JEE Main 12 April 2023 Shift 1 Question Paper

Question 1

The number of five digit numbers, greater than 40000 and divisible by 5, which can be formed using the digits 0, 1, 3, 5, 7 and 9 without repetition, is equal to

Accepted Answer

(A) 120

Answer

(B) 132

Answer

(C) 72

Answer

(D) 96

Question 2

Let $\alpha,\beta$ be the roots of the quadratic equation $x^2+\sqrt6\,x+3=0$. Then $\dfrac{\alpha^{23}+\beta^{23}+\alpha^{14}+\beta^{14}}{\alpha^{15}+\beta^{15}+\alpha^{10}+\beta^{10}}$ is equal to

Accepted Answer

(C) 81

Answer

(A) 729

Answer

(B) 72

Answer

(D) 9

Question 3

Let $\langle a_n\rangle$ be a sequence such that $a_1+a_2+\cdots+a_n=\dfrac{n^2+3n}{(n+1)(n+2)}$. If $28\sum_{k=1}^{10}\dfrac{1}{a_k}=p_1 p_2 p_3\cdots p_m$, where $p_1,p_2,\ldots,p_m$ are the first m prime numbers, then m is equal to

Accepted Answer

(B) 6

Answer

(A) 7

Answer

(C) 5

Answer

(D) 8

Question 4

Let the lines $l_1:\dfrac{x+5}{3}=\dfrac{y+4}{1}=\dfrac{z-\alpha}{-2}$ and $l_2:3x+2y+z-2=0=x-3y+2z-13$ be coplanar. If the point P$(a,b,c)$ on $l_1$ is nearest to the point Q$(-4,-3,2)$, then $|a|+|b|+|c|$ is equal to

Accepted Answer

(C) 10

Answer

(A) 12

Answer

(B) 14

Answer

(D) 8

Question 5

Let P$\left(\dfrac{2\sqrt3}{\sqrt7},\dfrac{6}{\sqrt7}\right)$, Q, R and S be four points on the ellipse $9x^2+4y^2=36$. Let PQ and RS be mutually perpendicular and pass through the origin. If $\dfrac{1}{(PQ)^2}+\dfrac{1}{(RS)^2}=\dfrac{p}{q}$, where p and q are coprime, then $p+q$ is equal to

Accepted Answer

(B) 157

Answer

(A) 143

Answer

(C) 137

Answer

(D) 147

Question 6

Let a, b, c be three distinct real numbers, none equal to one. If the vectors $a\hat i+\hat j+\hat k$, $\hat i+b\hat j+\hat k$ and $\hat i+\hat j+c\hat k$ are coplanar, then $\dfrac{1}{1-a}+\dfrac{1}{1-b}+\dfrac{1}{1-c}$ is equal to

Accepted Answer

(A) 1

Answer

(B) -1

Answer

(C) 3

Answer

(D) -2

Question 7

If the local maximum value of the function $f(x)=\left(\dfrac{\sqrt{3e}}{2\sin x}\right)^{\sin^2 x}$, $x\in\left(0,\dfrac{\pi}{2}\right)$, is $\dfrac{k}{e}$, then $\left(\dfrac{k}{e}\right)^8+\dfrac{k^8}{e^5}+k^5$ is equal to

Accepted Answer

(C) $e^3+e^5+e^{11}$

Answer

(A) $e^5+e^6+e^{11}$

Answer

(B) $e^3+e^6+e^{11}$

Answer

(D) $e^5+e^6+e^{10}$

Question 8

Let D be the domain of the function $f(x)=\sin^{-1}\left(\log_{3x}\left(\dfrac{6+2\log_3 x}{-5x}ight)ight)$. If the range of the function $g:D	o\mathbb{R}$ defined by $g(x)=x-[x]$ ($[x]$ is the greatest integer function) is $(\alpha,\beta)$, then $\alpha^2+\dfrac{5}{\beta}$ is equal to

Accepted Answer

(B) 135

Answer

(A) 46

Answer

(C) 136

Answer

(D) 45

Question 9

Let $y=y(x)$, $y>0$, be a solution curve of the differential equation $(1+x^2)\,dy=y(x-y)\,dx$. If $y(0)=1$ and $y(2\sqrt2)=\beta$, then

