JEE Main 31 January 2024 Shift 2 Question Paper

Question 1

The number of ways in which 21 identical apples can be distributed among three children such that each child gets at least 2 apples, is

Accepted Answer

(D) 136

Answer

(A) 406

Answer

(B) 130

Answer

(C) 142

Question 2

Let A($a$, $b$), B(3, 4) and C($-6$, $-8$) respectively denote the centroid, circumcentre and orthocentre of a triangle. Then, the distance of the point P($2a+3$, $7b+5$) from the line $2x+3y-4=0$ measured parallel to the line $x-2y-1=0$ is

Accepted Answer

(C) $\dfrac{17\sqrt{5}}{7}$

Answer

(A) $\dfrac{15\sqrt{5}}{7}$

Answer

(B) $\dfrac{17\sqrt{5}}{6}$

Answer

(D) $\dfrac{4\sqrt{5}}{17}$

Question 3

Let $z_1$ and $z_2$ be two complex numbers such that $z_1+z_2=5$ and $z_1^3+z_2^3=20+15i$. Then $\left|z_1^4+z_2^4\right|$ equals

Accepted Answer

(B) $75$

Answer

(A) $30\sqrt{3}$

Answer

(C) $15\sqrt{15}$

Answer

(D) $25\sqrt{3}$

Question 4

Let a variable line passing through the centre of the circle $x^2+y^2-16x-4y=0$, meet the positive co-ordinate axes at the points A and B. Then the minimum value of $OA+OB$, where O is the origin, is equal to

Accepted Answer

(B) 18

Answer

(A) 12

Answer

(C) 20

Answer

(D) 24

Question 5

Let $(\alpha,\beta,\gamma)$ be the mirror image of the point $(2,3,5)$ in the line $\dfrac{x-1}{2}=\dfrac{y-2}{3}=\dfrac{z-3}{4}$. Then $2\alpha+3\beta+4\gamma$ is equal to

Accepted Answer

(B) 33

Answer

(A) 32

Answer

(C) 31

Answer

(D) 34

Question 6

Let P be a parabola with vertex $(2,3)$ and directrix $2x+y=6$. Let an ellipse $E:\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1$, $a>b$, of eccentricity $\dfrac{1}{\sqrt{2}}$ pass through the focus of the parabola P. Then the square of the length of the latus rectum of E, is

Accepted Answer

(D) $\dfrac{656}{25}$

Answer

(A) $\dfrac{385}{8}$

Answer

(B) $\dfrac{347}{8}$

Answer

(C) $\dfrac{512}{25}$

Question 7

The temperature $T(t)$ of a body at time $t=0$ is $160^\circ$F and it decreases continuously as per the differential equation $\dfrac{dT}{dt}=-K(T-80)$, where K is a positive constant. If $T(15)=120^\circ$F, then $T(45)$ is equal to

Accepted Answer

(C) $90^\circ$F

Answer

(A) $85^\circ$F

Answer

(B) $95^\circ$F

Answer

(D) $80^\circ$F

Question 8

Let $2^{	ext{nd}}$, $8^{	ext{th}}$ and $44^{	ext{th}}$ terms of a non-constant A.P. be respectively the $1^{	ext{st}}$, $2^{	ext{nd}}$ and $3^{	ext{rd}}$ terms of G.P. If the first term of A.P. is 1, then the sum of first 20 terms is equal to

Accepted Answer

(D) 970

Answer

(A) 980

Answer

(B) 960

Answer

(C) 990

Question 9

Let $f:R	o(0,\infty)$ be strictly increasing function such that $\displaystyle\lim_{x	o\infty}\dfrac{f(7x)}{f(x)}=1$. Then the value of $\displaystyle\lim_{x	o\infty}\left[\dfrac{f(5x)}{f(x)}-1ight]$ is equal to

Accepted Answer

(B) 0

Answer

(A) 4

Answer

(C) $\dfrac{7}{5}$

Answer

(D) 1

Question 10

The area of the region enclosed by the parabola $y=4x-x^2$ and $3y=(x-4)^2$ is equal to

Accepted Answer

(C) 6

Answer

(A) $\dfrac{32}{9}$

Answer

(B) 4

Answer

(D) $\dfrac{14}{3}$

Question 11

Let the mean and the variance of 6 observations $a$, $b$, 68, 44, 48, 60 be 55 and 194, respectively. If $a>b$, then $a+3b$ is

