JEE Main 28 January 2026 Shift 2 Question Paper

Question 1

Given below two statements :
Statement I : $25^{13} + 20^{13} + 8^{13} + 3^{13}$ is divisible by 7.
Statement II : The integral part of $\left(7+4\sqrt{3}\right)^{25}$ is an odd number.
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 true.

Answer

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

Answer

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

Answer

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

Question 2

The sum of the coefficients of $x^{499}$ and $x^{500}$ in $(1 + x)^{1000} + x(1 + x)^{999} + x^{2}(1 + x)^{998} + \ldots\ldots + x^{1000}$ is

Accepted Answer

(B) $^{1002}C_{500}$

Answer

(A) $^{1001}C_{501}$

Answer

(C) $^{1002}C_{501}$

Answer

(D) $^{1000}C_{501}$

Question 3

Let A be the focus of the parabola $y^{2} = 8x$. Let the line $y = mx + c$ intersect the parabola at two distinct points B and C. If the centroid of the triangle ABC is $\left(\dfrac{7}{3}, \dfrac{4}{3}\right)$, then $(BC)^{2}$ is equal to :

Accepted Answer

(B) 80

Answer

(A) 41

Answer

(C) 89

Answer

(D) 32

Question 4

The probability distribution of a random variable X is given below :
$\begin{array}{|c|c|c|c|c|c|c|c|c|} \hline X & 4k & \frac{30}{7}k & \frac{32}{7}k & \frac{34}{7}k & \frac{36}{7}k & \frac{38}{7}k & \frac{40}{7}k & 6k \ \hline P(X) & \frac{2}{15} & \frac{1}{15} & \frac{2}{15} & \frac{1}{5} & \frac{1}{15} & \frac{2}{15} & \frac{1}{5} & \frac{1}{15} \ \hline \end{array}$
If $E(X) = \dfrac{263}{15}$, then $P(X < 20)$ is equal to :

Accepted Answer

(C) $\dfrac{11}{15}$

Answer

(A) $\dfrac{3}{5}$

Answer

(B) $\dfrac{8}{15}$

Answer

(D) $\dfrac{14}{15}$

Question 5

Let $f(x) = \lim\limits_{	heta 	o 0}\left(\dfrac{\cos \pi x - x^{\left(\frac{2}{	heta}ight)}\sin(x-1)}{1 + x^{\left(\frac{2}{	heta}ight)}(x-1)}ight), x \in R$.
Consider the following two statements :
(I) f(x) is discontinous at x = 1.
(II) f(x) is continous at x = - 1.
Then,

Accepted Answer

(A) Neither (I) nor (II) is True

Answer

(B) Both (I) and (II) are True

Answer

(C) Only (II) is True

Answer

(D) Only (I) is True

Question 6

Considering the principal values of inverse trigonometric functions, the value of the expression $	an\left(2\sin^{-1}\left(\dfrac{2}{\sqrt{13}}ight) - 2\cos^{-1}\left(\dfrac{3}{\sqrt{10}}ight)ight)$ is equal to :

Accepted Answer

(B) $\dfrac{33}{56}$

Answer

(A) $-\dfrac{33}{56}$

Answer

(C) $\dfrac{16}{63}$

Answer

(D) $-\dfrac{16}{63}$

Question 7

Let the arithmetic mean of $\dfrac{1}{a}$ and $\dfrac{1}{b}$ be $\dfrac{5}{16}$, a > 2.
If α is such that a, 4, α, b are in A.P., then the equation $\alpha x^{2} - ax + 2(\alpha - 2b) = 0$ has :

Accepted Answer

(A) One root in (1,4) and another in (–2,0)

Answer

(B) One root in (0,2) and another in (– 4, –2)

Answer

(C) Complex roots of magnitude less than 2

Answer

(D) Both roots in the interval (–2, 0)

Question 8

Given below are two statements :
Statement I : The function f : R → R defined by $f(x) = \dfrac{x}{1+|x|}$ is one-one.
Statement II : The function f : R → R defined by $f(x) = \dfrac{x^{2}+4x-30}{x^{2}-8x+18}$ is many-one.
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 true.