Accepted Answer

(A) $e^{1/\beta}=e(3+2\sqrt2)$

Answer

(B) $e^{1/\beta}=e^{-2}(5+4\sqrt2)$

Answer

(C) $e^{1/\beta}=e^{-2}(3+2\sqrt2)$

Answer

(D) $e^{1/\beta}=e(5+4\sqrt2)$

Question 10

Among the two statements (S1): $(p\Rightarrow q)\wedge(q\wedge(\sim q))$ is a contradiction and (S2): $(p\wedge q)\vee((\sim p)\wedge q)\vee(p\wedge(\sim q))\vee((\sim p)\wedge(\sim q))$ is a tautology

Accepted Answer

(D) both are true

Answer

(A) only (S2) is true

Answer

(B) only (S1) is true

Answer

(C) both are false

Question 11

Let $\lambda\in\mathbb{Z}$, $\vec a=2\lambda\hat i+\hat j-\hat k$ and $\vec b=3\hat i-\hat j+2\hat k$. Let $\vec c$ be a vector such that $(\vec a+\vec b+\vec c)	imes\vec c=\vec 0$, $\vec a\cdot\vec c=-17$ and $\vec b\cdot\vec c=-20$. Then $|\vec c	imes(\lambda\hat i+\hat j+\hat k)|^2$ is equal to

Accepted Answer

(B) 46

Answer

(A) 62

Answer

(C) 53

Answer

(D) 49

Question 12

The sum of the coefficients of the first 50 terms in the binomial expansion of $(1-x)^{100}$, is equal to

Accepted Answer

(C) $-{}^{99}C_{49}$

Answer

(A) $-{}^{100}C_{50}$

Answer

(B) ${}^{99}C_{49}$

Answer

(D) ${}^{100}C_{50}$

Question 13

The area of the region enclosed by the curve $y=x^3$ and its tangent at the point $(-1,-1)$ is

Accepted Answer

(A) $\dfrac{27}{4}$

Answer

(B) $\dfrac{19}{4}$

Answer

(C) $\dfrac{23}{4}$

Answer

(D) $\dfrac{31}{4}$

Question 14

Let $A=\begin{bmatrix}1&\frac{1}{51}\0&1\end{bmatrix}$. If $B=\begin{bmatrix}1&2\-1&-1\end{bmatrix}A\begin{bmatrix}-1&-2\1&1\end{bmatrix}$, then the sum of all the elements of the matrix $\sum_{n=1}^{50}B^n$ is equal to

Accepted Answer

(A) 100

Answer

(B) 50

Answer

(C) 75

Answer

(D) 125

Question 15

Let the plane P: $4x-y+z=10$ be rotated by an angle $\dfrac{\pi}{2}$ about its line of intersection with the plane $x+y-z=4$. If $\alpha$ is the distance of the point $(2,3,-4)$ from the new position of the plane P, then $35\alpha$ is equal to

Accepted Answer

(C) 126

Answer

(A) 90

Answer

(B) 85

Answer

(D) 170

Question 16

If $\dfrac{1}{n+1}\,{}^nC_n+\dfrac{1}{n}\,{}^nC_{n-1}+\cdots+\dfrac{1}{2}\,{}^nC_1+{}^nC_0=\dfrac{1023}{10}$ then n is equal to

Accepted Answer

(B) 9

Answer

(A) 6

Answer

(C) 8

Answer

(D) 7

Question 17

Let C be the circle in the complex plane with centre $z_0=\dfrac12(1+3i)$ and radius $r=1$. Let $z_1=1+i$ and the complex number $z_2$ be outside the circle C such that $|z_1-z_0|\,|z_2-z_0|=1$. If $z_0$, $z_1$ and $z_2$ are collinear, then the smaller value of $|z_2|^2$ is equal to