Accepted Answer

(C) 180

Answer

(A) 200

Answer

(B) 190

Answer

(D) 210

Question 12

If the function $f:(-\infty,-1]	o(a,b]$ defined by $f(x)=e^{x^3-3x+1}$ is one-one and onto, then the distance of the point $P(2b+4,\ a+2)$ from the line $x+e^{-3}y=4$ is

Accepted Answer

(A) $2\sqrt{1+e^6}$

Answer

(B) $4\sqrt{1+e^6}$

Answer

(C) $3\sqrt{1+e^6}$

Answer

(D) $\sqrt{1+e^6}$

Question 13

Consider the function $f:(0,\infty)	o R$ defined by $f(x)=e^{-\left|\log_e xight|}$. If $m$ and $n$ be respectively the number of points at which $f$ is not continuous and $f$ is not differentiable, then $m+n$ is

Accepted Answer

(C) 1

Answer

(A) 0

Answer

(B) 3

Answer

(D) 2

Question 14

The number of solutions, of the equation $e^{\sin x}-2e^{-\sin x}=2$ is

Accepted Answer

(D) 0

Answer

(A) 2

Answer

(B) more than 2

Answer

(C) 1

Question 15

If $a=\sin^{-1}(\sin(5))$ and $b=\cos^{-1}(\cos(5))$, then $a^2+b^2$ is equal to

Accepted Answer

(B) $8\pi^2-40\pi+50$

Answer

(A) $4\pi^2+25$

Answer

(C) $4\pi^2-20\pi+50$

Answer

(D) 25

Question 16

If for some $m$, $n$; $\ ^6C_m+2\left(^6C_{m+1}\right)+\ ^6C_{m+2}>\ ^8C_3$ and $\ ^{n-1}P_3:\ ^nP_4=1:8$, then $\ ^nP_{m+1}+\ ^{n+1}C_m$ is equal to

Accepted Answer

(D) 372

Answer

(A) 380

Answer

(B) 376

Answer

(C) 384

Question 17

A coin is biased so that a head is twice as likely to occur as a tail. If the coin is tossed 3 times, then the probability of getting two tails and one head is

Accepted Answer

(A) $\dfrac{2}{9}$

Answer

(B) $\dfrac{1}{9}$

Answer

(C) $\dfrac{2}{27}$

Answer

(D) $\dfrac{1}{27}$

Question 18

Let A be a $3	imes3$ real matrix such that $A\begin{pmatrix}1\0\1\end{pmatrix}=2\begin{pmatrix}1\0\1\end{pmatrix}$, $A\begin{pmatrix}-1\0\1\end{pmatrix}=4\begin{pmatrix}-1\0\1\end{pmatrix}$, $A\begin{pmatrix}0\1\0\end{pmatrix}=2\begin{pmatrix}0\1\0\end{pmatrix}$. Then, the system $(A-3I)\begin{pmatrix}x\y\z\end{pmatrix}=\begin{pmatrix}1\2\3\end{pmatrix}$ has

Accepted Answer

(A) unique solution

Answer

(B) exactly two solutions

Answer

(C) no solution

Answer

(D) infinitely many solutions

Question 19

The shortest distance between lines $L_1$ and $L_2$, where $L_1:\dfrac{x-1}{2}=\dfrac{y+1}{-3}=\dfrac{z+4}{2}$ and $L_2$ is the line passing through the points $A(-4,4,3)$, $B(-1,6,3)$ and perpendicular to the line $\dfrac{x-3}{-2}=\dfrac{y}{3}=\dfrac{z-1}{1}$, is

Accepted Answer

(C) $\dfrac{141}{\sqrt{221}}$

Answer

(A) $\dfrac{121}{\sqrt{221}}$

Answer

(B) $\dfrac{24}{\sqrt{117}}$

Answer

(D) $\dfrac{42}{\sqrt{117}}$

Question 20

$\left|\dfrac{120}{\pi^3}\displaystyle\int_0^{\pi}\dfrac{x^2\sin x\cos x}{\sin^4 x+\cos^4 x}\,dx\right|$ is equal to ______.