Answer

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

Answer

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

Answer

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

Question 9

An ellipse has its center at (1,-2), one focus at (3,-2) and one vertex at (5, - 2). Then the length of its latus rectum is :

Accepted Answer

(B) 6

Answer

(A) $\dfrac{16}{\sqrt{3}}$

Answer

(C) $4\sqrt{3}$

Answer

(D) $6\sqrt{3}$

Question 10

Let the ellipse $E : \dfrac{x^{2}}{144} + \dfrac{y^{2}}{169} = 1$ and the hyperbola $H : \dfrac{x^{2}}{16} - \dfrac{y^{2}}{\lambda^{2}} = -1$ have the same foci. If e and L respectively denote the eccentricity and the length of the latus rectum of H, then the value of 24(e + L) is :

Accepted Answer

(A) 296

Answer

(B) 126

Answer

(C) 148

Answer

(D) 67

Question 11

Let $P_{1} : y = 4x^{2}$ and $P_{2} : y = x^{2} + 27$ be two parabolas. If the area of the bounded region enclosed between $P_{1}$ and $P_{2}$ is six times the area of the bounded region enclosed between the line $y = \alpha x$, α > 0 and $P_{1}$, then α is equal to :

Accepted Answer

(C) 12

Answer

(A) 8

Answer

(B) 15

Answer

(D) 6

Question 12

Let the circle $x^{2} + y^{2} = 4$ intersect x-axis at the points A(a, 0), a > 0 and B(b,0). Let P(2 cosα, 2 sinα), $0 < \alpha < \dfrac{\pi}{2}$ and Q(2 cosβ, 2 sinβ) be two points such that $(\alpha - \beta) = \dfrac{\pi}{2}$. Then the point of intersection of AQ and BP lies on :

Accepted Answer

(A) $x^{2} + y^{2} - 4y - 4 = 0$

Answer

(B) $x^{2} + y^{2} - 4x - 4 = 0$

Answer

(C) $x^{2} + y^{2} - 4x - 4y = 0$

Answer

(D) $x^{2} + y^{2} - 4x - 4y - 4 = 0$

Question 13

Let [·] denote the greatest integer function. Then $\displaystyle\int\limits_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\left(\dfrac{12(3+[x])}{3+[\sin x]+[\cos x]}\right) dx$ is equal to:

Accepted Answer

(B) $11\pi + 2$

Answer

(A) $15\pi + 4$

Answer

(C) $13\pi + 1$

Answer

(D) $12\pi + 5$

Question 14

Let y = y(x) be the solution of the differential equation $x\frac{dy}{dx} - y = x^2 \cot x, x \in (0, \pi)$.
If $y\left(\frac{\pi}{2}\right) = \frac{\pi}{2}$, then $6y\left(\frac{\pi}{6}\right) - 8y\left(\frac{\pi}{4}\right)$ is equal to :

Accepted Answer

(C) - $\pi$

Answer

(A) $3\pi$

Answer

(B) - $3\pi$

Answer

(D) $\pi$

Question 15

The sum of all the elements in the range of f(x)=Sgn(sinx)+Sgn(cosx)+Sgn(tanx)+Sgn(cotx), $x 
eq \frac{n\pi}{2}$, n $\in$ $\mathbf{Z}$,
where Sgn(t) = $\begin{cases} 1, & 	ext{if} \quad t > 0 \ -1 & 	ext{if} \quad t < 0 \end{cases}$, is

Accepted Answer

(B) 2

Answer

(A) 4

Answer

(C) –2

Answer

(D) 0

Question 16

Let Q(a, b, c) be the image of the point P(3, 2, 1) in the line $\frac{x-1}{1} = \frac{y}{2} = \frac{z-1}{1}$. Then the distance of Q from the line $\frac{x-9}{3} = \frac{y-9}{2} = \frac{z-5}{-2}$ is

Accepted Answer

(C) 7

Answer

(A) 6

Answer

(B) 8

Answer

(D) 5

Question 17

Let P be a point in the plane of the vector $\overrightarrow{AB} = 3\hat{i} + \hat{j} - \hat{k}$ and $\overrightarrow{AC} = \hat{i} - \hat{j} + 3\hat{k}$ such that P is equidistant from the lines AB and AC. If $\left|\overrightarrow{AP}\right| = \frac{\sqrt{5}}{2}$, then the area of the triangle ABP is :

