

Consider an equilateral prism (refractive index $\sqrt{2}$). A ray of light is incident on its one surface at a certain angle $i$. If the emergent ray is found to graze along the other surface then the angle of refraction at the incident surface is close to ____.

Accepted Answer

(A) 15°

Answer

(B) 20°

Answer

(C) 40°

Answer

(D) 30°

Question 38

The volume of an ideal gas increases 8 times and temperature becomes $(1/4)^{th}$ of initial temperature during a reversible change. If there is no exchange of heat in this process (ΔQ = 0) then identify the gas from the following options (Assuming the gases given in the options are ideal gases) :

Accepted Answer

(D) He

Answer

(A) $CO_2$

Answer

(B) $O_2$

Answer

(C) $NH_3$

Question 39

Electric field in a region is given by $\vec{E} = Ax\hat{i} + By\hat{j}$, where $A$ = 10 V/m$^2$ and $B$ = 5 V/m$^2$. If the electric potential at a point (10, 20) is 500 V, then the electric potential at origin is ______ V.

Accepted Answer

Answer

(A) 1000

Answer

(B) 500

Answer

(D) 0

Question 40

A simple pendulum has a bob with mass $m$ and charge q. The pendulum string has negligible mass. When a uniform and horizontal electric field $\vec{E}$ is applied, the tension in the string changes. The final tension in the string, when pendulum attains an equilibrium position is ______.
(g : acceleration due to gravity)

Accepted Answer

(C) $\sqrt{m^2g^2 + q^2E^2}$

Answer

(A) $mg - qE$

Answer

(B) $mg + qE$

Answer

(D) $\sqrt{m^2g^2 - q^2E^2}$

Question 41

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 42

Three identical coils $C_1$, $C_2$ and $C_3$ are closely placed such that they share a common axis. $C_2$ is exactly midway. $C_1$ carries current $I$ in anti-clockwise direction while $C_3$ carries current $I$ in clockwise direction. An induced current flows through $C_2$ will be in clockwise direction when

Accepted Answer

(B) $C_1$ moves towards $C_2$ and $C_3$ moves away from $C_2$

Answer

(A) $C_1$ and $C_3$ move with equal speeds away from $C_2$

Answer

(C) $C_1$ moves away from $C_2$ and $C_3$ moves towards $C_2$

Answer

(D) $C_1$ and $C_3$ move with equal speeds towards $C_2$

Question 43

Two loudspeakers ($L_1$ and $L_2$) are placed with a separation of 10 m, as shown in figure. Both speakers are fed with an audio input signal of same frequency with constant volume. A voice recorder, initially at point $A$, at equidistance to both loud speakers, is moved by 25 m along the line $AB$ while monitoring the audio signal. The measured signal was found to undergo 10 cycles of minima and maxima during the movement. The frequency of the input signal is ______ Hz
(Speed of sound in air is 324 m/s and $\sqrt{5}$ = 2.23)

Accepted Answer

600

Question 44

The electric field of a plane electromagnetic wave, travelling in an unknown non-magnetic medium is given by,
$E_y = 20 \sin(3 	imes 10^{6}x - 4.5 	imes 10^{14}t)$ V/m
(where x, t and other values have S.I. units). The dielectric constant of the medium is ____.
(speed of light in free space is $3 	imes 10^{8}$ m/s)

Accepted Answer

4

Question 45

A parallel beam of light travelling in air (refractive index 1.0) is incident on a convex spherical glass surface of radius of curvature 50 cm. Refractive index of glass is 1.5. The rays converge to a point at a distance x cm from the centre of the curvature of the spherical surface. The value of x is ____ cm.

Accepted Answer

100

Question 46

A circular disc has radius $R_1$ and thickness $T_1$. Another circular disc made of the same material has radius $R_2$ and thickness $T_2$. If the moment of inertia of both discs are same and $\frac{R_1}{R_2} = 2$ then $\frac{T_1}{T_2} = \frac{1}{\alpha}$. The value of α is ____.

Accepted Answer

16

Question 47

Inductance of a coil with $10^4$ turns is 10 mH and it is connected to a dc source of 10 V with internal resistance of 10Ω. The energy density in the inductor when the current reaches $\left(\frac{1}{e}ight)$ of its maximum value is $\alpha\pi 	imes \frac{1}{e^2}$ J/m$^3$. The value of α is ____. ($\mu_0 = 4\pi 	imes 10^{-7}$ Tm/A).

