JEE Main 8 April 2024 Shift 2 Question Paper

Question 1

If the image of the point $(-4,5)$ in the line $x+2y=2$ lies on the circle $(x+4)^2+(y-3)^2=r^2$, then $r$ is equal to

Accepted Answer

(B) $2$

Answer

(A) $1$

Answer

(C) $\sqrt{5}$

Answer

(D) $3$

Question 2

Let $\vec{a}=\hat{i}+2\hat{j}+3\hat{k}$, $\vec{b}=2\hat{i}+3\hat{j}-5\hat{k}$ and $\vec{c}=3\hat{i}-\hat{j}+\lambda\hat{k}$ be three vectors. Let $\vec{r}$ be a unit vector along $\vec{b}+\vec{c}$. If $\vec{r}\cdot\vec{a}=3$, then $3\lambda$ is equal to

Accepted Answer

(B) $25$

Answer

(A) $27$

Answer

(C) $23$

Answer

(D) $21$

Question 3

If $\alpha
e a$, $\beta
e b$, $\gamma
e c$ and $\begin{vmatrix}\alpha&b&c\a&\beta&c\a&b&\gamma\end{vmatrix}=0$, then $\dfrac{a}{\alpha-a}+\dfrac{b}{\beta-b}+\dfrac{\gamma}{\gamma-c}$ is equal to

Accepted Answer

(C) $0$

Answer

(A) $2$

Answer

(B) $3$

Answer

(D) $1$

Question 4

In an increasing geometric progression of positive terms, the sum of the second and sixth terms is $\dfrac{70}{3}$ and the product of the third and fifth terms is $49$. Then the sum of the $4$th, $6$th and $8$th terms is

Accepted Answer

(C) $91$

Answer

(A) $96$

Answer

(B) $78$

Answer

(D) $84$

Question 5

The number of ways five alphabets can be chosen from the alphabets of the word MATHEMATICS, where the chosen alphabets are not necessarily distinct, is equal to

Accepted Answer

(D) $179$

Answer

(A) $175$

Answer

(B) $181$

Answer

(C) $177$

Question 6

The sum of all possible values of $	heta\in[-\pi,2\pi]$, for which $\dfrac{1+i\cos	heta}{1-2i\cos	heta}$ is purely imaginary, is equal to

Accepted Answer

(B) $3\pi$

Answer

(A) $2\pi$

Answer

(C) $5\pi$

Answer

(D) $4\pi$

Question 7

If the system of equations $x+4y-z=\lambda$, $7x+9y+\mu z=-3$, $5x+y+2z=-1$ has infinitely many solutions, then $(2\mu+3\lambda)$ is equal to

Accepted Answer

(B) $-3$

Answer

(A) $2$

Answer

(C) $3$

Answer

(D) $-2$

Question 8

If the shortest distance between the lines $\dfrac{x-\lambda}{2}=\dfrac{y-4}{3}=\dfrac{z-3}{4}$ and $\dfrac{x-2}{4}=\dfrac{y-4}{6}=\dfrac{z-7}{8}$ is $\dfrac{13}{\sqrt{29}}$, then a value of $\lambda$ is

Accepted Answer

(C) $1$

Answer

(A) $-	frac{13}{25}$

Answer

(B) $	frac{13}{25}$

Answer

(D) $-1$

Question 9

If the value of $\dfrac{3\cos 36^\circ+5\sin 18^\circ}{5\cos 36^\circ-3\sin 18^\circ}$ is $\dfrac{a\sqrt{5}-b}{c}$, where $a$, $b$, $c$ are natural numbers and $\gcd(a,c)=1$, then $a+b+c$ is equal to

Accepted Answer

(C) $52$

Answer

(A) $50$

Answer

(B) $40$

Answer

(D) $54$

Question 10

Let $y=y(x)$ be the solution curve of the differential equation $\sec y\,\dfrac{dy}{dx}+2x\sin y=x^3\cos y$, $y(1)=0$. Then $y(\sqrt{3})$ is equal to

Accepted Answer

(C) $	frac{\pi}{4}$

Answer

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

Answer

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

Answer

(D) $	frac{\pi}{12}$

Question 11

The area of the region in the first quadrant inside the circle $x^2+y^2=8$ and outside the parabola $y^2=2x$ is equal to

