JEE Main 29 January 2024 Shift 2 Question Paper

Question 1

Let $A=\begin{bmatrix}2 & 1 & 2\ 6 & 2 & 11\ 3 & 3 & 2\end{bmatrix}$ and $P=\begin{bmatrix}1 & 2 & 0\ 5 & 0 & 2\ 7 & 1 & 5\end{bmatrix}$. The sum of the prime factors of $|P^{-1}AP-2I|$ is equal to:

Accepted Answer

(A) 26

Answer

(B) 27

Answer

(C) 66

Answer

(D) 23

Question 2

Number of ways of arranging 8 identical books into 4 identical shelves where any number of shelves may remain empty is equal to:

Accepted Answer

(D) 15

Answer

(A) 18

Answer

(B) 16

Answer

(C) 12

Question 3

Let $P(3,2,3)$, $Q(4,6,2)$ and $R(7,3,2)$ be the vertices of $	riangle PQR$. Then, the angle $\angle QPR$ is:

Accepted Answer

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

Answer

(A) $\dfrac{\pi}{6}$

Answer

(B) $\cos^{-1}\left(\dfrac{7}{18}\right)$

Answer

(C) $\cos^{-1}\left(\dfrac{1}{18}\right)$

Question 4

If the mean and variance of five observations are $\dfrac{24}{5}$ and $\dfrac{194}{25}$ respectively and the mean of first four observations is $\dfrac{7}{2}$, then the variance of the first four observations is equal to:

Accepted Answer

(C) $\dfrac{5}{4}$

Answer

(A) $\dfrac{4}{5}$

Answer

(B) $\dfrac{77}{12}$

Answer

(D) $\dfrac{105}{4}$

Question 5

The function $f(x)=2x+3(x)^{\frac{2}{3}},\ x\in\mathbb{R}$, has:

Accepted Answer

(C) exactly one point of local maxima and exactly one point of local minima

Answer

(A) exactly one point of local minima and no point of local maxima

Answer

(B) exactly one point of local maxima and no point of local minima

Answer

(D) exactly two points of local maxima and exactly one point of local minima

Question 6

Let $r$ and $	heta$ respectively be the modulus and amplitude of the complex number $z=2-i\left(2	an\dfrac{5\pi}{8}ight)$, then $(r,	heta)$ is equal to:

Accepted Answer

(A) $\left(2\sec\dfrac{3\pi}{8},\dfrac{3\pi}{8}\right)$

Answer

(B) $\left(2\sec\dfrac{3\pi}{8},\dfrac{5\pi}{8}\right)$

Answer

(C) $\left(2\sec\dfrac{5\pi}{8},\dfrac{3\pi}{8}\right)$

Answer

(D) $\left(2\sec\dfrac{11\pi}{8},\dfrac{11\pi}{8}\right)$

Question 7

The sum of the solutions $x\in\mathbb{R}$ of the equation $\dfrac{3\cos 2x+\cos^3 2x}{\cos^6 x-\sin^6 x}=x^3-x^2+6$ is:

Accepted Answer

(C) $-1$

Answer

(A) 0

Answer

(B) 1

Answer

(D) 3

Question 8

Let $\overrightarrow{OA}=\vec a,\ \overrightarrow{OB}=12\vec a+4\vec b$ and $\overrightarrow{OC}=\vec b$, where $O$ is the origin. If $S$ is the parallelogram with adjacent sides $OA$ and $OC$, then $\dfrac{	ext{area of the quadrilateral }OABC}{	ext{area of }S}$ is equal to:

Accepted Answer

(D) 8

Answer

(A) 6

Answer

(B) 10

Answer

(C) 7

Question 9

If $\log_e a$, $\log_e b$, $\log_e c$ are in an A.P. and $\log_e a-\log_e 2b$, $\log_e 2b-\log_e 3c$, $\log_e 3c-\log_e a$ are also in an A.P., then $a:b:c$ is equal to:

Accepted Answer

(A) $9:6:4$

Answer

(B) $16:4:1$

Answer

(C) $25:10:4$

Answer

(D) $6:3:2$

Question 10

If $\displaystyle\int\dfrac{\sin^{\frac{3}{2}}x+\cos^{\frac{3}{2}}x}{\sqrt{\sin^3 x\,\cos^3 x\,\sin(x-	heta)}}\,dx=A\sqrt{\cos	heta	an x-\sin	heta}+B\sqrt{\cos	heta-\sin	heta\cot x}+C$, where $C$ is the integration constant, then $AB$ is equal to:

Accepted Answer

(D) $8\,\mathrm{cosec}(2	heta)$

Answer

(A) $4\,\mathrm{cosec}(2	heta)$

Answer

(B) $4\sec	heta$

Answer

(C) $2\sec	heta$

Question 11

The distance of the point $(2,3)$ from the line $2x-3y+28=0$, measured parallel to the line $\sqrt{3}x-y+1=0$, is equal to:

Accepted Answer

(D) $4+6\sqrt{3}$

Answer

(A) $4\sqrt{2}$

Answer

(B) $6\sqrt{3}$

Answer

(C) $3+4\sqrt{2}$

Question 12

If $\sin\left(\dfrac{y}{x}\right)=\log_e|x|+\dfrac{\alpha}{2}$ is the solution of the differential equation $x\cos\left(\dfrac{y}{x}\right)\dfrac{dy}{dx}=y\cos\left(\dfrac{y}{x}\right)+x$ and $y(1)=\dfrac{\pi}{3}$, then $\alpha^2$ is equal to:

Accepted Answer

(A) 3

Answer

(B) 12

Answer

(C) 4

Answer

(D) 9

Question 13

If each term of a geometric progression $a_1,a_2,a_3,\ldots$ with $a_1=\dfrac{1}{8}$ and $a_2
eq a_1$, is the arithmetic mean of the next two terms and $S_n=a_1+a_2+\ldots+a_n$, then $S_{20}-S_{18}$ is equal to:

Accepted Answer

(D) $-2^{15}$

Answer

(A) $2^{15}$

Answer

(B) $-2^{18}$

Answer

(C) $2^{18}$

Question 14

Let $A$ be the point of intersection of the lines $3x+2y=14$, $5x-y=6$ and $B$ be the point of intersection of the lines $4x+3y=8$, $6x+y=5$. The distance of the point $P(5,-2)$ from the line $AB$ is:

Accepted Answer

(D) 6

Answer

(A) $\dfrac{13}{2}$

Answer

(B) 8

Answer

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

Question 15

Let $x=\dfrac{m}{n}$ ($m$, $n$ are co-prime natural numbers) be a solution of the equation $\cos\left(2\sin^{-1}x\right)=\dfrac{1}{9}$ and let $\alpha,\beta\,(\alpha>\beta)$ be the roots of the equation $mx^2-nx-m+n=0$. Then the point $(\alpha,\beta)$ lies on the line:

Accepted Answer

(D) $5x+8y=9$

Answer

(A) $3x+2y=2$

Answer

(B) $5x-8y=-9$

Answer

(C) $3x-2y=-2$

Question 16

The function $f(x)=\dfrac{x}{x^2-6x-16},\ x\in\mathbb{R}-\{-2,8\}$:

Accepted Answer

(D) decreasing in $\mathbb{R}-\{-2,8\}$

Answer

(A) increasing in $(-2,8)$ and decreasing in $(-\infty,-2)\cup(8,\infty)$

Answer

(B) decreasing in $(-\infty,-2)\cup(-2,8)$ and increasing in $(8,\infty)$

Answer

(C) decreasing in $(-\infty,-2)\cup(8,\infty)$ and increasing in $(-2,8)$

Question 17

Let $y=\log_e\left(\dfrac{1-x^2}{1+x^2}\right),\ -1<x<1$. Then at $x=\dfrac{1}{2}$, the value of $225(y'-y'')$ is equal to:

Accepted Answer

(D) 736

Answer

(A) 732

Answer

(B) 746

Answer

(C) 742

Question 18

If $R$ is the smallest equivalence relation on the set $\{1,2,3,4\}$ such that $\{(1,2),(1,3)\}\subset R$, then the number of elements in $R$ is:

Accepted Answer

(A) 10

Answer

(B) 12

Answer

(C) 8

Answer

(D) 15

Question 19

An integer is chosen at random from the integers $1,2,3,\ldots,50$. The probability that the chosen integer is a multiple of atleast one of $4,6$ and $7$ is:

Accepted Answer

(B) $\dfrac{21}{50}$

Answer

(A) $\dfrac{8}{25}$

Answer

(C) $\dfrac{9}{50}$

Answer

(D) $\dfrac{14}{50}$

Question 20

Let a unit vector $\hat u=x\hat i+y\hat j+z\hat k$ make angles $\dfrac{\pi}{2},\dfrac{\pi}{3}$ and $\dfrac{2\pi}{3}$ with the vectors $\dfrac{1}{\sqrt2}\hat i+\dfrac{1}{\sqrt2}\hat j$, $\dfrac{1}{\sqrt2}\hat j+\dfrac{1}{\sqrt2}\hat k$ and $\dfrac{1}{\sqrt2}\hat i+\dfrac{1}{\sqrt2}\hat k$ respectively. If $\vec v=\dfrac{1}{\sqrt2}\hat i+\dfrac{1}{\sqrt2}\hat j+\dfrac{1}{\sqrt2}\hat k$, then $|\hat u-\vec v|^2$ is equal to:

Accepted Answer

(B) $\dfrac{5}{2}$

Answer

(A) $\dfrac{11}{2}$

Answer

(C) 9

Answer

(D) 7

Question 21

Let $\alpha,\beta$ be the roots of the equation $x^2-\sqrt6\,x+3=0$ such that $	ext{Im}(\alpha)>	ext{Im}(\beta)$. Let $a,b$ be integers not divisible by 3 and $n$ be a natural number such that $\dfrac{\alpha^{99}}{\beta}+\alpha^{98}=3^n(a+ib),\ i=\sqrt{-1}$. Then $n+a+b$ is equal to ___.

Accepted Answer

49

Question 22

Let for any three distinct consecutive terms $a,b,c$ of an A.P, the lines $ax+by+c=0$ be concurrent at the point $P$ and $Q\,(\alpha,\beta)$ be a point such that the system of equations $x+y+z=6$, $2x+5y+\alpha z=\beta$ and $x+2y+3z=4$, has infinitely many solutions. Then $(PQ)^2$ is equal to ___.

Accepted Answer

113

Question 23

Let $P(\alpha,\beta)$ be a point on the parabola $y^2=4x$. If $P$ also lies on the chord of the parabola $x^2=8y$ whose mid point is $\left(1,\dfrac{5}{4}\right)$. Then $(\alpha-28)(\beta-8)$ is equal to ___.

Accepted Answer

192

Question 24

If $\displaystyle\int_{\pi/6}^{\pi/3}\sqrt{1-\sin 2x}\,dx=\alpha+\beta\sqrt2+\gamma\sqrt3$, where $\alpha,\beta$ and $\gamma$ are rational numbers, then $3\alpha+4\beta-\gamma$ is equal to ___.

Accepted Answer

6

Question 25

Let the area of the region $\{(x,y):0\le x\le 3,\ 0\le y\le\min\{x^2+2,\,2x+2\}\}$ be $A$. Then $12A$ is equal to ___.

Accepted Answer

164

Question 26

Let $O$ be the origin, and $M$ and $N$ be the points on the lines $\dfrac{x-5}{4}=\dfrac{y-4}{1}=\dfrac{z-5}{3}$ and $\dfrac{x+8}{12}=\dfrac{y+2}{5}=\dfrac{z+11}{9}$ respectively such that $MN$ is the shortest distance between the given lines. Then $\overrightarrow{OM}\cdot\overrightarrow{ON}$ is equal to ___.

Accepted Answer

9

Question 27

Let $f(x)=\sqrt{\displaystyle\lim_{r	o x}\left\{\dfrac{2r^2[(f(r))^2-f(x)f(r)]}{r^2-x^2}-r^3 e^{\frac{f(r)}{r}}ight\}}$ be differentiable in $(-\infty,0)\cup(0,\infty)$ and $f(1)=1$. Then the value of $ea$, such that $f(a)=0$, is equal to ___.

Accepted Answer

2

Question 28

Remainder when $64^{32^{32}}$ is divided by $9$ is equal to ___.