Accepted Answer

20

Question 48

Consider the transition metal ions Mn$^{3+}$, Cr$^{3+}$, Fe$^{3+}$ and Co$^{3+}$ and all form low spin octahedral complexes. The correct decreasing order of unpaired electrons in their respective d-orbitals of the complexes is

Accepted Answer

(D) Cr$^{3+}$ > Mn$^{3+}$ > Fe$^{3+}$ > Co$^{3+}$

Answer

(A) Cr$^{3+}$ > Fe$^{3+}$ > Co$^{3+}$ > Mn$^{3+}$

Answer

(B) Mn$^{3+}$ > Fe$^{3+}$ > Co$^{3+}$ > Cr$^{3+}$

Answer

(C) Fe$^{3+}$ > Co$^{3+}$ > Mn$^{3+}$ > Cr$^{3+}$

Question 49

The formal changes on the atoms marked as (1) to (4) in the Lewis representation of HnO$_3$ molecule respectively are

Accepted Answer

(C) 0, +1, 0, –1

Answer

(A) +1, 0, 0, –1

Answer

(B) 0, –1, 0, +1

Answer

(D) 0, 0, –1, +1

Question 50

Given below are two statements :
Statement I : Phenol on treatment with CHCl$_3$/aq. KOH under refluxing condition, followed by acidification produces p-hydroxy benzladehyde as the major product and o-hydroxy benzaldehyde as the minor product.
Statement II : The mixture of p-hydroxybenzaldehyde and o-hydroxybenzaldehyde can be easily separated through steam distillation.
In the light of the above statements, choose the correct answer from the options given below :

Accepted Answer

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

Answer

(A) Both Statement I and Statement II are false

Answer

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

Answer

(C) Both Statement I and Statement II are true

Question 51

The energy required by electrons, present in the first Bohr orbit of hydrogen atom to be excited to second Bohr orbit is ________ J mol$^{-1}$.
Given : R$_H$ = 2.18 × 10$^{-11}$ ergs.

Accepted Answer

(B) 9.835 × 10$^{5}$

Answer

(A) 1.635 × 10$^{-18}$

Answer

(C) 9.835 × 10$^{12}$

Answer

(D) 1.635 × 10$^{-11}$

Question 52

A 'p'-block element (E) and hydrogen form a binary cation (EH$_x$)$^{+}$, while EH$_3$ on treatment with K$_2$HgI$_4$ in alkaline medium gives a precipitate of basic mercury(II)amido-iodine. Given below are first ionisation enthalpy values (kJ mol$^{-1}$) for first element each from group 13, 14, 15 and 16. Identify the correct first ionisation enthalpy value for element E.

Accepted Answer

(C) 1402

Answer

(A) 1312

Answer

(B) 1086

Answer

(D) 801

Question 53

In the reaction,
2Al(s) + 6HCl(aq) → 2Al$^{3+}$(aq) + 6Cl$^{-}$(aq) + 3H$_2$(g)

Accepted Answer

(A) 11.2 L H$_2$(g) at STP is produced for every mole of HCl consumed.

Answer

(B) 67.2 L H$_2$(g) at STP is produced for every mole of Al that reacts.

Answer

(C) 12 L HCl(aq) is consumed for every 6L H$_2$(g) produced.

Answer

(D) 33.6 L H$_2$(g) is produced regardless of temperature and pressure for every mole of Al that reacts.

Question 54

Consider a solution of CO$_2$(g) dissolved in water in a closed container.
Which one of the following plots correctly represents variation of log (partial pressure of CO$_2$ in vapour phase above water) [y-axis] with log (mole fraction of CO$_2$ in water) [x-axis] at 25°C ?

Accepted Answer

(C) (3)

Answer

(A) (1)

Answer

(B) (2)

Answer

(D) (4)

Question 55

A first row transition metla (M) does not liberate H$_2$ gas from dilute HCl. 1 mol of aqueous solution of MSO$_4$ is treated with excess of aqueous KCN and then H$_2$S(g) is passed through the solution. The amount of MS (metal sulphide) formed from the above reaction is _______ mol.

Accepted Answer

(D) 0

Answer

(A) 2

Answer

(B) 1

Answer

(C) 3

Question 56

The correct order of reactivity of CH$_3$Br in methanol with the following nucleophiles is
F$^{-}$, I$^{-}$, C$_2$H$_5$O$^{-}$ and C$_6$H$_5$O$^{-}$

Accepted Answer

(B) I$^{-}$ > C$_2$H$_5$O$^{-}$ > C$_6$H$_5$O$^{-}$ > F$^{-}$

Answer

(A) I$^{-}$ > C$_6$H$_5$O$^{-}$ > F$^{-}$ > C$_2$H$_5$O$^{-}$

Answer

(C) I$^{-}$ > C$_2$H$_5$O$^{-}$ > F$^{-}$ > C$_6$H$_5$O$^{-}$

Answer

(D) I$^{-}$ > F$^{-}$ > C$_6$H$_5$O$^{-}$ > C$_2$H$_5$O$^{-}$

Question 57

Match the LIST-I (Thermodynamic Process) with LIST-II (Magnitude in kJ)
Choose the correct answer from the option given below :

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 58

Given below are two statements :
Statement I : Benzene is nitrated to give nitrobenzene, which on further treatment with CH$_3$COCl / AlCl$_3$ will give
Statement II : NO$_2$ group is a m-directing, and deactivating group.
In the light of the above statements, choose the most appropriate answer from the options given below.