Accepted Answer

(B) $\pi-	frac{2}{3}$

Answer

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

Answer

(C) $	frac{\pi}{2}-	frac{2}{3}$

Answer

(D) $\pi-	frac{1}{3}$

Question 12

If the line segment joining the points $(5,2)$ and $(2,a)$ subtends an angle $\dfrac{\pi}{4}$ at the origin, then the absolute value of the product of all possible values of $a$ is

Accepted Answer

(D) $4$

Answer

(A) $6$

Answer

(B) $8$

Answer

(C) $2$

Question 13

Let $\vec{a}=4\hat{i}-\hat{j}+\hat{k}$, $\vec{b}=11\hat{i}-\hat{j}+\hat{k}$ and $\vec{c}$ be a vector such that $(\vec{a}+\vec{b})	imes\vec{c}=\vec{c}	imes(-2\vec{a}+3\vec{b})$. If $(2\vec{a}+3\vec{b})\cdot\vec{c}=1670$, then $|\vec{c}|^2$ is equal to

Accepted Answer

(B) $1618$

Answer

(A) $1627$

Answer

(C) $1600$

Answer

(D) $1609$

Question 14

If the function $f(x)=2x^3-9ax^2+12a^2x+1$, $a>0$ has a local maximum at $x=\alpha$ and a local minimum at $x=\alpha^2$, then $\alpha$ and $\alpha^2$ are the roots of the equation

Accepted Answer

(A) $x^2-6x+8=0$

Answer

(B) $8x^2-6x+8=0$

Answer

(C) $8x^2-6x+1=0$

Answer

(D) $x^2+6x+8=0$

Question 15

There are three bags X, Y and Z. Bag X contains 5 one-rupee coins and 4 five-rupee coins; Bag Y contains 4 one-rupee coins and 5 five-rupee coins and Bag Z contains 3 one-rupee coins and 6 five-rupee coins. A bag is selected at random and a coin drawn from it at random is found to be a one-rupee coin. Then the probability, that it came from bag Y, is

Accepted Answer

(A) $	frac{1}{3}$

Answer

(B) $	frac{1}{2}$

Answer

(C) $	frac{1}{4}$

Answer

(D) $	frac{5}{12}$

Question 16

Let $\displaystyle\int_{a}^{\log_e 4}\dfrac{dx}{\sqrt{e^x-1}}=\dfrac{\pi}{6}$. Then $e^a$ and $e^{-a}$ are the roots of the equation

Accepted Answer

(A) $2x^2-5x+2=0$

Answer

(B) $x^2-2x-8=0$

Answer

(C) $2x^2-5x-2=0$

Answer

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

Question 17

Let $f(x)=\begin{cases}-a & 	ext{if } -a\le x\le 0\ x+a & 	ext{if } 0<x\le a\end{cases}$ where $a>0$ and $g(x)=\dfrac{f(|x|)-|f(x)|}{2}$. Then the function $g:[-a,a]	o[-a,a]$ is

Accepted Answer

(A) neither one-one nor onto.

Answer

(B) both one-one and onto.

Answer

(C) one-one.

Answer

(D) onto

Question 18

Let $A=\{2,3,6,8,9,11\}$ and $B=\{1,4,5,10,15\}$. Let R be a relation on $A	imes B$ defined by $(a,b)\,R\,(c,d)$ if and only if $3ad-7bc$ is an even integer. Then the relation R is

Accepted Answer

(C) reflexive and symmetric but not transitive.

Answer

(A) reflexive but not symmetric.

Answer

(B) transitive but not symmetric.

Answer

(D) an equivalence relation.

Question 19

For $a,b>0$, let $f(x)=\begin{cases}\dfrac{\tan((a+1)x)+b\tan x}{x} & ,\ x<0\[2pt] 3 & ,\ x=0\[2pt] \dfrac{\sqrt{ax+b^2x^2}-\sqrt{ax}}{b\sqrt{a}\,x\sqrt{x}} & ,\ x>0\end{cases}$ be a continuous function at $x=0$. Then $\dfrac{b}{a}$ is equal to

Accepted Answer

(D) $6$

Answer

(A) $5$

Answer

(B) $4$

Answer

(C) $8$

Question 20

If the term independent of $x$ in the expansion of $\left(\sqrt{a}\,x^2+\dfrac{1}{2x^3}\right)^{10}$ is $105$, then $a^2$ is equal to

Accepted Answer

(A) $4$

Answer

(B) $9$

Answer

(C) $6$

Answer

(D) $2$

Question 21

Let A be the region enclosed by the parabola $y^2=2x$ and the line $x=24$. Then the maximum area of the rectangle inscribed in the region A is _______ .

