JEE Main 21 January 2026 Shift 2 Question Paper

Question 1

The positive integer n, for which the solutions of the equation
$x(x+2) + (x + 2)(x + 4) + \ldots + (x + 2n - 2)(x+2n) = \frac{8n}{3}$
are two consecutive even integers, is :-

Accepted Answer

(A) 3

Answer

(B) 6

Answer

(C) 12

Answer

(D) 9

Question 2

Let $f : \mathbf{R} 	o \mathbf{R}$ be a twice differentiable function such that $f''(x) > 0$ for all x∈$\mathbf{R}$ and $f'(a - 1) = 0$, where a is real number. Let $g(x) = f(	an^2 x - 2	an x + a)$, $0 < x < \frac{\pi}{2}$.
Consider the following two statements :
(I) g is increasing in $\left(0, \frac{\pi}{4}ight)$
(II) g is decreasing in $\left(\frac{\pi}{4}, \frac{\pi}{2}ight)$
Then,

Accepted Answer

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

Answer

(B) Only (II) is True

Answer

(C) Only (I) is True

Answer

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

Question 3

Let $f(x) = x^3 + x^2 f'(1) + 2x f''(2) + f'''(3)$, x ∈ R. Then the value of $f'(5)$ is :

Accepted Answer

(D) $\frac{117}{5}$

Answer

(A) $\frac{62}{5}$

Answer

(B) $\frac{657}{5}$

Answer

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

Question 4

In the line $\alpha x + 4y = \sqrt{7}$, where α ∈ R, touches the ellipse $3x^2 + 4y^2 = 1$ at the point P in the first quadrant, then one of the focal distances of P is :

Accepted Answer

(D) $\frac{1}{\sqrt{3}} + \frac{1}{2\sqrt{7}}$

Answer

(A) $\frac{1}{\sqrt{3}} - \frac{1}{2\sqrt{11}}$

Answer

(B) $\frac{1}{\sqrt{3}} + \frac{1}{2\sqrt{5}}$

Answer

(C) $\frac{1}{\sqrt{3}} - \frac{1}{2\sqrt{5}}$

Question 5

Let $y^2 = 12x$ be the parabola with its vertex at O. Let P be a point on the parabola and A be a point on the x-axis such that ∠OPA = 90°. Then the locus of the centroid of such triangles OPA is :

Accepted Answer

(C) $y^2 - 2x + 8 = 0$

Answer

(A) $y^2 - 6x + 4 = 0$

Answer

(B) $y^2 - 9x + 6 = 0$

Answer

(D) $y^2 - 4x + 8 = 0$

Question 6

Let one end of a focal chord of the parabola $y^2 = 16x$ be (16, 16). If P(α, β) divides this focal chord internally in the ratio 5 : 2, then the minimum value of α + β is equal to :

Accepted Answer

(B) 7

Answer

(A) 22

Answer

(C) 5

Answer

(D) 16

Question 7

Let the line L pass through the point (−3, 5, 2) and make equal angles with the positive coordinate axes. If the distance of L from the point (−2, r, 1) is $\sqrt{\frac{14}{3}}$, then the sum of all possible values of r is :

Accepted Answer

(D) 10

Answer

(A) 12

Answer

(B) 16

Answer

(C) 6

Question 8

Let the line $L_1$ be parallel to the vector $-3\hat{i} + 2\hat{j} + 4\hat{k}$ and pass through the point (2, 6, 7) and the line $L_2$ be parallel to the vector $2\hat{i} + \hat{j} + 3\hat{k}$ and pass through the point (4, 3, 5). If the line $L_3$ is parallel to the vector $-3\hat{i} + 5\hat{j} + 16\hat{k}$ and intersects the lines $L_1$ and $L_2$ at the points C and D, respectively, then $\left|\overrightarrow{CD}\right|^2$ is equal to :

Accepted Answer

(B) 290

Answer

(A) 171

Answer

(C) 312

Answer

(D) 89

Question 9

Let α and β be the roots of equation $x^2 + 2ax + (3a + 10) = 0$ such that α < 1 < β. Then the set of all possible values of a is :