Accepted Answer

(C) $\frac{\sqrt{30}}{4}$

Answer

(A) 2

Answer

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

Answer

(D) $\frac{\sqrt{26}}{4}$

Question 18

Let
$A = \left\{z \in \mathbb{C} : |z - 2| \leq 4ight\}$ and
$B = \left\{z \in \mathbb{C} : |z - 2| + |z + 2| = 5ight\}$.
Then the max $\left\{|z_1 - z_2| : z_1 \in A 	ext{ and } z_2 \in Bight\}$ is

Accepted Answer

(C) $\frac{17}{2}$

Answer

(A) $\frac{15}{2}$

Answer

(B) 8

Answer

(D) 9

Question 19

Let $f(x) = \int \frac{dx}{x^{\left(\frac{2}{3}\right)} + 2x^{\left(\frac{1}{2}\right)}}$ be such that $f(0) = -26 + 24 \log_e(2)$. If $f(1) = a + b \log_e(3)$, where a, b $\in$ $\mathbf{Z}$, then a + b is equal to:

Accepted Answer

(C) –11

Answer

(A) –18

Answer

(B) –5

Answer

(D) –26

Question 20

$\frac{6}{3^{26}} + \frac{10.1}{3^{25}} + \frac{10.2}{3^{24}} + \frac{10.2^2}{3^{23}} + ...+ \frac{10.2^{24}}{3}$ is equal to

Accepted Answer

(B) $2^{26}$

Answer

(A) $2^{25}$

Answer

(C) $3^{25}$

Answer

(D) $3^{26}$

Question 21

If $\sum_{r=1}^{25}\left(\frac{r}{r^4 + r^2 + 1}\right) = \frac{p}{q}$, where p and q are positive integers such that gcd (p, q) = 1, then p + q is equal to ______.

Accepted Answer

976

Question 22

Three persons enter in a lift at the ground floor. The lift will go upto $10^{th}$ floor. The number of ways, in which the three persons can exit the lift at three different floors, if the lift does not stop at first, second and third floors, is equal to _______ .

Accepted Answer

210

Question 23

Let f be a differentiable function satisfying
$f(x) = 1 - 2x + \int_0^x e^{(x-t)}\, f(t)\, dt$, x $\in$ $\mathbf{R}$ and let
$g(x) = \int_0^x (f(t) + 2)^{15}\, (t - 4)^6\, (t + 12)^{17}\, dt$, x $\in$ $\mathbf{R}$.
If p and q are respectively the points of local minima and local maxima of g, then the value of $|p + q|$ is equal to _________ .

Accepted Answer

9

Question 24

If the distance of the point P(43, $\alpha$, $\beta$), $\beta < 0$, from the line $\vec{r} = 4\hat{i} - \hat{k} + \mu(2\hat{i} + 3\hat{k})$, $\mu \in \mathbf{R}$ along a line with direction ratios 3, –1, 0 is $13\sqrt{10}$, then $\alpha^2 + \beta^2$ is equal to ________.

Accepted Answer

170

Question 25

Let A = $\begin{bmatrix} 3 & -4 \ 1 & -1 \end{bmatrix}$ and B be two matrices such that $A^{100} = 100B + I$. Then the sum of all the elements of $B^{100}$ is ______.

Accepted Answer

0

Question 26

A nucleus has mass number α and radius $R_{\alpha}$. Another nucleus has mass number β and radius $R_{\beta}$. If β = 8α then $R_{\alpha}/R_{\beta}$ is :

Accepted Answer

(D) 0.5

Answer

(A) 2

Answer

(B) 8

Answer

(C) 1

Question 27

A plane electromagnetic wave is moving in free space with velocity c = $3 	imes 10^{8}$ m/s and its electric field is given as $\vec{E} = 54\sin(kz - \omega t)\hat{j}$ V / m, where $\hat{j}$ is the unit vector along y-axis. The magnetic field vector $\vec{B}$ of the wave is :