Accepted Answer

(B) $\dfrac52$

Answer

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

Answer

(C) $\dfrac32$

Answer

(D) $\dfrac72$

Question 18

If the point $\left(\alpha,\dfrac{7\sqrt3}{3}ight)$ lies on the curve traced by the mid-points of the line segments of the lines $x\cos	heta+y\sin	heta=7$, $	heta\in\left(0,\dfrac{\pi}{2}ight)$ between the co-ordinate axes, then $\alpha$ is equal to

Accepted Answer

(A) 7

Answer

(B) -7

Answer

(C) $-7\sqrt3$

Answer

(D) $7\sqrt3$

Question 19

Two dice A and B are rolled. Let the numbers obtained on A and B be $\alpha$ and $\beta$ respectively. If the variance of $\alpha-\beta$ is $\dfrac{p}{q}$, where p and q are co-prime, then the sum of the positive divisors of p is equal to

Accepted Answer

(B) 48

Answer

(A) 36

Answer

(C) 31

Answer

(D) 72

Question 20

In a triangle ABC, if $\cos A+2\cos B+\cos C=2$ and the lengths of the sides opposite to the angles A and C are 3 and 7 respectively, then $\cos A-\cos C$ is equal to

Accepted Answer

(C) $\dfrac{10}{7}$

Answer

(A) $\dfrac37$

Answer

(B) $\dfrac97$

Answer

(D) $\dfrac57$

Question 21

A fair die with faces marked $1$ to $n$ ($n>1$) is tossed repeatedly until a number less than n appears. If the mean of the number of tosses required is $\dfrac{n}{9}$, then n is equal to

Accepted Answer

10

Question 22

Let the digits a, b, c be in A.P. Nine-digit numbers are to be formed using each of these three digits thrice such that three consecutive digits are in A.P. at least once. How many such numbers can be formed?

Accepted Answer

1260

Question 23

Let $[x]$ be the greatest integer $\le x$. Then the number of points in the interval $(-2,1)$, where the function $f(x)=|[x]|+\sqrt{x-[x]}$ is discontinuous is _________.

Accepted Answer

2

Question 24

Let the plane $x+3y-2z+6=0$ meet the co-ordinate axes at the points A, B, C. If the orthocentre of the triangle ABC is $\left(\alpha,\beta,\dfrac67\right)$, then $98(\alpha+\beta)^2$ is equal to _________.

Accepted Answer

288

Question 25

Let $I=\int\sqrt{\dfrac{x+7}{x}}\,dx$ and $I(1)=\alpha+7\log_e(1+2\sqrt2)$, then $\alpha^4$ is equal to _________.

Accepted Answer

64

Question 26

Let $D_k=\begin{vmatrix}1&2k&2k-1\n&n^2+n+2&n^2\n&n^2+n&n^2+n+2\end{vmatrix}$. If $\sum_{k=1}^{n}D_k=96$, then n is equal to

Accepted Answer

6

Question 27

Let the positive numbers $a_1,a_2,a_3,a_4$ and $a_5$ be in a G.P. Let their mean and variance be $\dfrac{31}{10}$ and $\dfrac{m}{n}$ respectively, where m and n are co-prime. If the mean of their reciprocals is $\dfrac{31}{40}$ and $a_3+a_4+a_5=14$, then $m+n$ is equal to _________.

Accepted Answer

211

Question 28

The number of relations, on the set $\{1,2,3\}$ containing $(1,2)$ and $(2,3)$, which are reflexive and transitive but not symmetric, is _________.

Accepted Answer

4

Question 29

If $\int_{-0.15}^{0.15}\left|100x^2-1\right|\,dx=\dfrac{k}{3000}$, then k is equal to _________.

Accepted Answer

575

Question 30

Two circles in the first quadrant of radii $r_1$ and $r_2$ touch the coordinate axes. Each of them cuts off an intercept of 2 units with the line $x+y=2$. Then $r_1^2+r_2^2-r_1 r_2$ is equal to _________.