Accepted Answer

15

Question 21

Let $a$, $b$, $c$ be the length of three sides of a triangle satisfying the condition $(a^2+b^2)x^2-2b(a+c)x+(b^2+c^2)=0$. If the set of all possible values of $x$ is the interval $(\alpha,\beta)$, then $12(\alpha^2+\beta^2)$ is equal to ______.

Accepted Answer

36

Question 22

Let $A(-2,-1)$, $B(1,0)$, $C(\alpha,\beta)$ and $D(\gamma,\delta)$ be the vertices of a parallelogram ABCD. If the point C lies on $2x-y=5$ and the point D lies on $3x-2y=6$, then the value of $|\alpha+\beta+\gamma+\delta|$ is equal to ______.

Accepted Answer

32

Question 23

Let the coefficient of $x^r$ in the expansion of $(x+3)^{n-1}+(x+3)^{n-2}(x+2)+(x+3)^{n-3}(x+2)^2+\ldots+(x+2)^{n-1}$ be $a_r$. If $\displaystyle\sum_{r=0}^{n}a_r=\beta^n-\alpha^n$, $\beta,\alpha\in N$, then the value of $\beta^2+\alpha^2$ equals ______.

Accepted Answer

25

Question 24

Let A be a $3	imes3$ matrix and $\det(A)=2$. If $n=\det\left(	ext{adj}\left(	ext{adj}\left(\ldots\left(	ext{adj}Aight)ight)ight)ight)$ (adj applied 2024 times). Then the remainder when $n$ is divided by 9 is equal to ______.

Accepted Answer

7

Question 25

Let $\vec{a}=3\hat{i}+2\hat{j}+\hat{k}$, $\vec{b}=2\hat{i}-\hat{j}+3\hat{k}$ and $\vec{c}$ be a vector such that $(\vec{a}+\vec{b})	imes\vec{c}=2(\vec{a}	imes\vec{b})+24\hat{j}-6\hat{k}$ and $(\vec{a}-\vec{b}+\hat{i})\cdot\vec{c}=-3$. Then $|\vec{c}|^2$ is equal to ______.

Accepted Answer

38

Question 26

If $\displaystyle\lim_{x	o0}\dfrac{ax^2e^x-b\log_e(1+x)+cxe^{-x}}{x^2\sin x}=1$, then $16(a^2+b^2+c^2)$ is equal to ______.

Accepted Answer

81

Question 27

A line passes through $A(4,-6,-2)$ and $B(16,-2,4)$. The point $P(a,b,c)$ where $a,b,c$ are non-negative integers, on the line AB lies at a distance of 21 units, from the point A. The distance between the points $P(a,b,c)$ and $Q(4,-12,3)$ is equal to ______.

Accepted Answer

22

Question 28

Let $y=y(x)$ be the solution of the differential equation $\sec^2 x\,dx+\left(e^{2y}	an^2 x+	an xight)dy=0$, $0<x<\dfrac{\pi}{2}$, $y\left(\dfrac{\pi}{4}ight)=0$. If $y\left(\dfrac{\pi}{6}ight)=\alpha$, Then $e^{8\alpha}$ is equal to ______.

Accepted Answer

9

Question 29

Let $A=\{1,2,3,\ldots\ldots100\}$. Let R be a relation on A defined by $(x,y)\in R$ if and only if $2x=3y$. Let $R_1$ be a symmetric relation on A such that $R\subset R_1$ and the number of elements in $R_1$ is $n$. Then the minimum value of $n$ is ______.

Accepted Answer

66

Question 30

A light string passing over a smooth light fixed pulley connects two blocks of masses $m_1$ and $m_2$. If the acceleration of the system is $\dfrac{g}{8}$, then the ratio of masses is

Accepted Answer

(A) $\dfrac{9}{7}$

Answer

(B) $\dfrac{8}{1}$

Answer

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

Answer

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

Question 31

A uniform magnetic field of $2	imes10^{-3}$ T acts along positive Y-direction. A rectangular loop of sides 20 cm and 10 cm with current of 5 A is in Y-Z plane. The current is in anticlockwise sense with reference to negative X axis. Magnitude and direction of the torque is

