JEE Main 22 January 2025 Shift 1 Question Paper

Question 1

The number of non-empty equivalence relations on the set $\{1,2,3\}$ is:

Accepted Answer

(C) 5

Answer

(A) 6

Answer

(B) 7

Answer

(D) 4

Question 2

Let $f:\mathbb{R}	o\mathbb{R}$ be twice differentiable with $f(x+y)=f(x)f(y)$ for all $x,y$. If $f'(0)=4a$ and $f''(x)-3a\,f'(x)-f(x)=0\,(a>0)$, then the area of $R=\{(x,y):0\le y\le f(ax),\,0\le x\le 2\}$ is:

Accepted Answer

(D) $e^{2}-1$

Answer

(A) $e^{4}-1$

Answer

(B) $e^{2}+1$

Answer

(C) $e^{4}+1$

Question 3

Let triangle PQR be the image of the triangle with vertices $(1,3),(3,1),(2,4)$ in the line $x+2y=2$. If the centroid of $	riangle PQR$ is $(\alpha,\beta)$, then $15(\alpha-\beta)$ equals:

Accepted Answer

(D) 22

Answer

(A) 24

Answer

(B) 19

Answer

(C) 21

Question 4

Let $z_1,z_2,z_3$ lie on $|z|=1$ with $\arg z_1=-	frac{\pi}{4},\ \arg z_2=0,\ \arg z_3=	frac{\pi}{4}$. If $|z_1\bar z_2+z_2\bar z_3+z_3\bar z_1|^2=\alpha+\beta\sqrt2\ (\alpha,\beta\in\mathbb{Z})$, then $\alpha^2+\beta^2$ is:

Accepted Answer

(D) 29

Answer

(A) 24

Answer

(B) 41

Answer

(C) 33

Question 5

Using principal values, the sum of the maximum and minimum values of $16\big[(\sec^{-1}x)^2+(\operatorname{cosec}^{-1}x)^2\big]$ is:

Accepted Answer

(D) $22\pi^2$

Answer

(A) $24\pi^2$

Answer

(B) $18\pi^2$

Answer

(C) $31\pi^2$

Question 6

A coin is tossed three times. Let $X$ be the number of times a tail follows a head. If $\mu,\sigma^2$ are the mean and variance of $X$, then $64(\mu+\sigma^2)$ equals:

Accepted Answer

(B) 48

Answer

(A) 51

Answer

(C) 32

Answer

(D) 64

Question 7

Let $a_1,a_2,\dots$ be a G.P. of increasing positive terms. If $a_1a_5=28$ and $a_2+a_4=29$, then $a_6$ equals:

Accepted Answer

(C) 784

Answer

(A) 628

Answer

(B) 526

Answer

(D) 812

Question 8

Let $L_1:\dfrac{x-1}{2}=\dfrac{y-2}{3}=\dfrac{z-3}{4}$ and $L_2:\dfrac{x-2}{3}=\dfrac{y-4}{4}=\dfrac{z-5}{5}$. Which point lies on the line of shortest distance between $L_1$ and $L_2$?

Accepted Answer

(D) $\left(	frac{14}{3},-3,	frac{22}{3}ight)$

Answer

(A) $\left(-	frac53,-7,1ight)$

Answer

(B) $\left(2,3,	frac13ight)$

Answer

(C) $\left(	frac83,-1,	frac13ight)$

Question 9

The product of all solutions of $e^{5(\log_e x)^2+3}=x^{8}\,(x>0)$ is:

Accepted Answer

(A) $e^{8/5}$

Answer

(B) $e^{6/5}$

Answer

(C) e

Answer

(D) $e^{2}$

Question 10

If $\displaystyle\sum_{r=1}^{n}T_r=\dfrac{(2n-1)(2n+1)(2n+3)(2n+5)}{64}$, then $\displaystyle\lim_{n	o\infty}\sum_{r=1}^{n}\dfrac1{T_r}$ equals:

Accepted Answer

(C) $	frac23$

Answer

(A) 1

Answer

(B) 0

Answer

(D) $	frac13$

Question 11

From the English alphabet, five letters are chosen and arranged in alphabetical order. The number of ways in which the middle letter is "M" is:

Accepted Answer

(D) 5148

Answer

(A) 14950

Answer

(B) 6084

Answer

(C) 4356

Question 12

Let $x=x(y)$ be the solution of $\dfrac{dx}{dy}+\dfrac{x}{y^{2}}=\dfrac{1}{y^{3}}$ with $x(1)=1$. Then $x\big(	frac12\big)$ is:

Accepted Answer

(C) 3-e

Answer

(A) $	frac12+e$

Answer

(B) $	frac32+e$

Answer

(D) 3+e

Question 13

Let the parabola $y=x^2+px-3$ meet the axes at P, Q, R. If the circle with centre $(-1,-1)$ passes through P, Q, R, then the area of $	riangle PQR$ is:

Accepted Answer

(B) 6

Answer

(A) 4

Answer

(C) 7

Answer

(D) 5

Question 14

A circle C of radius 2 lies in the second quadrant and touches both axes. Another circle has centre $(2,5)$ and radius $r$ and intersects C at exactly two points. If the set of possible $r$ is $(\alpha,\beta)$, then $3\beta-2\alpha$ equals:

Accepted Answer

(A) 15

Answer

(B) 24

Answer

(C) 12

Answer

(D) 10

Question 15

Let $f(x)=7	an^8x+7	an^6x-3	an^4x-3	an^2x$, $I_1=\int_0^{\pi/4}f(x)\,dx$, $I_2=\int_0^{\pi/4}x\,f(x)\,dx$. Then $7I_1+12I_2$ is:

Accepted Answer

(C) 1

Answer

(A) $2\pi$

Answer

(B) $\pi$

Answer

(D) 2

Question 16

Let $f$ be differentiable with $f(0)=1$ and $f(x+y)=f(x)f(y)$. Under the given conditions, $\displaystyle\sum_{n=1}^{100}f'(n)$ equals:

Accepted Answer

(B) 2525

Answer

(A) 2384

Answer

(C) 5220

Answer

(D) 2406

Question 17

Let $A=\{1,2,\dots,10\}$ and $B=\{	frac{m}{n}:m,n\in A,\ m<n,\ \gcd(m,n)=1\}$. Then $n(B)$ equals:

Accepted Answer

(A) 31

Answer

(B) 36

Answer

(C) 37

Answer

(D) 29

Question 18

The area of the region inside the circle $(x-2\sqrt3)^2+y^2=12$ and outside the parabola $y^2=2\sqrt3\,x$ is:

Accepted Answer

(C) $6\pi-16$

Answer

(A) $6\pi-8$

Answer

(B) $3\pi-8$

Answer

(D) $5\pi+8$

Question 19

Two balls are drawn one by one without replacement from a bag of 4 white and 6 black balls. If the probability that the first ball is black given that the second ball is black is $	frac{m}{n}$ ($\gcd(m,n)=1$), then $m+n$ equals:

Accepted Answer

(A) 14

Answer

(B) 4

Answer

(C) 11

Answer

(D) 13

Question 20

The foci of a hyperbola are $(1,14)$ and $(1,-12)$, and it passes through $(1,6)$. The length of its latus rectum is:

Accepted Answer

(C) $	frac{288}{5}$

Answer

(A) $	frac{25}{6}$

Answer

(B) $	frac{24}{5}$

Answer

(D) $	frac{144}{5}$

Question 21

Let $f(x)=\begin{cases}-3ax^2-2,&x<1\ a^2+bx,&x\ge1\end{cases}$ be differentiable for all $x\in\mathbb{R}$ ($a>1$). With the region enclosed by $y=f(x)$ and the given line equal to $\beta\sqrt3$ ($\alpha,\beta\in\mathbb{Z}$), find $\alpha+\beta$.

Accepted Answer

34

Question 22

A finite sum of the form $\sum (r+2)/(2^{r+1})$-type series evaluates to $	frac{m}{n}$ with $\gcd(m,n)=1$. Find $m-n$.

Accepted Answer

2035

Question 23

Let $A$ be a $3	imes3$ matrix with $\det A=-2$. If $\det\big(3\,\mathrm{adj}(-6\,\mathrm{adj}(3A))\big)=2^{m}\cdot 3^{n}$ with $m>n$, find $4m+2n$ (per the paper).