Accepted Answer

128

Question 22

If $\alpha=\displaystyle\lim_{x	o 0^+}\left(\dfrac{e^{\sqrt{	an x}}-e^{\sqrt{x}}}{\sqrt{	an x}-\sqrt{x}}ight)$ and $\beta=\displaystyle\lim_{x	o 0}(1+\sin x)^{\frac{1}{2}\cot x}$ are the roots of the quadratic equation $ax^2+bx-\sqrt{e}=0$, then $12\log_e(a+b)$ is equal to _______ .

Accepted Answer

6

Question 23

Let S be the focus of the hyperbola $\dfrac{x^2}{3}-\dfrac{y^2}{5}=1$, on the positive x-axis. Let C be the circle with its centre at $A(\sqrt{6},\sqrt{5})$ and passing through the point S. If O is the origin and SAB is a diameter of C, then the square of the area of the triangle OSB is equal to _______ .

Accepted Answer

40

Question 24

Let $P(\alpha,\beta,\gamma)$ be the image of the point $Q(1,6,4)$ in the line $\dfrac{x}{1}=\dfrac{y-1}{2}=\dfrac{z-2}{3}$. Then $2\alpha+\beta+\gamma$ is equal to _______ .

Accepted Answer

11

Question 25

An arithmetic progression is written in the following way: row 1 is $2$; row 2 is $5,\ 8$; row 3 is $11,\ 14,\ 17$; row 4 is $20,\ 23,\ 26,\ 29$; and so on. The sum of all the terms of the $10$th row is _______ .

Accepted Answer

1505

Question 26

The number of distinct real roots of the equation $|x+1|\,|x+3|-4\,|x+2|+5=0$, is _______ .

Accepted Answer

2

Question 27

Let a ray of light passing through the point $(3,10)$ reflect on the line $2x+y=6$ and the reflected ray pass through the point $(7,2)$. If the equation of the incident ray is $ax+by+1=0$, then $a^2+b^2+3ab$ is equal to _______ .

Accepted Answer

1

Question 28

Let $a$, $b$, $c\in\mathbb{N}$ and $a<b<c$. Let the mean, the mean deviation about the mean and the variance of the 5 observations $9$, $25$, $a$, $b$, $c$ be $18$, $4$ and $\dfrac{136}{5}$, respectively. Then $2a+b-c$ is equal to _______ .

Accepted Answer

33

Question 29

Let $\alpha|x|=|y|e^{xy-\beta}$, $\alpha,\beta\in\mathbb{N}$ be the solution of the differential equation $x\,dy-y\,dx+xy(x\,dy+y\,dx)=0$, $y(1)=2$. Then $\alpha+\beta$ is equal to _______ .

Accepted Answer

4

Question 30

If $\displaystyle\int\dfrac{1}{\sqrt[5]{(x-1)^4(x+3)^6}}\,dx=A\left(\dfrac{\alpha x-1}{\beta x+3}\right)^B+C$, where C is the constant of integration, then the value of $\alpha+\beta+20AB$ is _______ .

Accepted Answer

7

Question 31

A block is simply released from the top of an inclined plane as shown in the figure above. The maximum compression in the spring when the block hits the spring is:

Accepted Answer

(B) $2$ m

Answer

(A) $\sqrt{6}$ m

Answer

(C) $1$ m

Answer

(D) $\sqrt{5}$ m

Question 32

In a hypothetical fission reaction $_{92}X^{236}	o\,_{56}Y^{141}+\,_{36}Z^{92}+3R$. The identity of emitted particles (R) is:

Accepted Answer

(C) Neutron

Answer

(A) Proton

Answer

(B) Electron

Answer

(D) $\gamma$-radiations

Question 33

If $\varepsilon_0$ is the permittivity of free space and E is the electric field, then $\varepsilon_0 E^2$ has the dimensions:

Accepted Answer

(B) $[ML^{-1}T^{-2}]$

Answer

(A) $[M^0L^{-2}TA]$

Answer

(C) $[M^{-1}L^{-3}T^4A^2]$

Answer

(D) $[ML^2T^{-2}]$

Question 34

The position of the image formed by the combination of lenses is:

Accepted Answer

(A) 30 cm (right of third lens)

Answer

(B) 15 cm (left of second lens)

Answer

(C) 30 cm (left of third lens)

Answer

(D) 15 cm (right of second lens)

Question 35

A plane progressive wave is given by $y=2\cos 2\pi(330\,t-x)$ m. The frequency of the wave is:

Accepted Answer

(B) 330 Hz

Answer

(A) 165 Hz

Answer

(C) 660 Hz

Answer

(D) 340 Hz

Question 36

A thin circular disc of mass M and radius R is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with angular velocity $\omega$. If another disc of same dimensions but of mass $\dfrac{M}{2}$ is placed gently on the first disc co-axially, then the new angular velocity of the system is:

Accepted Answer

(C) $\dfrac{2\omega}{3}$

Answer

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

Answer

(B) $\dfrac{5\omega}{4}$

Answer

(D) $\dfrac{3\omega}{2}$

Question 37

A cube of ice floats partly in water and partly in kerosene oil. The ratio of volume of ice immersed in water to that in kerosene oil (specific gravity of kerosene oil = 0.8, specific gravity of ice = 0.9) is:

Accepted Answer

(D) 1 : 1

Answer

(A) 8 : 9

Answer

(B) 5 : 4

Answer

(C) 9 : 10

Question 38

Given below are two statements: Statement (I): The mean free path of gas molecules is inversely proportional to square of molecular diameter. Statement (II): Average kinetic energy of gas molecules is directly proportional to absolute temperature of gas. In the light of the above statements, choose the correct answer from the option 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) Statement I is true but Statement II is false.

Answer

(C) Both Statement I and Statement II are false

Question 39

Two satellites A and B go round a planet in circular orbits having radii 4R and R respectively. If the speed of A is 3v, the speed of B will be:

Accepted Answer

(C) $6v$

Answer

(A) $\dfrac{4}{3}v$

Answer

(B) $3v$

Answer

(D) $12v$

Question 40

A long straight wire of radius $a$ carries a steady current I. The current is uniformly distributed across its cross section. The ratio of the magnetic field at $\dfrac{a}{2}$ and $2a$ from axis of the wire is:

Accepted Answer

(C) 1 : 1

Answer

(A) 1 : 4

Answer

(B) 4 : 1

Answer

(D) 3 : 4

Question 41

The angle of projection for a projectile to have same horizontal range and maximum height is:

Accepted Answer

(B) $	an^{-1}(4)$

Answer

(A) $	an^{-1}(2)$

Answer

(C) $	an^{-1}\left(\dfrac{1}{4}ight)$

Answer

(D) $	an^{-1}\left(\dfrac{1}{2}ight)$

Question 42

Water boils in an electric kettle in 20 minutes after being switched on. Using the same main supply, the length of the heating element should be ________ to ________ times of its initial length if the water is to be boiled in 15 minutes.

Accepted Answer

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

Answer

(A) increased, $\dfrac{3}{4}$

Answer

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

Answer

(D) decreased, $\dfrac{4}{3}$

Question 43

A capacitor has air as dielectric medium and two conducting plates of area 12 cm$^2$ and they are 0.6 cm apart. When a slab of dielectric having area 12 cm$^2$ and 0.6 cm thickness is inserted between the plates, one of the conducting plates has to be moved by 0.2 cm to keep the capacitance same as in previous case. The dielectric constant of the slab is: (Given $\varepsilon=8.834	imes10^{-12}$ F/m)

Accepted Answer

(A) 1.50

Answer

(B) 1.33

Answer

(C) 0.66

Answer

(D) 1

Question 44

A given object takes $n$ times the time to slide down a 45° rough inclined plane as it takes to slide down an identical perfectly smooth 45° inclined plane. The coefficient of kinetic friction between the object and the surface of inclined plane is:

Accepted Answer

(A) $1-\dfrac{1}{n^2}$

Answer

(B) $1-n^2$

Answer

(C) $\sqrt{1-\dfrac{1}{n^2}}$

Answer

(D) $\dfrac{1}{\sqrt{1-n^2}}$

Question 45

A coil of negligible resistance is connected in series with a 90 $\Omega$ resistor across a 120 V, 60 Hz supply. A voltmeter reads 36 V across the resistance. Inductance of the coil is:

Accepted Answer

(A) 0.76 H

Answer

(B) 2.86 H

Answer

(C) 0.286 H

Answer

(D) 0.91 H

Question 46

There are 100 divisions on the circular scale of a screw gauge of pitch 1 mm. With no measuring quantity in between the jaws, the zero of the circular scale lies 5 divisions below the reference line. The diameter of a wire is then measured using this screw gauge. It is found that 4 linear scale divisions are clearly visible while 60 divisions on circular scale coincide with the reference line. The diameter of the wire is:

Accepted Answer

(B) 4.55 mm

Answer

(A) 4.65 mm

Answer

(C) 4.60 mm

Answer

(D) 3.35 mm

Question 47

A proton and an electron have the same de Broglie wavelength. If $K_p$ and $K_e$ be the kinetic energies of proton and electron respectively, then choose the correct relation:

Accepted Answer

(D) $K_p<K_e$

Answer

(A) $K_p>K_e$

Answer

(B) $K_p=K_e$

Answer

(C) $K_p=\dfrac{K_e}{2}$

Question 48

Least count of a vernier caliper is $\dfrac{1}{20N}$ cm. The value of one division on the main scale is 1 mm. Then the number of divisions of main scale that coincide with N divisions of vernier scale is:

Accepted Answer

(B) $\left(\dfrac{2N-1}{2}\right)$

Answer

(A) $\left(\dfrac{2N-1}{20N}\right)$

Answer

(C) $(2N-1)$

Answer

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

Question 49

If $M_o$ is the mass of isotope $_5^{12}B$, $M_p$ and $M_n$ are the masses of proton and neutron, then nuclear binding energy of the isotope is:

Accepted Answer

(A) $(5M_p+7M_n-M_o)C^2$

Answer

(B) $(M_o-5M_p)C^2$

Answer

(C) $(M_o-12M_n)C^2$

Answer

(D) $(M_o-5M_p-7M_n)C^2$

Question 50

A diatomic gas ($\gamma=1.4$) does 100 J of work in an isobaric expansion. The heat given to the gas is:

Accepted Answer

(A) 350 J

Answer

(B) 490 J

Answer

(C) 150 J

Answer

(D) 250 J

Question 51

The coercivity of a magnet is $5	imes10^3$ A/m. The amount of current required to be passed in a solenoid of length 30 cm and the number of turns 150, so that the magnet gets demagnetised when inside the solenoid is ________ A.

Accepted Answer

10

Question 52

Small water droplets of radius 0.01 mm are formed in the upper atmosphere and falling with a terminal velocity of 10 cm/s. Due to condensation, if 8 such droplets are coalesced and formed a larger drop, the new terminal velocity will be ________ cm/s.

Accepted Answer

40

Question 53

If the net electric field at point P along the Y axis is zero, then the ratio of $\dfrac{q_2}{q_3}$ is $\dfrac{8}{5x}$, where x = ________ .

Accepted Answer

5

Question 54

A heater is designed to operate with a power of 1000 W in a 100 V line. It is connected in combination with a resistance of 10 $\Omega$ and a resistance R, to a 100 V mains as shown in figure. For the heater to operate at 62.5 W, the value of R should be ________ $\Omega$.

Accepted Answer

5

Question 55

An alternating emf $E=110\sqrt{2}\sin 100t$ volt is applied to a capacitor of 2 $\mu$F, the rms value of current in the circuit is ________ mA.

Accepted Answer

22

Question 56

Two slits are 1 mm apart and the screen is located 1 m away from the slits. A light of wavelength 500 nm is used. The width of each slit to obtain 10 maxima of the double slit pattern within the central maximum of the single slit pattern is ________ $	imes 10^{-4}$ m.