Accepted Answer

(B) $2	imes10^{-4}$ N–m along negative Z-direction

Answer

(A) $2	imes10^{-4}$ N–m along positive Z-direction

Answer

(C) $2	imes10^{-4}$ N–m along positive X-direction

Answer

(D) $2	imes10^{-4}$ N–m along positive Y-direction

Question 32

The measured value of the length of a simple pendulum is 20 cm with 2 mm accuracy. The time for 50 oscillations was measured to be 40 seconds with 1 second resolution. From these measurements, the accuracy in the measurement of acceleration due to gravity is N%. The value of N is:

Accepted Answer

(C) 6

Answer

(A) 4

Answer

(B) 8

Answer

(D) 5

Question 33

Force between two point charges $q_1$ and $q_2$ placed in vacuum at '$r$' cm apart is F. Force between them when placed in a medium having dielectric $K=5$ at '$r/5$' cm apart will be:

Accepted Answer

(B) 5F

Answer

(A) $\dfrac{F}{25}$

Answer

(C) $\dfrac{F}{5}$

Answer

(D) 25F

Question 34

An AC voltage $V=20\sin 200\pi t$ is applied to a series LCR circuit which drives a current $I=10\sin\left(200\pi t+\dfrac{\pi}{3}\right)$. The average power dissipated is:

Accepted Answer

(D) 50 W

Answer

(A) 21.6 W

Answer

(B) 200 W

Answer

(C) 173.2 W

Question 35

When unpolarized light is incident at an angle of $60^\circ$ on a transparent medium from air. The reflected ray is completely polarized. The angle of refraction in the medium is

Accepted Answer

(A) $30^\circ$

Answer

(B) $60^\circ$

Answer

(C) $90^\circ$

Answer

(D) $45^\circ$

Question 36

The speed of sound in oxygen at S.T.P. will be approximately: (Given, $R=8.3\ 	ext{JK}^{-1}$, $\gamma=1.4$)

Accepted Answer

(A) 310 m/s

Answer

(B) 333 m/s

Answer

(C) 341 m/s

Answer

(D) 325 m/s

Question 37

A gas mixture consists of 8 moles of argon and 6 moles of oxygen at temperature T. Neglecting all vibrational modes, the total internal energy of the system is

Accepted Answer

(C) 27 RT

Answer

(A) 29 RT

Answer

(B) 20 RT

Answer

(D) 21 RT

Question 38

The resistance per centimeter of a meter bridge wire is $r$, with $X\,\Omega$ resistance in left gap. Balancing length from left end is at 40 cm with $25\,\Omega$ resistance in right gap. If the wire is replaced by another wire of double the resistance per centimeter, the new balancing length from same settings will be at

Accepted Answer

(D) 40 cm

Answer

(A) 20 cm

Answer

(B) 10 cm

Answer

(C) 80 cm

Question 39

Given below are two statements:
Statement-I: Electromagnetic waves carry energy as they travel through space and this energy is equally shared by the electric and magnetic fields.
Statement-II: When electromagnetic waves strike a surface, a pressure is exerted on the surface.
In the light of the above statements, choose the most appropriate answer from the options given below:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 40

In a photoelectric effect experiment a light of frequency 1.5 times the threshold frequency is made to fall on the surface of photosensitive material. Now if the frequency is halved and intensity is doubled, the number of photo electrons emitted will be:

Accepted Answer

(C) Zero

Answer

(A) Doubled

Answer

(B) Quadrupled

Answer

(D) Halved

Question 41

By what percentage will the illumination of the lamp decrease if the current drops by 20%?

Accepted Answer

(C) 36%

Answer

(A) 46%

Answer

(B) 26%

Answer

(D) 56%

Question 42

If two vectors $\vec{A}$ and $\vec{B}$ having equal magnitude R are inclined at an angle $	heta$, then

Accepted Answer

(C) $\left|\vec{A}+\vec{B}ight|=2R\cos\left(\dfrac{	heta}{2}ight)$

Answer

(A) $\left|\vec{A}-\vec{B}ight|=\sqrt{2}\,R\sin\left(\dfrac{	heta}{2}ight)$

Answer

(B) $\left|\vec{A}+\vec{B}ight|=2R\sin\left(\dfrac{	heta}{2}ight)$

Answer

(D) $\left|\vec{A}-\vec{B}ight|=2R\cos\left(\dfrac{	heta}{2}ight)$

Question 43

The mass number of nucleus having radius equal to half of the radius of nucleus with mass number 192 is:

Accepted Answer

(A) 24

Answer

(B) 32

Answer

(C) 40

Answer

(D) 20

Question 44

The mass of the moon is $\dfrac{1}{144}$ times the mass of a planet and its diameter is $\dfrac{1}{16}$ times the diameter of a planet. If the escape velocity on the planet is $v$, the escape velocity on the moon will be:

Accepted Answer

(B) $\dfrac{v}{3}$

Answer

(A) $\dfrac{v}{4}$

Answer

(C) $\dfrac{v}{12}$

Answer

(D) $\dfrac{v}{6}$

Question 45

A small spherical ball of radius $r$, falling through a viscous medium of negligible density has terminal velocity $v$. Another ball of the same mass but of radius $2r$, falling through the same viscous medium will have terminal velocity:

Accepted Answer

(A) $\dfrac{v}{2}$

Answer

(B) $\dfrac{v}{4}$

Answer

(C) $4v$

Answer

(D) $2v$

Question 46

A body of mass 2 kg begins to move under the action of a time dependent force given by $\vec{F}=\left(6t\,\hat{i}+6t^2\,\hat{j}\right)$ N. The power developed by the force at the time $t$ is given by

Accepted Answer

(D) $\left(9t^3+6t^5\right)$ W

Answer

(A) $\left(6t^4+9t^5\right)$ W

Answer

(B) $\left(3t^3+6t^5\right)$ W

Answer

(C) $\left(9t^5+6t^3\right)$ W

Question 47

The output of the given circuit diagram (shown in the figure) is

Accepted Answer

(C) A,B,Y: (0,0)→0, (1,0)→0, (0,1)→0, (1,1)→0

Answer

(A) A,B,Y: (0,0)→0, (1,0)→0, (0,1)→0, (1,1)→1

Answer

(B) A,B,Y: (0,0)→0, (1,0)→1, (0,1)→1, (1,1)→0

Answer

(D) A,B,Y: (0,0)→0, (1,0)→0, (0,1)→1, (1,1)→0

Question 48

Consider two physical quantities A and B related to each other as $E=\dfrac{B-x^2}{At}$ where E, $x$ and $t$ have dimensions of energy, length and time respectively. The dimension of AB is

Accepted Answer

(B) $L^2M^{-1}T^1$

Answer

(A) $L^{-2}M^1T^0$

Answer

(C) $L^{-2}M^{-1}T^1$

Answer

(D) $L^0M^1T^{-1}$

Question 49

In the following circuit, the battery has an emf of 2 V and an internal resistance of $\dfrac{2}{3}\,\Omega$. The power consumption in the entire circuit is ______ W.

Accepted Answer

3

Question 50

Light from a point source in air falls on a convex curved surface of radius 20 cm and refractive index 1.5. If the source is located at 100 cm from the convex surface, the image will be formed at ______ cm from the object.

Accepted Answer

200

Question 51

The magnetic flux $\phi$ (in weber) linked with a closed circuit of resistance $8\,\Omega$ varies with time (in seconds) as $\phi=5t^2-36t+1$. The induced current in the circuit at $t=2$ s is ______ A.

Accepted Answer

2

Question 52

Two blocks of mass 2 kg and 4 kg are connected by a metal wire going over a smooth pulley as shown in figure. The radius of wire is $4.0	imes10^{-5}$ m and Young's modulus of the metal $2.0	imes10^{11}$ N/m$^2$. The longitudinal strain developed in the wire is $\dfrac{1}{\alpha\pi}$. The value of $\alpha$ is ______. [Use $g=10\ 	ext{m/s}^2$]

Accepted Answer

12

Question 53

A body of mass '$m$' is projected with a speed '$u$' making an angle of $45^\circ$ with the ground. The angular momentum of the body about the point of projection, at the highest point is expressed as $\dfrac{\sqrt{2}\,mu^3}{Xg}$. The value of '$X$' is ______.