Accepted Answer

(A) $-1.8 	imes 10^{-7}\sin(kz - \omega t)\hat{i}$ T

Answer

(B) $1.4 	imes 10^{-7}\sin(kz - \omega t)\hat{k}$ T

Answer

(C) $1.4 	imes 10^{-7}\sin(kz - \omega t)\hat{i}$ T

Answer

(D) $+1.8 	imes 10^{-7}\sin(kz - \omega t)\hat{i}$ T

Question 28

A biconvex lens is formed by using two thin planoconvex lenses, as shown in the figure. The refractive index and radius of curved surfaces are also mentioned in figure. When an object is placed on the left side of lens at a distance of 30 cm from the biconvex lens, the magnification of the image will be :

Accepted Answer

(A) –2

Answer

(B) +2

Answer

(C) +2.5

Answer

(D) –2.5

Question 29

The mean free path of a molecule of diameter $5 	imes 10^{-10}$ m at the temperature 41°C and pressure $1.38 	imes 10^{5}$ Pa, is given as ____m. (Given $k_{B} = 1.38 	imes 10^{-23}$ J/K).

Accepted Answer

(C) $2\sqrt{2} 	imes 10^{-8}$

Answer

(A) $2\sqrt{2} 	imes 10^{-10}$

Answer

(B) $10\sqrt{2} 	imes 10^{-8}$

Answer

(D) $2 	imes 10^{-8}$

Question 30

Two p-n junction diodes $D_{1}$ and $D_{2}$ are connected as shown in figure. A and B are input signals and C is the output. The given circuit will function as a ____.

Accepted Answer

(D) AND Gate

Answer

(A) OR Gate

Answer

(B) NOR Gate

Answer

(C) NAND Gate

Question 31

A wheatstone bridge is initially at room temperature and all arms of the bridge have same value of resistances ($R_{1} = R_{2} = R_{3} = R_{4}$). When $R_{3}$ resistance is heated to some temperature, its resistance value has gone up by 10%. The potential difference ($V_{a} - V_{b}$) (after $R_{3}$ is heated) is _____V.

Accepted Answer

(C) 0.95

Answer

(A) 1.05

Answer

(B) 0

Answer

(D) 2

Question 32

In an experiment, a set of reading are obtained –1.24 mm, 1.25 mm, 1.23 mm, 1.21 mm. The expected least count of the instrument used in recording these readings is _____mm.

Accepted Answer

(A) 0.01

Answer

(B) 0.001

Answer

(C) 0.1

Answer

(D) 0.05

Question 33

A particle starts moving from time t = 0 and its coordinate is given as $x(t) = 4t^{3} - 3t$.
A. The particle returns to its original position (origin) 0.866 units later
B. The particle is 1 unit away from origin at its turning point.
C. Acceleration of the particle is non-negative.
D. The particle is 0.5 units away from origin at its turning point.
E. Particle never turns back as acceleration is non-negative.
Choose the correct answer from the options given below :

Accepted Answer

(B) A,B,C only

Answer

(A) A,C,D only

Answer

(C) C,E only

Answer

(D) A,C only

Question 34

The speed of a longitudinal wave in a metallic bar is 400 m/s. If the density and Young's modulus of the bar material are increased by 0.5% and 1% respectively then the speed of the wave is changed approximately to _____ m/s.

Accepted Answer

(D) 401

Answer

(A) 399

Answer

(B) 398

Answer

(C) 402

Question 35

Identify the correct statements :
A. Effective capacitance of a series combination of capacitors is always smaller than the smallest capacitance of the capacitor in the combination.
B. When a dielectric medium is placed between the charged plates of a capacitor, displacement of charges cannot occur due to insulation property of dielectric.
C. Increasing of area of capacitor plate or decreasing of thickness of dielectric is an alternate method to increase the capacitance.
D. For a point charge, concentric spherical shells centered at the location of the charge are equipotential surfaces.
Choose the correct answer from the options given below.