Accepted Answer

7

Question 31

An ice cube has a bubble inside. When viewed from one side the apparent distance of the bubble is 12 cm. When viewed from the opposite side, the apparent distance of the bubble is observed as 4 cm. If the side of the ice cube is 24 cm, the refractive index of the ice cube is

Accepted Answer

(B) $\dfrac32$

Answer

(A) $\dfrac43$

Answer

(C) $\dfrac23$

Answer

(D) $\dfrac65$

Question 32

Two satellites A and B move round the earth in the same orbit. The mass of A is twice the mass of B. The quantity which is same for the two satellites will be:

Accepted Answer

(D) Speed

Answer

(A) Potential energy

Answer

(B) Total energy

Answer

(C) Kinetic energy

Question 33

The amplitude of 15 sin(1000$\pi$t) signal is modulated by 10 sin(4$\pi$t) signal. The amplitude modulated signal contains frequencies of 1. 500 Hz 2. 2 Hz 3. 250 Hz 4. 498 Hz 5. 502 Hz. Choose the correct answer from the options given below:

Accepted Answer

(D) (1), (4) and (5) only

Answer

(A) (1) and (3) only

Answer

(B) (2) and (4) only

Answer

(C) (3) and (2) only

Question 34

In an n-p-n common emitter (CE) transistor the collector current changes from 5 mA to 16 mA for the change in base current from 100 $\mu$A and 200 $\mu$A, respectively. The current gain of transistor is _________.

Accepted Answer

(A) 110

Answer

(B) 0.9

Answer

(C) 210

Answer

(D) 9

Question 35

If the r.m.s. speed of chlorine molecule is 490 m/s at 27°C, the r.m.s. speed of argon molecules at the same temperature will be (Atomic mass of argon = 39.9u, molecular mass of chlorine = 70.9u)

Accepted Answer

(C) 651.7 m/s

Answer

(A) 751.7 m/s

Answer

(B) 451.7 m/s

Answer

(D) 551.7 m/s

Question 36

A proton and an $\alpha$-particle are accelerated from rest by 2V and 4V potentials, respectively. The ratio of their de-Broglie wavelength is:

Accepted Answer

(A) 4:1

Answer

(B) 2:1

Answer

(C) 8:1

Answer

(D) 16:1

Question 37

Given below are two statements:
Statement I: The diamagnetic property depends on temperature.
Statement II: The induced magnetic dipole moment in a diamagnetic sample is always opposite to the magnetizing field. In the light of given statement, choose the correct answer from the options given below:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 38

A wire of resistance 160 $\Omega$ is melted and drawn in wire of one-fourth of its length. The new resistance of the wire will be

Accepted Answer

(A) 10 $\Omega$

Answer

(B) 640 $\Omega$

Answer

(C) 40 $\Omega$

Answer

(D) 16 $\Omega$

Question 39

Match List I (physical quantities: spring constant, angular speed, angular momentum, moment of inertia) with List II (dimensional formulae). Choose the correct answer from the options given below:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 40

Three forces $F_1=10$ N, $F_2=8$ N, $F_3=6$ N are acting on a particle of mass 5 kg. The forces $F_2$ and $F_3$ are applied perpendicular so that particle remains at rest. If the force $F_1$ is removed, then the acceleration of the particle is:

Accepted Answer

(A) 2 ms$^{-2}$

Answer

(B) 0.5 ms$^{-2}$

Answer

(C) 4.8 ms$^{-2}$

Answer

(D) 7 ms$^{-2}$

Question 41

A body cools from 80°C to 60°C in 5 minutes. The temperature of the surrounding is 20°C. The time it takes to cool from 60°C to 40°C is:

Accepted Answer

(A) 500 s

Answer

(B) $\dfrac{25}{3}$ s

Answer

(C) 450 s

Answer

(D) 420 s

Question 42

An engine operating between the boiling and freezing points of water will have 1. efficiency more than 27% 2. efficiency less than the efficiency of a Carnot engine operating between the same two temperatures 3. efficiency equal to 27% 4. efficiency less than 27%. Choose the correct answer from the options given below:

Accepted Answer

(C) 2 and 4 only

Answer

(A) 2, 3 and 4 only

Answer

(B) 2 and 3 only

Answer

(D) 1 and 2 only

Question 43

Given below are two statements:
Statement I: A truck and a car moving with same kinetic energy are brought to rest by applying brakes which provide equal retarding forces. Both come to rest in equal distance.
Statement II: A car moving towards east takes a turn and moves towards north, the speed remains unchanged. The acceleration of the car is zero. In the light of given 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 correct but II not explanation of I