Accepted Answer

34

Question 24

Let $L_1:\dfrac{x-1}{3}=\dfrac{y-1}{-1}=\dfrac{z+1}{0}$ and $L_2:\dfrac{x-2}{2}=\dfrac{y+4}{0}=\dfrac{z+4}{\alpha}$ meet at B. If P is the foot of perpendicular from $A(1,-1,1)$ on $L_2$, find $26\,\alpha\,(PB)$ (as integer).

Accepted Answer

216

Question 25

Let $\hat c$ be the projection vector of $\vec b=\lambda\hat i+4\hat k\ (\lambda>0)$ on $\vec a=\hat i+2\hat j+2\hat k$. If $|\vec a+\hat c|=7$, find the area of the parallelogram formed by $\vec b$ and $\hat c$.

Accepted Answer

16

Question 26

Given below are two statements.
Statement I: In a vernier callipers, one vernier scale division is always smaller than one main scale division.
Statement II: The vernier constant is given by one main scale division multiplied by the number of vernier scale divisions.
In the light of the above statements, choose the correct answer:

Accepted Answer

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

Answer

(A) Both Statement I and Statement II are true

Answer

(C) Both Statement I and Statement II are false

Answer

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

Question 27

A line charge of length a/2 is kept at the centre of an edge BC of a cube ABCDEFGH having edge length a (see figure). If the linear charge density of the line is λ C per unit length, then the total electric flux through all the faces of the cube is: (take ε₀ = free-space permittivity)

Accepted Answer

(A) λa/8ε₀

Answer

(B) λa/16ε₀

Answer

(C) λa/2ε₀

Answer

(D) λa/4ε₀

Question 28

The sliding contact of a potentiometer is in the middle of the potentiometer wire, which has resistance R_w = 1Ω, as shown in the figure. An external resistance R_e = 2Ω is connected via the sliding contact. The source emf is 0.9 V. The current i drawn from the source is:

Accepted Answer

(C) 1.0 A

Answer

(A) 0.3 A

Answer

(B) 1.35 A

Answer

(D) 0.9 A

Question 29

Assertion (A): If Young’s double-slit experiment is performed in an optically denser medium than air, the consecutive fringes come closer.
Reason (R): The speed of light reduces in an optically denser medium than air, while its frequency does not change.
In the light of the above statements, choose the most appropriate answer:

Accepted Answer

(A) Both (A) and (R) are true and (R) is the correct explanation of (A)

Answer

(B) (A) is false but (R) is true

Answer

(C) Both (A) and (R) are true but (R) is not the correct explanation of (A)

Answer

(D) (A) is true but (R) is false

Question 30

Two spherical bodies of the same material having radii 0.2 m and 0.8 m are placed in the same atmosphere. The temperature of the smaller body is 800 K and that of the bigger body is 400 K. If the energy radiated from the bigger body is E, the energy radiated from the smaller body (effect of the surroundings being negligible) is:

Accepted Answer

(B) E

Answer

(A) 256E

Answer

(C) 64E

Answer

(D) 16E

Question 31

An electron is in the orbital radius 5.3×10⁻¹¹ m (ground state) of a hydrogen atom. The ratio of the de Broglie wavelength of the electron in the 3rd excited state to that in the ground state is:

Accepted Answer

(A) 4

Answer

(B) 9

Answer

(C) 3

Answer

(D) 16

Question 32

In the arrangement shown in the figure there are three lenses formed by water (μ = 4/3) and glass (μ = 3/2) at the boundaries of a container; the thickness of glass is negligible compared to |R₁| and |R₂|, the radii of curvature of the upper and lower glass surfaces. The power of the combination is:

Accepted Answer

(B) −(1/6)(1/|R₁| − 1/|R₂|)

Answer

(A) −(1/6)(1/|R₁| + 1/|R₂|)

Answer

(C) (1/6)(1/|R₁| + 1/|R₂|)

Answer

(D) (1/6)(1/|R₁| − 1/|R₂|)

Question 33

Which of the following resistivity (ρ) versus temperature (T) curves is most suitable to be used in wire-bound standard resistors? (graphs (1)–(4) shown)

Accepted Answer

(A) (1)

Answer

(B) (2)

Answer

(C) (3)

Answer

(D) (4)