Accepted Answer

(C) A, C and D only

Answer

(A) A, B and C only

Answer

(B) C and D only

Answer

(D) B and D only

Question 36

Number of photons of equal energy emitted per second by a 6 mW laser source operating at 663 nm is _____.
(Given : h = $6.63 	imes 10^{-34}$ J.s and c = $3 	imes 10^{8}$ m/s)

Accepted Answer

(D) $2 	imes 10^{16}$

Answer

(A) $5 	imes 10^{16}$

Answer

(B) $5 	imes 10^{15}$

Answer

(C) $10 	imes 10^{15}$

Question 37

When the position vector $\vec{r} = x\hat{i} + y\hat{j} + z\hat{k}$ changes sign as $-\vec{r}$, which one of the following vector will not flip under sign change ?

Accepted Answer

(D) Angular momentum

Answer

(A) Linear momentum

Answer

(B) Velocity

Answer

(C) Acceleration

Question 38

Which one of the following is not a measurable quantity ?

Accepted Answer

(C) Voltage

Answer

(A) Voltage difference

Answer

(B) Resistance

Answer

(D) Displacement current

Question 39

A long cylindrical conductor with large cross section carries an electric current distributed uniformly over its cross-section. Magnetic field due to this current is :
A. maximum at either ends of the conductor and minimum at the midpoint
B. maximum at the axis of the conductor
C. minimum at the surface of the conductor
D. minimum at the axis of the conductor
E. same at all points in the cross-section of the conductor
Choose the correct answer from the options given below :

Accepted Answer

(A) D Only

Answer

(B) A, D Only

Answer

(C) B, C Only

Answer

(D) E Only

Question 40

A small block of mass m slides down from the top of a frictionless inclined surface, while the inclined plane is moving towards left with constant acceleration $a_0$. The angle between the inclined plane and ground is θ and its base length is L. Assuming that initially the small block is at the top of the inclined plane, the time it takes to reach the lowest point of the inclined plane is _________.

Accepted Answer

(B) $\sqrt{\dfrac{4L}{g\sin 2	heta - a_0(1 + \cos 2	heta)}}$

Answer

(A) $\sqrt{\dfrac{2L}{g\sin 2	heta - a_0(1 + \cos 2	heta)}}$

Answer

(C) $\sqrt{\dfrac{4L}{g\cos^2 	heta - a_0 \sin	heta\cos	heta}}$

Answer

(D) $\sqrt{\dfrac{2L}{g\sin 	heta - a_0 \cos	heta}}$

Question 41

Identify the correct statements :
A. Electrostatic field lines form closed loops.
B. The electric field lines point radially outward when charge is greater than zero.
C. The Gauss-Law is valid only for inverse-square force.
D. The workdone in moving a charged particle in a static electric field around a closed path is zero.
E. The motion of a particle under Coulomb's force must take place in a plane.
Choose the correct answer from the options given below :

Accepted Answer

(C) B, C, D, E Only

Answer

(A) A, B, D, E Only

Answer

(B) A, B, C, D Only

Answer

(D) A, C, E Only

Question 42

As shown in the figure, a spring is kept in a stretched position with some extension by holding the masses 1 kg and 0.2 kg with a separation more than spring natural length and are released. Assuming the horizontal surface to be frictionless, the angular frequency (in SI unit) of the system is :

Accepted Answer

(A) 30

Answer

(B) 27

Answer

(C) 20

Answer

(D) 5

Question 43

For a transparent prism, if the angle of minimum deviation is equal to its refracting angle, the refractive index n of the prism satisfies.

Accepted Answer

(D) $\sqrt{2} < n < 2$

Answer

(A) $\sqrt{2} < n < 2\sqrt{2}$

Answer

(B) $1 < n < 2$

Answer

(C) $n \geq 2$

Question 44

The time period of a simple harmonic oscillator is $T = 2\pi\sqrt{\dfrac{k}{m}}$ . The measured value of mass (m) of the object is 10 g with an accuracy of 10 mg, and time for 50 oscillations of the spring is found to be 60 s using a watch of 2 s resolution. Percentage error in determination of spring constant(k) is _______%.

Accepted Answer

(D) 6.76

Answer

(A) 3.43

Answer

(B) 3.35

Answer

(C) 7.60

Question 45

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 46

Two tuning forks A and B are sounded together giving rise to 8 beats in 2 s. When fork A is loaded with wax, the beat frequency is reduced to 4 beats in 2 s. If the original frequency of tuning fork B is 380 Hz, then the original frequency of tuning fork A is _______ Hz.