Accepted Answer

1

Question 29

Let the set $C=\{(x,y)\mid x^2-2^y=2023,\ x,y\in\mathbb{N}\}$. Then $\displaystyle\sum_{(x,y)\in C}(x+y)$ is equal to ___.

Accepted Answer

46

Question 30

Let the slope of the line $45x+5y+3=0$ be $27r_1+\dfrac{9r_2}{2}$ for some $r_1,r_2\in\mathbb{R}$. Then $\displaystyle\lim_{x	o 3}\left(\int_3^x\dfrac{8t^2}{\dfrac{3r_2 x}{2}-r_2 x^2-r_1 x^3-3x}\,dtight)$ is equal to ___.

Accepted Answer

12

Question 31

Two sources of light emit with a power of 200 W. The ratio of number of photons of visible light emitted by each source having wavelengths 300 nm and 500 nm respectively, will be:

Accepted Answer

(D) 3 : 5

Answer

(A) 1 : 5

Answer

(B) 1 : 3

Answer

(C) 5 : 3

Question 32

The truth table for the given circuit is:

Accepted Answer

(B) (2)

Answer

(A) (1)

Answer

(C) (3)

Answer

(D) (4)

Question 33

A physical quantity $Q$ is found to depend on quantities $a$, $b$, $c$ by the relation $Q=\dfrac{a^{4}b^{3}}{c^{2}}$. The percentage error in $a$, $b$ and $c$ are 3%, 4% and 5% respectively. Then, the percentage error in $Q$ is:

Accepted Answer

(C) 34%

Answer

(A) 66%

Answer

(B) 43%

Answer

(D) 14%

Question 34

In an a.c. circuit, voltage and current are given by: $V=100\sin(100\,t)$ V and $I=100\sin\left(100\,t+\dfrac{\pi}{3}\right)$ mA respectively. The average power dissipated in one cycle is:

Accepted Answer

(C) 2.5 W

Answer

(A) 5 W

Answer

(B) 10 W

Answer

(D) 25 W

Question 35

The temperature of a gas having $2.0	imes10^{25}$ molecules per cubic meter at 1.38 atm (Given, $k=1.38	imes10^{-23}$ JK$^{-1}$) is:

Accepted Answer

(A) 500 K

Answer

(B) 200 K

Answer

(C) 100 K

Answer

(D) 300 K

Question 36

A stone of mass 900 g is tied to a string and moved in a vertical circle of radius 1 m making 10 rpm. The tension in the string, when the stone is at the lowest point is (if $\pi^{2}=9.8$ and $g=9.8$ m/s$^{2}$):

Accepted Answer

(B) 9.8 N

Answer

(A) 97 N

Answer

(C) 8.82 N

Answer

(D) 17.8 N

Question 37

The bob of a pendulum was released from a horizontal position. The length of the pendulum is 10 m. If it dissipates 10% of its initial energy against air resistance, the speed with which the bob arrives at the lowest point is: [Use $g=10$ ms$^{-2}$]

Accepted Answer

(A) $6\sqrt{5}$ ms$^{-1}$

Answer

(B) $5\sqrt{6}$ ms$^{-1}$

Answer

(C) $5\sqrt{5}$ ms$^{-1}$

Answer

(D) $2\sqrt{5}$ ms$^{-1}$

Question 38

If the distance between object and its two times magnified virtual image produced by a curved mirror is 15 cm, the focal length of the mirror must be:

Accepted Answer

(C) $-10$ cm

Answer

(A) 15 cm

Answer

(B) $-12$ cm

Answer

(D) $\dfrac{10}{3}$ cm

Question 39

Two particles X and Y having equal charges are being accelerated through the same potential difference. Thereafter they enter normally in a region of uniform magnetic field and describe circular paths of radii $R_{1}$ and $R_{2}$ respectively. The mass ratio of X and Y is:

Accepted Answer

(B) $\left(\dfrac{R_{1}}{R_{2}}\right)^{2}$

Answer

(A) $\left(\dfrac{R_{2}}{R_{1}}\right)^{2}$

Answer

(C) $\left(\dfrac{R_{1}}{R_{2}}\right)$

Answer

(D) $\left(\dfrac{R_{2}}{R_{1}}\right)$

Question 40

In Young's double slit experiment, light from two identical sources are superimposing on a screen. The path difference between the two lights reaching at a point on the screen is $\dfrac{7\lambda}{4}$. The ratio of intensity of fringe at this point with respect to the maximum intensity of the fringe is:

Accepted Answer

(A) $\dfrac{1}{2}$

Answer

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

Answer

(C) $\dfrac{1}{3}$

Answer

(D) $\dfrac{1}{4}$

Question 41

A small liquid drop of radius R is divided into 27 identical liquid drops. If the surface tension is T, then the work done in the process will be:

Accepted Answer

(A) $8\pi R^{2}T$

Answer

(B) $3\pi R^{2}T$

Answer

(C) $\dfrac{1}{8}\pi R^{2}T$

Answer

(D) $4\pi R^{2}T$

Question 42

A bob of mass 'm' is suspended by a light string of length 'L'. It is imparted a minimum horizontal velocity at the lowest point A such that it just completes half circle reaching the top most position B. The ratio of kinetic energies $\dfrac{(K.E.)_{A}}{(K.E.)_{B}}$ is:

Accepted Answer

(B) 5 : 1

Answer

(A) 3 : 2

Answer

(C) 2 : 5

Answer

(D) 1 : 5

Question 43

A wire of length L and radius r is clamped at one end. If its other end is pulled by a force F, its length increases by $l$. If the radius of the wire and the applied force both are reduced to half of their original values keeping original length constant, the increase in length will become:

Accepted Answer

(D) 2 times

Answer

(A) 3 times

Answer

(B) $\dfrac{3}{2}$ times

Answer

(C) 4 times

Question 44

A planet takes 200 days to complete one revolution around the Sun. If the distance of the planet from Sun is reduced to one fourth of the original distance, how many days will it take to complete one revolution?

Accepted Answer

(A) 25

Answer

(B) 50

Answer

(C) 100

Answer

(D) 20

Question 45

A plane electromagnetic wave of frequency 35 MHz travels in free space along the X-direction. At a particular point (in space and time) $\vec{E}=9.6\,\hat{j}$ V/m. The value of magnetic field at this point is:

Accepted Answer

(A) $3.2	imes10^{-8}\,\hat{k}$ T

Answer

(B) $3.2	imes10^{-8}\,\hat{i}$ T

Answer

(C) $9.6\,\hat{j}$ T

Answer

(D) $9.6	imes10^{-8}\,\hat{k}$ T

Question 46

In the given circuit, the current in resistance $R_{3}$ is:

Accepted Answer

(A) 1 A

Answer

(B) 1.5 A

Answer

(C) 2 A

Answer

(D) 2.5 A

Question 47

A particle is moving in a straight line. The variation of position 'x' as a function of time 't' is given as $x=(t^{3}-6t^{2}+20t+15)$ m. The velocity of the body when its acceleration becomes zero is:

Accepted Answer

(B) 8 m/s

Answer

(A) 4 m/s

Answer

(C) 10 m/s

Answer

(D) 6 m/s

Question 48

N moles of a polyatomic gas ($f=6$) must be mixed with two moles of a monoatomic gas so that the mixture behaves as a diatomic gas. The value of N is:

Accepted Answer

(C) 4

Answer

(A) 6

Answer

(B) 3

Answer

(D) 2

Question 49

Given below are two statements:
Statement I: Most of the mass of the atom and all its positive charge are concentrated in a tiny nucleus and the electrons revolve around it, is Rutherford’s model.
Statement II: An atom is a spherical cloud of positive charges with electrons embedded in it, is a special case of Rutherford’s model.
In the light of the above statements, choose the most appropriate from the options given below.

Accepted Answer

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

Answer

(A) Both statement I and statement II are false

Answer

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

Answer

(D) Both statement I and statement II are true

Question 50

An electric field is given by $(6\hat{i}+5\hat{j}+3\hat{k})$ N/C. The electric flux through a surface area $30\hat{i}$ m$^{2}$ lying in YZ-plane (in SI unit) is:

Accepted Answer

(C) 180

Answer

(A) 90

Answer

(B) 150

Answer

(D) 60

Question 51

Two metallic wires P and Q have same volume and are made up of same material. If their area of cross sections are in the ratio 4 : 1 and force $F_{1}$ is applied to P, an extension of $\Delta l$ is produced. The force which is required to produce same extension in Q is $F_{2}$. The value of $\dfrac{F_{1}}{F_{2}}$ is ___.