Accepted Answer

8

Question 54

Two circular coils P and Q of 100 turns each have same radius of $\pi$ cm. The currents in P and Q are 1 A and 2 A respectively. P and Q are placed with their planes mutually perpendicular with their centers coincide. The resultant magnetic field induction at the center of the coils is $\sqrt{x}$ mT, where $x=$ ______. [Use $\mu_0=4\pi	imes10^{-7}$ T A m$^{-1}$]

Accepted Answer

20

Question 55

The distance between charges $+q$ and $-q$ is $2\ell$ and between $+2q$ and $-2q$ is $4\ell$. The electrostatic potential at point P at a distance $r$ from centre O is $-\alpha\dfrac{q\ell}{r^2}	imes10^9$ V, where the value of $\alpha$ is ______. (Use $\dfrac{1}{4\pi\varepsilon_0}=9	imes10^9$ Nm$^2$C$^{-2}$)

Accepted Answer

27

Question 56

Two identical spheres each of mass 2 kg and radius 50 cm are fixed at the ends of a light rod so that the separation between the centers is 150 cm. Then, moment of inertia of the system about an axis perpendicular to the rod and passing through its middle point is $\dfrac{x}{20}$ kg m$^2$, where the value of $x$ is ______.

Accepted Answer

53

Question 57

The time period of simple harmonic motion of mass M in the given figure is $\pi\sqrt{\dfrac{\alpha M}{5K}}$, where the value of $\alpha$ is ______.

Accepted Answer

12

Question 58

A nucleus has mass number $A_1$ and volume $V_1$. Another nucleus has mass number $A_2$ and volume $V_2$. If relation between mass number is $A_2=4A_1$, then $\dfrac{V_2}{V_1}=$ ______.

Accepted Answer

4

Question 59

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 60

A sample of CaCO$_3$ and MgCO$_3$ weighed 2.21 g is ignited to constant weight of 1.152 g. The composition of mixture is: (Given molar mass in g mol$^{-1}$ CaCO$_3$:100, MgCO$_3$:84)

Accepted Answer

(A) 1.187 g CaCO$_3$ + 1.023 g MgCO$_3$

Answer

(B) 1.023 g CaCO$_3$ + 1.023 g MgCO$_3$

Answer

(C) 1.187 g CaCO$_3$ + 1.187 g MgCO$_3$

Answer

(D) 1.023 g CaCO$_3$ + 1.187 g MgCO$_3$

Question 61

Identify A and B in the following reaction sequence (shown in the figure).

Accepted Answer

(A) (1)

Answer

(B) (2)

Answer

(C) (3)

Answer

(D) (4)

Question 62

Given below are two statements:
Statement-I: $S_8$ solid undergoes disproportionation reaction under alkaline conditions to form $S^{2-}$ and $S_2O_3^{2-}$.
Statement-II: $ClO_4^-$ can undergo disproportionation reaction under acidic condition.
In the light of the above statements, choose the most appropriate answer from the options given below:

Accepted Answer

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

Answer

(B) Statement I is incorrect but statement II is correct

Answer

(C) Both Statement I and Statement II are incorrect

Answer

(D) Both Statement I and statement II are correct

Question 63

Identify major product 'P' formed in the following reaction (shown in the figure).

Accepted Answer

(D) (4)

Answer

(A) (1)

Answer

(B) (2)

Answer

(C) (3)

Question 64

Major product of the following reaction is (shown in the figure).

Accepted Answer

(C) (3)

Accepted Answer

(D) (4)

Answer

(A) (1)

Answer

(B) (2)

List-I (Complex ion)	List-II (Electronic Configuration)
A. $[Cr(H_2O)_6]^{3+}$	I. $t_{2g}^{2}e_g^{0}$
B. $[Fe(H_2O)_6]^{3+}$	II. $t_{2g}^{3}e_g^{0}$
C. $[Ni(H_2O)_6]^{2+}$	III. $t_{2g}^{3}e_g^{2}$
D. $[V(H_2O)_6]^{3+}$	IV. $t_{2g}^{6}e_g^{2}$

JEE Main 31 January 2024 Shift 2 Question Paper with Answers

Physics — JEE Main 31 January 2024 Shift 2

Chemistry — JEE Main 31 January 2024 Shift 2

Mathematics — JEE Main 31 January 2024 Shift 2

Chapters tested in this paper

Attempt this paper under exam timing.