Accepted Answer

(D) $\left(-\infty, \frac{-11}{5}\right)$

Answer

(A) $\left(-\infty, \frac{-11}{5}\right) \cup (5, \infty)$

Answer

(B) $(-\infty, -2) \cup (5, \infty)$

Answer

(C) $(-\infty, -3)$

Question 10

A random variable X takes values 0, 1, 2, 3 with probabilities $\frac{2a+1}{30}, \frac{8a-1}{30}, \frac{4a+1}{30}$, b respectively, where a, b ∈$\mathbf{R}$. Let μ and σ respectively be the mean and standard deviation of X such that $\sigma^2 + \mu^2 = 2$. Then $\frac{a}{b}$ is equal to :

Accepted Answer

(C) 60

Answer

(A) 30

Answer

(B) 3

Answer

(D) 12

Question 11

If the area of the region $\{(x, y) : 1 - 2x \le y \le 4 - x^2, x \ge 0, y \ge 0\}$ is $\frac{\alpha}{\beta}$, α, β, ∈ N, gcd (α, β) = 1, then the value of (α + β) is :

Accepted Answer

(A) 73

Answer

(B) 85

Answer

(C) 91

Answer

(D) 67

Question 12

Let $a_1, \frac{a_2}{2}, \frac{a_3}{2^2}, \ldots, \frac{a_{10}}{2^9}$ be a G.P. of common ratio $\frac{1}{\sqrt{2}}$. If $a_1 + a_2 + \ldots + a_{10} = 62$, then $a_1$ is equal to :

Accepted Answer

(A) $2\left(\sqrt{2} - 1\right)$

Answer

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

Answer

(C) $\sqrt{2} - 1$

Answer

(D) $2(2 - \sqrt{2})$

Question 13

Let $A = \{x : |x^2 - 10| \le 6\}$ and $B = \{x : |x - 2| > 1\}$. Then

Accepted Answer

(D) $B - A = (-\infty, -4) \cup (-2, 1) \cup (4, \infty)$

Answer

(A) $A \cup B = (-\infty, 1] \cup (2, \infty)$

Answer

(B) $A - B = [2, 3)$

Answer

(C) $A \cap B = [-4, -2] \cup [3, 4]$

Question 14

For the matrices $A = \begin{bmatrix} 3 & -4 \ 1 & -1 \end{bmatrix}$ and $B = \begin{bmatrix} -29 & 49 \ -13 & 18 \end{bmatrix}$, if $(A^{15} + B)\begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 0 \ 0 \end{bmatrix}$, then among the following which one is true?

Accepted Answer

(C) $x = 11$, $y = 2$

Answer

(A) $x = 5$, $y = 7$

Answer

(B) $x = 18$, $y = 11$

Answer

(D) $x = 16$, $y = 3$

Question 15

For a triangle ABC, let $\vec{p} = \overrightarrow{BC}$, $\vec{q} = \overrightarrow{CA}$ and $\vec{r} = \overrightarrow{BA}$. If $|\vec{p}| = 2\sqrt{3}$, $|\vec{q}| = 2$ and $\cos	heta = \frac{1}{\sqrt{3}}$, where $	heta$ is the angle between $\vec{P}$ and $\vec{q}$, then $\left|\vec{p} 	imes \left(\vec{q} - 3\vec{r}ight)ight|^{2} + 3\left|\vec{r}ight|^{2}$ is equal to:

Accepted Answer

(D) 200

Answer

(A) 340

Answer

(B) 220

Answer

(C) 410

Question 16

Let $y = y(x)$ be the solution of the differential equation $\sec x \frac{dy}{dx} - 2y = 2 + 3\sin x$, $x \in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$, $y(0) = -\frac{7}{4}$. Then $y\left(\frac{\pi}{6}\right)$ is equal to:

Accepted Answer

(A) $-\frac{5}{2}$

Answer

(B) $-\frac{5}{4}$

Answer

(C) $-3\sqrt{3} - 7$

Answer

(D) $-3\sqrt{2} - 7$

Question 17

Let $A = \{2, 3, 5, 7, 9\}$. Let R be the relation on A defined by $x$ R $y$ if and only if $2x \le 3y$. Let $\ell$ be the number of elements in R, and m be the minimum number of elements required to be added in R to make it a symmetric relation. Then $\ell + m$ is equal to:

Accepted Answer

(B) 25

Answer

(A) 23

Answer

(C) 21

Answer

(D) 27

Question 18

If the system of equations
$3x + y + 4z = 3$
$2x + \alpha y - z = -3$
$X + 2y + z = 4$
has no solution, then the value of $\alpha$ is equal to:

Accepted Answer

(A) 19

Answer

(B) 4

Answer

(C) 13

Answer

(D) 23

Question 19

Let z be the complex number satisfying $|z - 5| \le 3$ and having maximum positive principal argument. Then $34\left|\frac{5z - 12}{5iz + 16}\right|^{2}$ is equal to:

Accepted Answer

(D) 20

Answer

(A) 16

Answer

(B) 12

Answer

(C) 26

Question 20

The largest $n \in N$, for which $7^{n}$ divides $101!$, is :

Accepted Answer

(A) 16

Answer

(B) 18

Answer

(C) 15

Answer

(D) 19

Question 21

Let $[\cdot]$ denote the greatest integer function and $f(x) = \lim_{n 	o \infty} \frac{1}{n^{3}} \sum_{k=1}^{n} \left[\frac{k^{2}}{3^{x}}ight]$. Then $12\sum_{j=1}^{\infty} f(j)$ is equal to _______.

Accepted Answer

2

Question 22

If $\int_{0}^{1} 4\cot^{-1}(1 - 2x + 4x^{2})dx = a	an^{-1}(2) - b\log_{e}(5)$, where $a, b \in N$, then $(2a + b)$ is equal to _______.

Accepted Answer

9

Question 23

Let the maximum value of $(\sin^{-1}x)^{2} + (\cos^{-1}x)^{2}$ for $x \in \left[-\frac{\sqrt{3}}{2}, \frac{1}{\sqrt{2}}\right]$ be $\frac{m}{n}\pi^{2}$, where gcd $(m, n) = 1$. Then $m + n$ is equal to _______.

Accepted Answer

65

Question 24

If $\left(\frac{1}{{}^{15}C_{0}} + \frac{1}{{}^{15}C_{1}}\right)\left(\frac{1}{{}^{15}C_{1}} + \frac{1}{{}^{15}C_{2}}\right)\cdots\left(\frac{1}{{}^{15}C_{12}} + \frac{1}{{}^{15}C_{13}}\right) = \frac{\alpha^{13}}{{}^{14}C_{0}\,{}^{14}C_{1}\cdots{}^{14}C_{12}}$, then $30\alpha$ is equal to _______.

Accepted Answer

32

Question 25

If P is a point on the circle $x^{2} + y^{2} = 4$, Q is a point on the straight line $5x + y + 2 = 0$ and $x - y + 1 = 0$ is the perpendicular bisector of PQ, then 13 times the sum of abscissa of all such point P is _______.

Accepted Answer

2

Question 26

Consider two identical metallic spheres of radius $R$ each having charge $Q$ and mass $m$. Their centers have an initial separation of $4R$. Both the spheres are given an initial speed of $u$ towards each other. The minimum value of u, so that they can just touch each other is :
(Take $k = \frac{1}{4\pi \in_0}$ and assume $kQ^2 > Gm^2$ where G is the Gravitational constant)

Accepted Answer

(A) $\sqrt{\frac{kQ^2}{4mR}\left(1 - \frac{Gm^2}{kQ^2}\right)}$

Answer

(B) $\sqrt{\frac{kQ^2}{4mR}\left(1 + \frac{Gm^2}{kQ^2}\right)}$

Answer

(C) $\sqrt{\frac{kQ^2}{2mR}\left(1 - \frac{Gm^2}{kQ^2}\right)}$

Answer

(D) $\sqrt{\frac{kQ^2}{2mR}\left(1 - \frac{Gm^2}{2kQ^2}\right)}$

Question 27

The charge stored by the capacitor C in the given circuit in the steady state is ………. $\mu$C.