Accepted Answer

16

Question 52

A horizontal straight wire 5 m long extending from east to west is falling freely at right angle to horizontal component of earth's magnetic field $0.60	imes10^{-4}$ Wbm$^{-2}$. The instantaneous value of emf induced in the wire when its velocity is 10 ms$^{-1}$ is ___ $	imes10^{-3}$ V.

Accepted Answer

3

Question 53

Hydrogen atom is bombarded with electrons accelerated through a potential difference of V, which causes excitation of hydrogen atoms. If the experiment is being performed at $T=0$ K, the minimum potential difference needed to observe any Balmer series lines in the emission spectra will be $\dfrac{\alpha}{10}$ V, where $\alpha=$ ___.

Accepted Answer

121

Question 54

A charge of 4.0 $\mu$C is moving with a velocity of $4.0	imes10^{6}$ ms$^{-1}$ along the positive y-axis under a magnetic field $\vec{B}$ of strength $(2\hat{k})$ T. The force acting on the charge is $x\hat{i}$ N. The value of $x$ is ___.

Accepted Answer

32

Question 55

A simple harmonic oscillator has an amplitude A and time period $6\pi$ second. Assuming the oscillation starts from its mean position, the time required by it to travel from $x=A$ to $x=\dfrac{\sqrt{3}}{2}A$ will be $\dfrac{\pi}{x}$ s, where $x=$ ___.

Accepted Answer

2

Question 56

In the given figure, the charge stored in 6 $\mu$F capacitor, when points A and B are joined by a connecting wire is ___ $\mu$C.

Accepted Answer

36

Question 57

In a single slit diffraction pattern, a light of wavelength 6000 Å is used. The distance between the first and third minima in the diffraction pattern is found to be 3 mm when the screen is placed 50 cm away from slits. The width of the slit is ___ $	imes10^{-4}$ m.

Accepted Answer

2

Question 58

In the given circuit, the current flowing through the resistance 20 $\Omega$ is 0.3 A, while the ammeter reads 0.9 A. The value of $R_{1}$ is ___ $\Omega$.

Accepted Answer

30

Question 59

A particle is moving in a circle of radius 50 cm in such a way that at any instant the normal and tangential components of its acceleration are equal. If its speed at $t=0$ is 4 m/s, the time taken to complete the first revolution will be $\dfrac{1}{\alpha}\left[1-e^{-2\pi}\right]$ s, where $\alpha=$ ___.

Accepted Answer

8

Question 60

A body of mass 5 kg is moving with a uniform speed $3\sqrt{2}$ ms$^{-1}$ in X–Y plane along the line $y=x+4$. The angular momentum of the particle about the origin will be ___ kg m$^{2}$s$^{-1}$.

Accepted Answer

60

Question 61

The ascending acidity order of the following H atoms is:

Accepted Answer

(A) C < D < B < A

Answer

(B) A < B < C < D

Answer

(C) A < B < D < C

Answer

(D) D < C < B < A

Question 62

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 63

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 64

Which of the following reaction is correct?

Accepted Answer

(B) (2)

Answer

(A) (1)

Answer

(C) (3)

Answer

(D) (4)

List I (Bio Polymer)	List II (Monomer)
A.Starch	I.nucleotide
B.Cellulose	II. $\alpha$ -glucose
C.Nucleic acid	III. $\beta$ -glucose
D.Protein	IV. $\alpha$ -amino acid

List I (Compound)	List II (pKa value)
A.Ethanol	I.10.0
B.Phenol	II.15.9
C.m-Nitrophenol	III.7.1
D.p-Nitrophenol	IV.8.3

List I (Spectral Series for Hydrogen)	List II (Spectral Region)
A.Lyman	I.Infrared region
B.Balmer	II.UV region
C.Paschen	III.Infrared region
D.Pfund	IV.Visible region

JEE Main 29 January 2024 Shift 2 Question Paper with Answers

Physics — JEE Main 29 January 2024 Shift 2

Chemistry — JEE Main 29 January 2024 Shift 2

Mathematics — JEE Main 29 January 2024 Shift 2

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