Accepted Answer

384

Question 47

A thermodynamic system is taken through the cyclic process ABC as shown in the figure. The total work done by the system during the cycle ABC is _______ J.

Accepted Answer

300

Question 48

An inductor stores 16 J of magnetic field energy and dissipates 32 W of thermal energy due to its resistance when an a.c. current of 2 A (rms) and frequency 50 Hz flows through it. The ratio of inductive reactance to its resistance is _________.
(π = 3.14)

Accepted Answer

314

Question 49

A beam of light consisting of wavelengths 650 nm and 550 nm illuminates the Young's double slits with separation of 2 mm such that the interference fringes are formed on a screen, placed at a distance of 1.2 m from the slits. The least distance of a point from the central maximum, where the bright fringes due to both the wavelengths coincide, is _______ $	imes 10^{-5}$ m.

Accepted Answer

429

Question 50

A fly wheel having mass 3 kg and radius 5 m is free to rotate about a horizontal axis. A string having negligible mass is wound around the wheel and the loose end of the string is connected to a 3 kg mass. The mass is kept at rest initially and released. Kinetic energy of the wheel when the mass descends by 3 m is _______ J. (g = 10 m/s²)

Accepted Answer

30

Question 51

Identify the correct statements :
The presence of $-NO_2$ group in benzene ring
A. activates the ring towards electrophilic substitutions.
B. deactivates the ring towards electrophilic substitutions.
C. activates the ring towards nucleophilic substitutions.
D. deactivates the ring towards nucleophilic substitutions.

Accepted Answer

(D) B and C Only

Answer

(A) B and D Only

Answer

(B) C and A Only

Answer

(C) A and D Only

Question 52

Given below are two statements :
Statement I : The increasing order of boiling point of hydrogen halides is HCl < HBr < HI < HF.
Statement II : The increasing order of melting point of hydrogen halides is HCl < HBr < HF < HI.
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) Statement I is true but Statement II is false

Answer

(C) Both Statement I and Statement II are false

Answer

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

Question 53

Consider the elements N, P, O, S, Cl and F. The number of valence electrons present in the elements with most and least metallic character from the above list is respectively.

Accepted Answer

(C) 5 and 7

Answer

(A) 7 and 5

Answer

(B) 5 and 6

Answer

(D) 6 and 7

Question 54

Observe the following equilibrium in a 1 L flask.
$A(g) \rightleftharpoons B(g)$
At T(K), the equilibrium concentrations of A and B are 0.5 M and 0.375 M respectively. 0.1 moles of A is added into the flask and heated to T(K) to establish the equilibrium again. The new equilibrium concentrations (in M) of A and B are respectively.

Accepted Answer

(D) 0.557, 0.418

Answer

(A) 0.367, 0.275

Answer

(B) 0.53, 0.4

Answer

(C) 0.742, 0.557

Question 55

The plot of $\log_{10}K$ vs $\frac{1}{T}$ gives a straight line. The intercept and slope respectively are (where K is equilibrium constant).

Accepted Answer

(B) $\frac{\Delta S^\circ}{2.303R}$ , $-\frac{\Delta H^\circ}{2.303R}$

Answer

(A) $\frac{2.303R}{\Delta H^\circ}$ , $\frac{2.303R}{\Delta S^\circ}$

Answer

(C) $-\frac{\Delta S^\circ R}{2.303}$ , $\frac{\Delta H^\circ R}{2.303}$

Answer

(D) $-\frac{\Delta H^\circ}{2.303R}$ , $\frac{\Delta S^\circ}{2.303R}$

Question 56

The reactions which produce alcohol as the product area :
A. $CH_4 + O_2 \xrightarrow[\Delta]{Mo_2O_3}$
B. $2CH_3CH_3 + 3O_2 \xrightarrow[\Delta]{(CH_3COO)_2\,Mn}$
C. $(CH_3)_3CH \xrightarrow{KMnO_4}$
D. $2CH_4 + O_2 \xrightarrow{Cu/523\,K/100\,atm.}$
E. $CH_3-CH=CH-CH_3 \xrightarrow{KMnO_4/H^+}$
Choose the correct answer from the options given below :