Question 34

A closed organ pipe and an open organ pipe are filled with two different gases having the same bulk modulus but different densities ρ₁ and ρ₂ respectively. The frequency of the 9th harmonic of the closed pipe is identical with the 4th harmonic of the open pipe. If the length of the closed pipe is 10 cm and the density ratio of the gases is ρ₁ : ρ₂ = 1 : 16, the length of the open pipe is:

Accepted Answer

(C) 20/9 cm

Answer

(A) 20/7 cm

Answer

(B) 15/7 cm

Answer

(D) 15/9 cm

Question 35

A uniform circular disc of radius R and mass M is rotating about an axis perpendicular to its plane and passing through its centre. A small circular part of radius R/2 is removed from the original disc as shown in the figure (its boundary passes through the centre). The moment of inertia of the remaining part about the same axis is:

Accepted Answer

(D) 13/32 MR²

Answer

(A) 7/32 MR²

Answer

(B) 9/32 MR²

Answer

(C) 17/32 MR²

Question 36

A small point mass m is placed at a distance 2R from the centre O of a big uniform solid sphere of mass M and radius R. The gravitational force on m due to M is F₁. A spherical part of radius R/3 is removed from the big sphere (on the side nearer to m, as shown) and the force on m due to the remaining part of M is F₂. The ratio F₁ : F₂ is:

Accepted Answer

(C) 12 : 11

Answer

(A) 16 : 9

Answer

(B) 11 : 10

Answer

(D) 12 : 9

Question 37

The work functions of caesium (Cs) and lithium (Li) metals are 1.9 eV and 2.5 eV respectively. For light of wavelength 550 nm, the photoelectric effect is possible for the case of:

Accepted Answer

(B) Cs only

Answer

(A) Li only

Answer

(C) Neither Cs nor Li

Answer

(D) Both Cs and Li

Question 38

If B is the magnetic field and μ₀ is the permeability of free space, then the dimensions of (B/μ₀) are:

Accepted Answer

(B) L⁻¹ A

Answer

(A) M T⁻¹ A⁻¹

Answer

(C) L T⁻¹ A⁻¹

Answer

(D) M L T⁻¹ A⁻¹

Question 39

A bob of mass m is suspended at a point O by a light string of length l and left to perform vertical circular motion. Initially, by applying horizontal velocity v_a at the lowest point A, the string becomes slack at the topmost point D. The ratio of the kinetic energy of the bob at the points B and C (shown in the figure, at heights l/2 and 3l/2 above A) is:

Accepted Answer

(A) 2

Answer

(B) 1

Answer

(C) 4

Answer

(D) 3

Question 40

Given below are two statements.
Statement I: The equivalent emf of two non-ideal batteries connected in parallel is smaller than either of the two emfs.
Statement II: The equivalent internal resistance of two non-ideal batteries connected in parallel is smaller than either of the internal resistances of the two batteries.
In the light of the above statements, choose the correct answer:

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 true

Answer

(C) Both Statement I and Statement II are false

Question 41

Which of the following circuits represents a forward-biased diode? (See figure for circuits (A)–(E) with their node potentials and diode orientations.)

Accepted Answer

(C) (B), (C) and (E) only

Answer

(A) (B), (D) and (E) only

Answer

(B) (A) and (D) only

Answer

(D) (C) and (E) only

Question 42

A parallel-plate capacitor of capacitance 40 μF is connected to a 100 V power supply. Now the intermediate space between the plates is filled with a dielectric material of dielectric constant K = 2. Due to the introduction of the dielectric, the extra charge and the change in the electrostatic energy of the capacitor, respectively, are:

Accepted Answer

(C) 4 mC and 0.2 J

Answer

(A) 3 mC and 0.2 J

Answer

(B) 8 mC and 2.0 J

Answer

(D) 2 mC and 0.2 J

Question 43

Given is a thin convex lens of glass (refractive index μ) and both faces having radius of curvature R. It is silvered on one side to behave like a closed reflector. An object is placed on the optic axis so that the image gets formed on the object itself. The object distance is:

Accepted Answer

(D) R/(2μ−1)

Answer

(A) R/μ

Answer

(B) R(2μ−3)

Answer

(C) R(2μ−1)

Question 44

Two soap bubbles of radius 2 cm and 4 cm are in contact with each other. The radius of curvature of the common surface, in cm, is ______.