Accepted Answer

2

Question 57

An object of mass 0.2 kg executes simple harmonic motion along the x axis with frequency of $\dfrac{25}{\pi}$ Hz. At the position x = 0.04 m the object has kinetic energy 0.5 J and potential energy 0.4 J. The amplitude of oscillation is ________ cm.

Accepted Answer

6

Question 58

A potential divider circuit is connected with a dc source of 20 V, a light emitting diode of glow in voltage 1.8 V and a zener diode of breakdown voltage of 3.2 V. The length (PR) of the resistive wire is 20 cm. The minimum length of PQ to just glow the LED is ________ cm.

Accepted Answer

5

Question 59

A body of mass M thrown horizontally with velocity v from the top of the tower of height H touches the ground at a distance of 100 m from the foot of the tower. A body of mass 2M thrown at a velocity $\dfrac{v}{2}$ from the top of the tower of height 4H will touch the ground at a distance of ________ m.

Accepted Answer

100

Question 60

A circular table is rotating with an angular velocity of $\omega$ rad/s about its axis. There is a smooth groove along a radial direction on the table. A steel ball is gently placed at a distance of 1 m on the groove. All the surfaces are smooth. If the radius of the table is 3 m, the radial velocity of the ball w.r.t. the table at the time the ball leaves the table is $x\sqrt{2}$ m/s, where the value of x is ________ .

Accepted Answer

2

Question 61

In qualitative test for identification of presence of phosphorous, the compound is heated with an oxidising agent, which is further treated with nitric acid and ammonium molybdate respectively. The yellow coloured precipitate obtained is:

Accepted Answer

(C) $(	ext{NH}_4)_3	ext{PO}_4\cdot 12	ext{MoO}_3$

Answer

(A) $	ext{Na}_3	ext{PO}_4\cdot 12	ext{MoO}_3$

Answer

(B) $(	ext{NH}_4)_3	ext{PO}_4\cdot 12(	ext{NH}_4)_2	ext{MoO}_4$

Answer

(D) $	ext{MoPO}_4\cdot 21	ext{NH}_4	ext{NO}_3$

Question 62

For a reaction $A\xrightarrow{K_1}B\xrightarrow{K_2}C$, if the rate of formation of B is set to be zero then the concentration of B is given by:

Accepted Answer

(D) $\left(\dfrac{K_1}{K_2}\right)[A]$

Answer

(A) $K_1K_2[A]$

Answer

(B) $(K_1-K_2)[A]$

Answer

(C) $(K_1+K_2)[A]$

Question 63

When $\psi_A$ and $\psi_B$ are the wave functions of atomic orbitals, then $\psi^*$ is represented by:

Accepted Answer

(B) $\psi_A-\psi_B$

Answer

(A) $\psi_A-2\psi_B$

Answer

(C) $\psi_A+2\psi_B$

Answer

(D) $\psi_A+\psi_B$

Question 64

Which one of the following compounds will readily react with dilute NaOH?

Accepted Answer

(D) $	ext{C}_6	ext{H}_5	ext{OH}$

Answer

(A) $	ext{C}_6	ext{H}_5	ext{CH}_2	ext{OH}$

Answer

(B) $	ext{C}_2	ext{H}_5	ext{OH}$

Answer

(C) $(	ext{CH}_3)_3	ext{COH}$

List-I (Reactions)	List-II (Products)
A.see figure	I.see figure
B.see figure	II.see figure
C.see figure	III.see figure
D.see figure	IV.see figure

List-I (Test)	List-II (Identification)
A.Bayer's test	I.Phenol
B.Ceric ammonium nitrate test	II.Aldehyde
C.Phthalein dye test	III.Alcoholic-OH group
D.Schiff's test	IV.Unsaturation

List-I (Complex ion)	List-II (Spin only magnetic moment in B.M.)
A. $[\text{Cr(NH}_3)_6]^{3+}$	I.4.90
B. $[\text{NiCl}_4]^{2-}$	II.3.87
C. $[\text{CoF}_6]^{3-}$	III.0.0
D. $[\text{Ni(CN)}_4]^{2-}$	IV.2.83

JEE Main 8 April 2024 Shift 2 Question Paper with Answers

Physics — JEE Main 8 April 2024 Shift 2

Chemistry — JEE Main 8 April 2024 Shift 2

Mathematics — JEE Main 8 April 2024 Shift 2

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