Accepted Answer

(C) C and D Only

Answer

(A) A and D Only

Answer

(B) A, C and E Only

Answer

(D) B, D and E Only

Question 57

Consider the following statements about manganate and permanganate ions. Identify the correct statements :
A. The geometry of both manganate and permanganate ions is tetrahedral.
B. The oxidation states of Mn in manganate and permanganate are +7 and +6, respectively.
C. Oxidation of Mn(II) salt by peroxodisulphate gives manganate ion as the final product.
D. Manganate ion is paramagnetic and permanganate ions is diamagnetic.
E. Acidified permanganate ion reduces oxalate, nitrite and iodide ions.
Choose the correct answer from the options given below:

Accepted Answer

(D) A and D Only

Answer

(A) A, C and D Only

Answer

(B) A, B and C Only

Answer

(C) A, D and E Only

Question 58

Which of the following reaction is NOT correctly represented ?

Accepted Answer

(A) (1)

Answer

(B) (2)

Answer

(C) (3)

Answer

(D) (4)

Question 59

The wavelength of photon 'A' is 400 nm. The frequency of photon 'B' is $10^{16}s^{-1}$. The wave number of photon 'C' is $10^4$ $cm^{-1}$. The correct order of energy of these photons is :

Accepted Answer

(B) B > A > C

Answer

(A) C > B > A

Answer

(C) A > B > C

Answer

(D) A > C > B

Question 60

The cyclic cations having the same number of hyperconjugation are :
Choose the correct answer from the options given below :

Accepted Answer

(A) A and C Only

Answer

(B) B and C Only

Answer

(C) A and B Only

Answer

(D) A, C and D only

Question 61

Structures of four disaccharides are given below. Among the given disaccharides, the non-reducing sugar is :

Accepted Answer

(A) (1)

Answer

(B) (2)

Answer

(C) (3)

Answer

(D) (4)

Question 62

Match List-I with List-II according to shape.
Choose the correct answer from the options given below :

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 63

A student performed analysis of aliphatic organic compound 'X' which on analysis gave C = 61.01%, H=15.25%, N=23.74%.
This compound, on treatment with $HNO_2/H_2O$ produced another compound 'Y' which did not contain any nitrogen atom. However, the compound 'Y' upon controlled oxidation produced another compound 'Z' that responded to iodoform test.
The structure of 'X' is:

Accepted Answer

(C) (3)

Answer

(A) (1)

Answer

(B) (2)

Answer

(D) (4)

Question 64

Consider the following aqueous solutions.
I. 2.2 g Glucose in 125 mL of solution.
II. 1.9 g Calcium chloride in 250 mL of solution.
III. 9.0 g Urea in 500 mL of solution.
IV. 20.5 g Aluminium sulphate in 750 mL of solution.
The correct increasing order of boiling point of these solutions will be:
[Given: Molar mass in g $mol^{-1}$: H=1, C=12, N=14, O=16, Cl=35.5, Ca=40, Al=27 and S=32]

Accepted Answer

(A) I < II < III < IV

Answer

(B) III < I < II < IV

Answer

(C) II < III < I < IV

Answer

(D) II < III < IV < I

List-I	List-II
A.Coefficient of viscosity	I.[ML $^{–1}$ T $^{–2}$ ]
B.Surface tension	II.[ML $^{2}$ T $^{–2}$ ]
C.Pressure	III.[ML $^{0}$ T $^{–2}$ ]
D.Surface energy	IV.[ML $^{–1}$ T $^{–1}$ ]

List-I	List-II
A.XeO $_{3}$	I.BrF $_{5}$
B.XeF $_{2}$	II.NH $_{3}$
C.XeO $_{2}$ F $_{2}$	III.[I $_{3}$ ] $^{–}$
D.XeOF $_{4}$	IV.SF $_{4}$

JEE Main 28 January 2026 Shift 2 Question Paper with Answers

Physics — JEE Main 28 January 2026 Shift 2

Chemistry — JEE Main 28 January 2026 Shift 2

Mathematics — JEE Main 28 January 2026 Shift 2

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