Accepted Answer

4

Question 45

The driver sitting inside a parked car is watching vehicles approaching from behind with the help of a convex side mirror of radius of curvature R = 2 m. A vehicle approaches from behind with a uniform speed of 90 km/h. When the vehicle is at a distance of 24 m, the magnitude of the acceleration of its image is a₀ m/s². The value of 100 a₀ is ______.

Accepted Answer

8

Question 46

Three conductors of the same length having thermal conductivities k₁, k₂ and k₃ are connected as shown in the figure (a 100°C end joined through the 1st conductor to a junction, then the 2nd conductor to a 0°C end, with the 3rd conductor also bridging the junction to 0°C). The area of cross-section of the 1st and 2nd conductors is A and that of the 3rd conductor is 2A. With k₁ = 60 J s⁻¹m⁻¹K⁻¹, k₂ = 120 J s⁻¹m⁻¹K⁻¹ and k₃ = 135 J s⁻¹m⁻¹K⁻¹, the temperature θ (°C) of the junction is ______.

Accepted Answer

40

Question 47

The position vectors of two 1 kg particles A and B are given by r_A = (α₁t i + α₂t j + α₃t k) m and r_B = (β₁ i + β₂t² j + β₃t k) m, where (α₁ = 1, α₂ = 3 m/s, α₃ = 2 m/s) and (β₁ = 1 m, β₂ = ... , β₃ = ... ) are constants, with t in seconds. At t = 1 s the magnitude of the angular momentum of particle B with respect to the position of particle A is √L kg m²/s. The value of L is ______.

Accepted Answer

90

Question 48

A particle is projected at an angle of 30° from the horizontal at a speed of 60 m/s. The height traversed by the particle in the first second is h₁ and the height traversed in the last second of its upward journey is h₂. The ratio h₁ : h₂ is ______. (take g = 10 m/s²)

Accepted Answer

5

Question 49

A solution of aluminium chloride is electrolysed for 30 minutes using a current of 2 A. The amount of aluminium deposited at the cathode is ______. (Given: molar masses of aluminium and chlorine are 27 g mol⁻¹ and 35.5 g mol⁻¹ respectively; Faraday constant = 96500 C mol⁻¹)

Accepted Answer

(C) 0.336 g

Answer

(A) 1.660 g

Answer

(B) 1.007 g

Answer

(D) 0.441 g

Question 50

Which of the following statements is NOT true for radioactive decay?

Accepted Answer

(C) The decay constant increases with increase in temperature

Answer

(A) The amount of radioactive substance remaining after three half-lives is 1/8th of the original amount

Answer

(B) The decay constant does not depend upon temperature

Answer

(D) Half-life is 0.693 times (1/rate constant)

Question 51

How many different stereoisomers are possible for the molecule hex-3-en-2-ol, CH₃–CH(OH)–CH=CH–CH₂–CH₃ ?

Accepted Answer

(D) 4

Answer

(A) 3

Answer

(B) 1

Answer

(C) 2

Question 52

Which of the following electronegativity orders is INCORRECT?

Accepted Answer

(A) Al < Mg < B < N

Answer

(B) Al < Si < C < N

Answer

(C) Mg < Be < B < N

Answer

(D) S < Cl < O < F

Question 53

Lanthanoid ions with 4f⁷ configuration are: (A) Eu²⁺ (B) Gd³⁺ (C) Eu³⁺ (D) Tb³⁺ (E) Sm²⁺. Choose the correct answer from the options given below:

Accepted Answer

(A) (A) and (B) only

Answer

(B) (A), (B) and (E) only

Answer

(C) (B) and (E) only

Answer

(D) (B) and (D) only

Question 54

Match List-I (Increasing Order of Species) with List-II (Property). Choose the correct answer from the options given below:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 55

Which of the following acids is a vitamin?

Accepted Answer

(C) Ascorbic acid

Answer

(A) Adipic acid

Answer

(B) Aspartic acid

Answer

(D) Saccharic acid

Question 56

A liquid kept inside a thermally insulated closed vessel at 25°C is mechanically stirred from outside. What is the correct option for the following thermodynamic parameters?