Accepted Answer

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

Answer

(A) Statement I is correct but Statement II is incorrect.

Answer

(B) Both Statement I and Statement II are correct.

Answer

(D) Both Statement I and Statement II is are incorrect.

Question 59

A → products (First order reaction).
Three sets of experiment were performed for a reaction under similar experimental conditions.
Run 1 ⇒ 100 mL of 10 M solution of reactant A
Run 2 ⇒ 200 mL of 10 M solution of reactant A
Run 3 ⇒ 100 mL of 10 M solution of reactant A+ 100 mL of H$_2$O added.
The correct variation of rate of reaction is

Accepted Answer

(B) Run 3 < Run 1 = Run 2

Answer

(A) Run 1 = Run 2 = Run 3

Answer

(C) Run 3 < Run 1 < Run 2

Answer

(D) Run 1 < Run 2 < Run 3

Question 60

Match the LIST-I (Reagents) with LIST-II (Name of Reaction involving carbonyl compound)
Choose the correct answer from the options given below

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 61

Given below are two statements :
Statement I : The halogen that makes longest bond with hydrogen in HX, has the smallest covalent radius in its group.
Statement II : A group 15 element's hydride EH$_3$ has the lowest boiling point among corresponding hydrides of other group 15 elements. The maximum covalency of that element E is 4.
In the light of the above statements, choose the correct answer from the options given below.

Accepted Answer

(C) Both Statement I and Statement II are false.

Answer

(A) Both Statement I and Statement II are true.

Answer

(B) Statement I is false but Statement II is true.

Answer

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

Question 62

Given below are two statements:
Statement I : Sucrose is dextrorotatory. However sucrose upon hydrolysis gives a solution having mixture of products. This solution shows laevorotation.
Statement II : Hydrolysis of sucrose gives glucose and fructose. Since the laevorotation of glucose is more than the dextrorotation of fructose the resulting solution becomes laevorotatory.
In the light of the above statements, choose the correct answer from the options given below.

Accepted Answer

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

Answer

(A) Statement I is false but Statement II is true.

Answer

(B) Both Statement I and Statement II are false.

Answer

(C) Both Statement I and Statement II are true.

Question 63

'A' is a neutral organic compound (M. F : C$_8$H$_9$ON ). On treatment with aqueous Br$_2$/HO$^{(-)}$, 'A' forms a compound 'B' which is soluble in dilute acid. 'B' on treatment with aqueous NaNO$_2$/HCl(0–5°C) produces a compound 'C' which on treatment with CuCN/NaCN produces 'D' Hydrolysis of 'D' produces 'E' which is also obtainable from the hydrolysis of 'A'. 'E' on treatment with acidified KMnO$_4$ produces 'F'. 'F' contains two different types of hydrogen atoms. The structure of 'A' is

Accepted Answer

(C) (3)

Answer

(A) (1)

Answer

(B) (2)

Answer

(D) (4)

Question 64

The correct order of the rate of reaction of the following reactants with nucleophile by S$_N$1 mechanism is :
(Given : Structure I and II are rigid)

Accepted Answer

(C) II < I< III < IV

Answer

(A) IV < III < II < I

Answer

(B) III < I < II < IV

Answer

(D) I < II < III < IV

List-I	List-II
A.Spring constant	I. $ML^2T^{-2}K^{-1}$
B.Thermal conductivity	II. $ML^0T^{-2}$
C.Boltzmann constant	III. $ML^2T^{-3}A^{-2}$
D.Inductive reactance	IV. $MLT^{-3}K^{-1}$

List-I (Thermodynamic Process)	List-II (Magnitude in kJ)
A.Work done in reversible, isothermal expansion of 2 mol of ideal gas from 2 dm $^3$ to 20 dm $^3$ at 300 K.	I.4
B.Work done in irreversible isothermal expansion of 1 mol ideal gas from 1 m $^3$ to 3 m $^3$ at 300 K against A constant pressure of 3kPa.	II.11.5
C.Change in internal energy for adiabatic expansion of a 1 mol ideal gas with change of temperature = 320 K and $\overline{C}_V = \frac{3}{2}R$ .	III.6
D.Change in enthalpy at constant pressure of 1 mole ideal gas with change of temperature = 337 K and $\overline{C}_P = \frac{5}{2}R$ .	IV.7

List-I (Reagents)	List-II (Name of Reaction involving carbonyl compound)
A.NH $_2$ – NH $_2$ , KOH	I.Tollen's Test
B.Ag(NH $_3$ ) $_2$ OH	II.Clemmensen Reduction
C.Aq. CuSO $_4$ , Sodium Potassium tartarate, KOH	III.Wolff-Kishner Reduction
D.Zn – Hg, HCl	IV.Fehling's Test

JEE Main 22 January 2026 Shift 1 Question Paper with Answers

Physics — JEE Main 22 January 2026 Shift 1

Chemistry — JEE Main 22 January 2026 Shift 1

Mathematics — JEE Main 22 January 2026 Shift 1

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