Accepted Answer

(B) 10

Answer

(A) 12.5

Answer

(C) 7.5

Answer

(D) 5

Question 28

The total length of potentiometer wire AB is 50 cm in the arrangement as shown in figure. If P is the point where the galvanometer shows zero reading then the length AP is ………. cm.

Accepted Answer

(B) 30

Answer

(A) 15

Answer

(C) 25

Answer

(D) 20

Question 29

A capacitor C is first charged fully with potential difference of $V_0$ and disconnected from the battery. The charged capacitor is connected across an inductor having inductance L. In t s 25% of the initial energy in the capacitor is transferred to the inductor. The value of t is________s.

Accepted Answer

(B) $\frac{\pi\sqrt{LC}}{6}$

Answer

(A) $\frac{\pi\sqrt{LC}}{3}$

Answer

(C) $\frac{\pi\sqrt{LC}}{2}$

Answer

(D) $\pi\sqrt{\frac{LC}{2}}$

Question 30

The r.m.s speed of oxygen molecules at $47^\circ$C is equal to that of the hydrogen molecules kept at______$^\circ$C. (Mass of oxygen molecule/mass of hydrogen molecule=32/2)

Accepted Answer

(C) −253

Answer

(A) −235

Answer

(B) −100

Answer

(D) −20

Question 31

Two cars A and B each of mass $10^3$ kg are moving on parallel tracks separated by a distance of 10 m, in same direction with speeds 72 km/h and 36 km/h. The magnitude of angular momentum of car A with respect to car B is ___ J.s.

Accepted Answer

(B) $10^5$

Answer

(A) $3.6 	imes 10^5$

Answer

(C) $3 	imes 10^5$

Answer

(D) $2 	imes 10^5$

Question 32

The pulley shown in figure is made using a thin rim and two rods of length equal to diameter of the rim. The rim and each rod have a mass of M. Two blocks of mass of M and m are attached to two ends of a light string passing over the pulley, which is hinged to rotate freely in vertical plane about its centre. The magnitudes of the acceleration experienced by the blocks is____ (assume no slipping of string on pulley.)

Accepted Answer

(C) $\frac{(M-m)g}{\left[\left(\frac{8}{3}\right)M + m\right]}$

Answer

(A) $\frac{(M-m)g}{\left[\left(\frac{13}{6}\right)M + m\right]}$

Answer

(B) $\frac{(M-m)g}{M+m}$

Answer

(D) $\frac{(M-m)g}{2M+m}$

Question 33

The kinetic energy of a simple harmonic oscillator is oscillating with angular frequency of 176 rad/s. The frequency of this simple harmonic oscillator is_____Hz. $\left[	ext{take } \pi = \frac{22}{7}ight]$

Accepted Answer

(A) 14

Answer

(B) 88

Answer

(C) 28

Answer

(D) 176

Question 34

Given below are two statements:
Statement I : In a Young's double slit experiment, the angular separation of fringes will increase as the screen is moved away from the plane of the slits
Statement II : In a Young's double slit experiment, the angular separation of fringes will increase when monochromatic source is replaced by another monochromatic source of higher wavelength
In the light of the above statements, choose the correct answer from the options given below:

Accepted Answer

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

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 true but Statement II is false

Question 35

A battery with EMF E and internal resistance r is connected across a resistance R. The power consumption in R will be maximum when :

Accepted Answer

(D) $R = r$

Answer

(A) $R = 2r$

Answer

(B) $R = \frac{r}{2}$

Answer

(C) $R = \sqrt{2}r$

Question 36

Keeping the significant figures in view, the sum of the physical quantities 52.01m, 153.2 m and 0.123 m is :