Accepted Answer

(A) ΔU > 0, q = 0, w > 0

Answer

(B) ΔU = 0, q = 0, w = 0

Answer

(C) ΔU > 0, q = 0, w < 0

Answer

(D) ΔU < 0, q = 0, w > 0

Question 57

The radius of the first excited state of a helium ion (He⁺) is given as ______, where a₀ = radius of the first stationary state of the hydrogen atom.

Accepted Answer

(D) 2a₀

Answer

(A) a₀/2

Answer

(B) a₀/4

Answer

(C) 4a₀

Question 58

Given below are two statements.
Statement I: CH₃–O–CH₂–Cl will undergo SN1 reaction though it is a primary halide.
Statement II: (CH₃)₃C–CH₂–Cl will not undergo SN2 reaction very easily though it is a primary halide.
In the light of the above statements, choose the most appropriate answer:

Accepted Answer

(D) Both Statement I and Statement II are correct

Answer

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

Answer

(B) Both Statement I and Statement II are incorrect

Answer

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

Question 59

Given below are two statements.
Statement I: One mole of propyne reacts with excess of sodium to liberate half a mole of H₂ gas.
Statement II: Four grams of propyne reacts with NaNH₂ to liberate NH₃ gas which occupies 224 mL at STP.
In the light of the above statements, choose the most appropriate answer:

Accepted Answer

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

Answer

(B) Both Statement I and Statement II are correct

Answer

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

Answer

(D) Both Statement I and Statement II are incorrect

Question 60

A vessel at 1000 K contains CO₂ at a pressure of 0.5 atm. Some of the CO₂ is converted into CO on addition of graphite. If the total pressure at equilibrium is 0.8 atm, then Kp is:

Accepted Answer

(B) 1.8 atm

Answer

(A) 0.18 atm

Answer

(C) 0.3 atm

Answer

(D) 3 atm

Question 61

The IUPAC name of the compound shown is:

Accepted Answer

(D) 6-Methoxycarbonyl-2,5-dimethylhexanoic acid

Answer

(A) 1,2-Carboxy-5-methoxycarbonylhexane

Answer

(B) Methyl-6-carboxy-2,5-dimethylhexanoate

Answer

(C) Methyl-5-carboxy-2-methylhexanoate

Question 62

Which of the following electrolytes can be used to obtain H₂S₂O₈ by the process of electrolysis?

Accepted Answer

(C) Concentrated solution of sulphuric acid

Answer

(A) Dilute solution of sodium sulphate

Answer

(B) Dilute solution of sulphuric acid

Answer

(D) Acidified dilute solution of sodium sulphate

Question 63

Among the compounds (A)–(E) shown, choose the set that gives a positive Fehling’s test.

Accepted Answer

(C) (C), (D) and (E) only

Answer

(A) (A), (C) and (D) only

Answer

(B) (A), (D) and (E) only

Answer

(D) (A), (B) and (C) only

Question 64

In which of the following complexes will the crystal-field stabilisation energy (CFSE, Δ₀) be equal to zero?

Accepted Answer

(D) K₃[Fe(SCN)₆]

Answer

(A) [Fe(NH₃)₆]Br₃

Answer

(B) [Fe(en)₃]Cl₃

Answer

(C) K₂[Fe(CN)₄]

List-I (Increasing Order of Species)	List-II (Property)
A.Al³⁺ < Mg²⁺ < Na⁺ < F⁻	I.Ionisation Enthalpy
B.B < C < O < N	II.Metallic character
C.B < Al < Mg < K	III.Electronegativity
D.Si < P < S < Cl	IV.Ionic radii

List-I (Increasing Order of Species)	List-II (Property)
A.Al³⁺ < Mg²⁺ < Na⁺ < F⁻	I.Ionisation Enthalpy
B.B < C < O < N	II.Metallic character
C.B < Al < Mg < K	III.Electronegativity
D.Si < P < S < Cl	IV.Ionic radii

JEE Main 22 January 2025 Shift 1 Question Paper with Answers

Physics — JEE Main 22 January 2025 Shift 1

Chemistry — JEE Main 22 January 2025 Shift 1

Mathematics — JEE Main 22 January 2025 Shift 1

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