Answer

(D) Both Statement I and Statement II are correct

Question 44

A particle is executing Simple Harmonic Motion (SHM). The ratio of potential energy and kinetic energy of the particle when its displacement is half of its amplitude will be:

Accepted Answer

(D) 1 : 3

Answer

(A) 1 : 1

Answer

(B) 2 : 1

Answer

(C) 1 : 4

Question 45

A ball is thrown vertically upward with an initial velocity of 150 m/s. The ratio of velocity after 3 s and 5 s is $\dfrac{x+1}{x}$. The value of x is _________. (Take $g=10$ m/s$^2$)

Accepted Answer

(B) 5

Answer

(A) 6

Answer

(C) -5

Answer

(D) 10

Question 46

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: If we move from poles to equator, the direction of acceleration due to gravity of earth always points downward.
Reason R: Electric dipole consists of two equal and opposite charges. In the light of above statements, choose the correct answer from the options given below:

Accepted Answer

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

Answer

(B) A is true but R is false

Answer

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

Answer

(D) A is false but R is true

Question 47

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: EM waves used for optical communication have longer wavelengths than that of microwave, employed in Radar technology.
Reason R: Infrared EM waves are more energetic than microwaves (used in Radar). In the light of given statements, choose the correct answer from the options given below:

Accepted Answer

(A) A is false but R is true

Answer

(B) A is true but R is false

Answer

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

Answer

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

Question 48

A 12.5 eV electron beam is used to bombard gaseous hydrogen at room temperature. The number of spectral lines emitted will be:

Accepted Answer

(C) 3

Answer

(A) 2

Answer

(B) 1

Answer

(D) 4

Question 49

The ratio of escape velocity of a planet to the escape velocity of earth will be: Given: Mass of the planet is 16 times mass of the earth and 4 times the radius of earth.

Accepted Answer

(B) 2 : 1

Answer

(A) 4 : 1

Answer

(C) 1 : $\sqrt2$

Answer

(D) 1 : 4

Question 50

Given below are two statements:
Statement I: When the frequency of an a.c. source in a series LCR circuit increases, the current in the circuit first increases, attains a maximum value and then decreases.
Statement II: In a series LCR circuit, the value of power factor at resonance is one. In the light of given statements, choose the most appropriate answer from the options given below:

Accepted Answer

(D) Both Statement I and Statement II are true.

Answer

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

Answer

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

Answer

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

Question 51

For a certain organ pipe, the first three resonance frequencies are in the ratio of 1:3:5 respectively. If the frequency of fifth harmonic is 405 Hz and the speed of sound in air is 324 m s$^{-1}$, the length of the organ pipe is _________ m.

Accepted Answer

1

Question 52

For a rolling spherical shell, the ratio of rotational kinetic energy and total kinetic energy is $\dfrac{x}{5}$. The value of x is _________.

Accepted Answer

2

Question 53

A compass needle oscillates 20 times per minute at a place where the dip is 30° and 30 times per minute where the dip is 60°. The ratio of total magnetic field due to the earth at the two places respectively is $\dfrac{4}{\sqrt{x}}$. The value of x is _________.

Accepted Answer

243

Question 54

A conducting circular loop is placed in a uniform magnetic field of 0.4 T with its plane perpendicular to the field. Somehow, the radius of the loop starts expanding at a constant rate of 1 mm/s. The magnitude of induced emf in the loop at an instant when the radius of the loop is 1 cm will be _________ $\mu$V.

Accepted Answer

50

Question 55

To maintain a speed of 80 km/h by a bus of mass 500 kg on a plane rough road for 4 km distance, the work done by the engine of the bus will be _________ kJ. [The coefficient of friction between tyre of bus and road is 0.04]

Accepted Answer

784

Question 56

Consider an example of alpha decay $_{92}^{238}U\rightarrow{}_{90}^{234}Th+{}_2^4He+Q$. Given: $_{92}^{238}U=238.05060u$, $_{90}^{234}Th=234.04360u$, $_2^4He=4.00260u$, and $1u=931.5\,\dfrac{MeV}{c^2}$. The energy released (Q) during the alpha decay of $_{92}^{238}U$ is _________ MeV.