Accepted Answer

(D) 205.3 m

Answer

(A) 205 m

Answer

(B) 205.333 m

Answer

(C) 205.33 m

Question 37

A spherical body of radius r and density σ falls freely through a viscous liquid having density ρ and viscosity η and attains a terminal velocity $v_0$. Estimated maximum error in the quantity η is : (Ignore errors associated with σ, ρ and g, gravitational acceleration)

Accepted Answer

(B) $\frac{2\Delta r}{r} + \frac{\Delta v_0}{v_0}$

Answer

(A) $2\frac{\Delta r}{r} - \frac{\Delta v_0}{v_0}$

Answer

(C) $2\left[\frac{\Delta r}{r} + \frac{\Delta v_0}{v_0}\right]$

Answer

(D) $2\left[\frac{\Delta r}{r} - \frac{\Delta v_0}{v_0}\right]$

Question 38

Surface tension of two liquids (having same densities), $T_1$ and $T_2$, are measured using capillary rise method utilizing two tubes with inner radii of $r_1$ and $r_2$ where $r_1 > r_2$. The measured liquid heights in these tubes are $h_1$ and $h_2$ respectively. [Ignore the weight of the liquid about the lowest point of miniscus]. The heights $h_1$ and $h_2$ and surface tensions $T_1$ and $T_2$ satisfy the relation :

Accepted Answer

(A) $h_1 < h_2$ and $T_1 = T_2$

Answer

(B) $h_1 = h_2$ and $T_1 = T_2$

Answer

(C) $h_1 > h_2$ and $T_1 = T_2$

Answer

(D) $h_1 > h_2$ and $T_1 < T_2$

Question 39

A river of width 200 m is flowing from west to east with a speed of 18 km/h. A boat, moving with speed of 36 km/h in still water, is made to travel one-round trip (bank to bank of the river). Minimum time taken by the boat for this journey and also the displacement along the river bank are ______ and ______ respectively.

Accepted Answer

(C) 40 s and 200 m

Answer

(A) 20 s and 100 m

Answer

(B) 40 s and 0 m

Answer

(D) 40 s and 100 m

Question 40

Two known resistance of R $\Omega$ and 2R $\Omega$ and and one unknown resistance X $\Omega$ are connected in a circuit as shown in the figure. If the equivalent resistance between points A and B in the circuit is X $\Omega$, then the value of X is ________ $\Omega$.

Accepted Answer

(A) $\left(\sqrt{3}-1ight)	ext{R}$

Answer

(B) $	ext{R}$

Answer

(C) $2\left(\sqrt{3}-1ight)	ext{R}$

Answer

(D) $\left(\sqrt{3}+1ight)	ext{R}$

Question 41

The energy of an electron in an orbit of the Bohr's atom is $-0.04	ext{E}_0$ eV where $	ext{E}_0$ is the ground state energy. If L is the angular momentum of the electron in this orbit and h is the Planck's constant, then $\dfrac{2\pi	ext{L}}{	ext{h}}$ is __________ :

Accepted Answer

(C) 5

Answer

(A) 2

Answer

(B) 4

Answer

(D) 6

Question 42

An infinitely long straight wire carrying current I is bent in a planer shape as shown in the diagram. The radius of the circular part is r. The magnetic field at the centre O of the circular loop is :

Accepted Answer

(B) $-\dfrac{\mu_0}{2\pi}\dfrac{	ext{I}}{	ext{r}}\left(\pi-1ight)\hat{	ext{i}}$

Answer

(A) $\dfrac{\mu_0}{2\pi}\dfrac{	ext{I}}{	ext{r}}\left(\pi+1ight)\hat{	ext{i}}$

Answer

(C) $\dfrac{\mu_0}{2\pi}\dfrac{	ext{I}}{	ext{r}}\left(\pi-1ight)\hat{	ext{i}}$

Answer

(D) $-\dfrac{\mu_0}{2\pi}\dfrac{	ext{I}}{	ext{r}}\left(\pi+1ight)\hat{	ext{i}}$

Question 43

A large drum having radius R is spinning around its axis with angular velocity $\omega$, as shown in figure. The minimum value of $\omega$ so that a body of mass M remains stuck to the inner wall of the drum, taking the coefficient of friction between the drum surface and mass M is $\mu$, is :

Accepted Answer

(D) $\sqrt{\dfrac{	ext{g}}{\mu	ext{R}}}$

Answer

(A) $\sqrt{\dfrac{\mu	ext{g}}{	ext{R}}}$

Answer

(B) $\sqrt{\dfrac{2	ext{g}}{\mu	ext{R}}}$

Answer

(C) $\sqrt{\dfrac{	ext{g}}{2\mu	ext{R}}}$

Question 44

A body of mass 2 kg is moving along x-direction such that its displacement as function of time is given by $	ext{x(t)} = \alpha	ext{t}^2 + \beta	ext{t} + \gamma\,	ext{m}$, where $\alpha = 1\ 	ext{m/s}^2$, $\beta = 1$ m/s and $\gamma = 1$m. The work done on the body during the time interval t = 2 s to t = 3 s, is ________ J.

Accepted Answer

(C) 24

Answer

(A) 49

Answer

(B) 42

Answer

(D) 12

Question 45

As shown in the diagram, when the incident ray is parallel to base of the prism, the emergent ray grazes along the second surface.
If refractive index of the material of prism is $\sqrt{2}$, the angle $	heta$ of prism is.

Accepted Answer

(A) 60°

Answer

(B) 75°

Answer

(C) 90°

Answer

(D) 45°

Question 46

An electromagnetic wave of frequency 100 MHz propagates through a medium of conductivity, $\sigma = 10$ mho/m. The ratio of maximum conducting current density to maximum displacement current density is __________.
$\left[	ext{Take }\dfrac{1}{4\pi\in_0} = 9	imes10^9\,	ext{Nm}^2/	ext{C}^2ight]$

Accepted Answer

1800

Question 47

The terminal velocity of a metallic ball of radius 6 mm in a viscous fluid is 20 cm/s. The terminal velocity of another ball of same material and having radius 3 mm in the same fluid will be ________ cm/s.

Accepted Answer

5

Question 48

A particle having electric charge $3	imes10^{-19}$ C and mass $6	imes10^{-27}$ kg is accelerated by applying an electric potential of 1.21 V. Wavelength of the matter wave associated with the particle is $\alpha	imes10^{-12}$ m. The value of $\alpha$ is __________.
(Take Planck's constant $= 6.6	imes10^{-34}$ J.s)

Accepted Answer

10

Question 49

In a Young's double slit experiment set up, the two slits are kept 0.4. mm apart and screen is placed at 1 m from slits. If a thin transparent sheet of thickness 20 μm is introduced in front of one of the slits then centre bring fringe shifts by 20 mm on the screen. The refractive index of transparent sheet is given by $\dfrac{\alpha}{10}$, where $\alpha$ is ________.

Accepted Answer

14

Question 50

A diatomic gas ($\gamma = 1.4$) does 100 J of work when it is expanded isobarically. Then the heat given to the gas __________ J.

Accepted Answer

350

Question 51

Consider the following spectral lines for atomic hydrogen:
A. First line of Paschen series
B. Second line of Balmer series
C. Third line of Paschen series
D. Fourth line of Bracket sereis
The correct arrangement of the above lines in ascending order of energy is:

Accepted Answer

(D) $	ext{D} < 	ext{A} < 	ext{C} < 	ext{B}$

Answer

(A) $	ext{D} < 	ext{C} < 	ext{A} < 	ext{B}$

Answer

(B) $	ext{A} < 	ext{B} < 	ext{C} < 	ext{D}$

Answer

(C) $	ext{C} < 	ext{D} < 	ext{B} < 	ext{A}$

Question 52

Match List-I (Pair of Compounds) with List-II (Type of Isomers). Choose the correct answer from the options given below:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 53