Accepted Answer

4

Question 57

The current flowing through a conductor connected across a source is 2A and 1.2 A at 0°C and 50°C respectively. The current flowing through the conductor at 50°C will be _________ ×10$^2$ mA.

Accepted Answer

15

Question 58

Two convex lenses of focal length 20 cm each are placed coaxially with a separation of 60 cm between them. The image of the distant object formed by the combination is at _________ cm from the first lens.

Accepted Answer

100

Question 59

10 resistors each of resistance 10 $\Omega$ can be connected in such as to get maximum and minimum equivalent resistance. The ratio of maximum and minimum equivalent resistance will be _________.

Accepted Answer

100

Question 60

64 identical drops each charged upto potential of 10 mV are combined to form a bigger drop. The potential of the bigger drop will be _________ mV.

Accepted Answer

160

Question 61

In the reaction shown, a Grignard reagent is formed with Mg and then treated with H$_2$O to give the major product 'A'. 'A' is

Accepted Answer

(D) (4)

Answer

(A) (1)

Answer

(B) (2)

Answer

(C) (3)

Question 62

Four gases A, B, C and D have critical temperatures 5.3, 33.2, 126.0 and 154.3K respectively. For their adsorption on fixed amount of charcoal, the correct order is:

Accepted Answer

(D) D > C > B > A

Answer

(A) C > B > D > A

Answer

(B) C > D > B > A

Answer

(C) D > C > A > B

Question 63

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: 5f electrons can participate in bonding to a far greater extent than 4f electrons.
Reason R: 5f orbitals are not as buried as 4f orbitals.
In the light of the above statements, choose the correct answer from the options given below:

Accepted Answer

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

Answer

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

Answer

(C) A is false but R is true

Answer

(D) A is true but R is false

Question 64

The incorrect statement regarding the reaction of the given secondary amine 'A' (shown) with $NaNO_2$ and HX to give 'B' is

Accepted Answer

(B) ‘B’ is N-nitroso ammonium compound

Answer

(A) The electrophile involved in the reaction is NO$^+$

Answer

(C) The reaction occurs at low temperature

Answer

(D) The product ‘B’ formed in the above reaction is p-nitroso compound at low temperature

List I	List II
A.Spring constant	I. $[T^{-1}]$
B.Angular speed	II. $[MT^{-2}]$
C.Angular momentum	III. $[ML^2]$
D.Moment of Inertia	IV. $[ML^2T^{-1}]$

List I (Complex)	List II (CFSE/$\Delta_0$)
A. $[Cu(NH_3)_4]^{2+}$	I. $-0.6$
B. $[Ti(H_2O)_6]^{3+}$	II. $-2.0$
C. $[Fe(CN)_6]^{3-}$	III. $-1.2$
D. $[NiF_6]^{2-}$	IV. $-0.4$

List I (Examples)	List II (Examples)
A.2-Chloro-1,3-butadiene	I.Biodegradable polymer
B.Nylon 2-nylon 6	II.Synthetic Rubber
C.Polyacrylonitrile	III.Polyester
D.Dacron	IV.Addition Polymer

List I	List II
A.Nitrogen oxides in air	I.Eutrophication
B.Methane in air	II.pH of rain water becomes 5.6
C.Carbon dioxide	III.Global warming
D.Phosphate fertilisers in water	IV.Acid rain

List I (Type of hydride)	List II (Example)
A.Electron deficient hydride	I.MgH $_2$
B.Electron rich hydride	II.HF
C.Electron precise hydride	III.B $_2$ H $_6$
D.Saline hydride	IV.CH $_4$

JEE Main 12 April 2023 Shift 1 Question Paper with Answers

Physics — JEE Main 12 April 2023 Shift 1

Chemistry — JEE Main 12 April 2023 Shift 1

Mathematics — JEE Main 12 April 2023 Shift 1

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