(1) $	ext{Br}_{2}/	ext{FeBr}_{3}/\Delta$
(2) $	ext{Sn}/	ext{HCl}/\Delta$
(3) pH neutralisation
(4) $	ext{Br}_{2}/	ext{H}_{2}	ext{O}$
(5) $	ext{NaNO}_{2}/	ext{HBr}$, 0-5$^{\circ}$C
(6) $	ext{CuBr}/	ext{NaBr}$
$ightarrow$ Major Product (P)
Consider the above sequence of reactions. The number of bromine atom(s) in the final product (P) will be:

Accepted Answer

(C) 5

Answer

(A) 1

Answer

(B) 6

Answer

(D) 3

Question 54

Aqueous HCl reacts with $	ext{MnO}_{2}	ext{(s)}$ to form $	ext{MnCl}_{2}	ext{(aq)}$, $	ext{Cl}_{2}	ext{(g)}$ and $	ext{H}_{2}	ext{O}(l)$. What is the weight (in g) of $	ext{Cl}_{2}$ liberated when 8.7 g of $	ext{MnO}_{2}	ext{(s)}$ is reacted with excess aqueous HCl solution ? (Given Molar mass in $	ext{g mol}^{-1}$ Mn = 55, Cl = 35.5, O = 16, H = 1)

Accepted Answer

(A) 7.1

Answer

(B) 71

Answer

(C) 21.3

Answer

(D) 14.2

Question 55

By usual analysis, 1.00g of compound (X) gave 1.79g of magnesium pyrophosphate. The percentage of phosphorus in compound (X) is: (nearest integer)
(Given, molar mass in $	ext{g mol}^{-1}$: O = 16, Mg = 24, P = 31)

Accepted Answer

(A) 50

Answer

(B) 30

Answer

(C) 20

Answer

(D) 40

Question 56

Consider the following data:
$\Delta_{	ext{f}}	ext{H}^{\ominus}$(methane, g) = $-	ext{X kJ mol}^{-1}$
Enthalpy of sublimation of graphite = $	ext{Y kJ mol}^{-1}$
Dissociation enthalpy of $	ext{H}_{2}$ = $	ext{Z kJ mol}^{-1}$
The bond enthalpy of C $-$ H bond is given by:

Accepted Answer

(A) $\frac{	ext{X} + 	ext{Y} + 2	ext{Z}}{4}$

Answer

(B) $\frac{	ext{X} + 	ext{Y} + 4	ext{Z}}{2}$

Answer

(C) $	ext{X} + 	ext{Y} + 	ext{Z}$

Answer

(D) $\frac{-	ext{X} + 	ext{Y} + 	ext{Z}}{4}$

Question 57

Match List-I (Reagents) with List-II (Reaction Name (Involving aldehydes)). 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-III, C-IV, D-I

Answer

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

Answer

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

Question 58

Decomposition of A is a first order reaction at T(K) and is given by $	ext{A(g)} ightarrow 	ext{B(g)} + 	ext{C(g)}$. In a closed 1 L vessel, 1 bar A(g) is allowed to decompose at T(K). After 100 minutes, the total pressure was 1.5 bar. What is the rate constant (in $	ext{min}^{-1}$) of the reaction ? (log 2 = 0.3)

Accepted Answer

(B) $6.9 	imes 10^{-3}$

Answer

(A) $6.9 	imes 10^{-1}$

Answer

(C) $6.9 	imes 10^{-2}$

Answer

(D) $6.9 	imes 10^{-4}$

Question 59

The correct order of reactivity of the following benzyl halides towards reaction with KCN is:

Accepted Answer

(B) b > a > d > c

Answer

(A) a > b > c > d

Answer

(C) b > a > c > d

Answer

(D) a > b > d > d

Question 60

Given below are two statements:
Statement-I: The correct order in terms of atomic/ionic radii is $	ext{Al} > 	ext{Mg} > 	ext{Mg}^{2+} > 	ext{Al}^{3+}$.
Statement-II: The correct order in terms of the magnitude of electron gain enthalpy is $	ext{Cl} > 	ext{Br} > 	ext{S} > 	ext{O}$.
In the light of the above statements, choose the correct answer from the options given below:

Accepted Answer

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

Answer

(A) Both Statement I and Statement II are false

Answer

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

Answer

(D) Both Statement I and Statement II are true

Question 61

The correct statements are:
A. Activation energy for enzyme catalysed hydrolysis of sucrose is lower than that of acid catalysed hydrolysis.
B. During denaturation, secondary and tertiary structures of a protein are destroyed but primary structure remains intact.
C. Nucleotides are joined together by glycosidic linkage between $	ext{C}_{1}$ and $	ext{C}_{4}$ carbons of the pentose sugar
D. Quaternary structure of proteins represents overall folding of the polypeptide chain.
Choose the correct answer from the options given below:

Accepted Answer

(C) A and B Only

Answer

(A) A, C and D Only

Answer

(B) A, B and D Only

Answer

(D) B and C Only

Question 62

The correct order of the rate of the reaction for the following reaction with respect to nucleophiles is:
$	ext{CH}_{3}	ext{Br} + 	ext{Nu}^{\ominus} \longrightarrow 	ext{CH}_{3}	ext{Nu} + 	ext{Br}^{\ominus}$

Accepted Answer

(D) ${}^{-}	ext{OH} > 	ext{PhO}^{-} > 	ext{CH}_{3}	ext{COO}^{-} > 	ext{ClO}_{4}^{-}$

Answer

(A) $	ext{PhO}^{-} > {}^{-}	ext{OH} > 	ext{CH}_{3}	ext{COO}^{-} > 	ext{ClO}_{4}^{-}$

Answer

(B) $	ext{ClO}_{4}^{-} > 	ext{CH}_{3}	ext{COO}^{-} > {}^{-}	ext{OH} > 	ext{PhO}^{-}$

Answer

(C) $	ext{CH}_{3}	ext{COO}^{-} > 	ext{PhO}^{-} > {}^{-}	ext{OH} > 	ext{ClO}_{4}^{-}$

Question 63

Given below are two statements:
Statement I: Crystal Field Stabilization Energy (CFSE) of $	ext{[Cr(H}_{2}	ext{O)}_{6}	ext{]}^{2+}$ is greater than that of $	ext{[Mn(H}_{2}	ext{O)}_{6}	ext{]}^{2+}$.
Statement II: Potassium ferricyanide has a greater spin-only magnetic moment than sodium Ferrocyanide.
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 64

The correct increasing order of $	ext{C}-	ext{H}(	ext{A})$, $	ext{C}-	ext{O}(	ext{B})$, $	ext{C}=	ext{O}(	ext{C})$ and $	ext{C}\equiv 	ext{N}(	ext{D})$ bonds in terms of covalent bond length is:

Accepted Answer

(B) $	ext{A} < 	ext{D} < 	ext{C} < 	ext{B}$

Answer

(A) $	ext{A} < 	ext{B} < 	ext{C} < 	ext{D}$

Answer

(C) $	ext{D} < 	ext{C} < 	ext{B} < 	ext{A}$

Answer

(D) $	ext{D} < 	ext{C} < 	ext{A} < 	ext{B}$

Pair of Compounds	Type of Isomers
A.2-Methylpropene and but-1-ene	I.Stereoisomers
B.Cis-but-2-ene and trans-but-2-ene	II.Position isomers
C.2-Butanol and diethyl ether	III.Chain isomers
D.But-1-ene and but-2-ene	IV.Functional group isomers

Reagents	Reaction Name (Involving aldehydes)
A. $ext{H}_{2}$ , $ext{Pd-BaSO}_{4}$	I.Etard Reaction
B. $ext{SnCl}_{2}$ , HCl	II.Rosenmund Reduction
C. $ext{CrO}_{2} ext{Cl}_{2}$ , $ext{CS}_{2}$	III.Gatterman - Koch Reaction
D. $ext{CO,HCl}$ , Anhyd. $ext{AlCl}_{3}$	IV.Stephen Reaction

JEE Main 21 January 2026 Shift 2 Question Paper with Answers

Physics — JEE Main 21 January 2026 Shift 2

Chemistry — JEE Main 21 January 2026 Shift 2

Mathematics — JEE Main 21 January 2026 Shift 2

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