JEE Main 29 January 2024 Shift 1 Question Paper

Question 1

If in a G.P. of 64 terms, the sum of all the terms is 7 times the sum of the odd terms of the G.P., then the common ratio of the G.P. is equal to

Accepted Answer

(D) 6

Answer

(A) 7

Answer

(B) 4

Answer

(C) 5

Question 2

In an A.P., the sixth term $a_6=2$. If the $a_1 a_4 a_5$ is the greatest, then the common difference of the A.P., is equal to

Accepted Answer

(B) $\dfrac{8}{5}$

Answer

(A) $\dfrac{3}{2}$

Answer

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

Answer

(D) $\dfrac{5}{8}$

Question 3

If $f(x)=\begin{cases}2+2x, & -1\le x<0\ 1-\dfrac{x}{3}, & 0\le x\le 3\end{cases}$ ; $g(x)=\begin{cases}-x, & -3\le x\le 0\ x, & 0<x\le 1\end{cases}$, then range of $(f\circ g)(x)$ is

Accepted Answer

(C) $[0,1]$

Answer

(A) $(0,1]$

Answer

(B) $[0,3)$

Answer

(D) $[0,1)$

Question 4

A fair die is thrown until 2 appears. Then the probability, that 2 appears in even number of throws, is

Accepted Answer

(C) $\dfrac{5}{11}$

Answer

(A) $\dfrac{5}{6}$

Answer

(B) $\dfrac{1}{6}$

Answer

(D) $\dfrac{6}{11}$

Question 5

If $z=\dfrac{1}{2}-2i$, is such that $|z+1|=\alpha z+\beta(1+i)$, $i=\sqrt{-1}$ and $\alpha,\beta\in R$, then $\alpha+\beta$ is equal to

Accepted Answer

(B) $3$

Answer

(A) $-4$

Answer

(C) $2$

Answer

(D) $-1$

Question 6

$\displaystyle\lim_{x	o\frac{\pi}{2}}\left(\dfrac{1}{\left(x-\dfrac{\pi}{2}ight)^2}\int_{x^3}^{\left(\frac{\pi}{2}ight)^3}\cos\left(t^{1/3}ight)dtight)$ is equal to

Accepted Answer

(C) $\dfrac{3\pi^2}{8}$

Answer

(A) $\dfrac{3\pi}{8}$

Answer

(B) $\dfrac{3\pi^2}{4}$

Answer

(D) $\dfrac{3\pi}{4}$

Question 7

In a $	riangle ABC$, suppose $y=x$ is the equation of the bisector of the angle B and the equation of the side AC is $2x-y=2$. If $2AB=BC$ and the point A and B are respectively $(4,6)$ and $(\alpha,\beta)$, then $\alpha+2\beta$ is equal to

Accepted Answer

(A) $42$

Answer

(B) $39$

Answer

(C) $48$

Answer

(D) $45$

Question 8

Let $\vec{a},\vec{b}$ and $\vec{c}$ be three non-zero vectors such that $\vec{b}$ and $\vec{c}$ are non-collinear. If $\vec{a}+5\vec{b}$ is collinear with $\vec{c}$, $\vec{b}+6\vec{c}$ is collinear with $\vec{a}$ and $\vec{a}+\alpha\vec{b}+\beta\vec{c}=\vec{0}$, then $\alpha+\beta$ is equal to

Accepted Answer

(A) $35$

Answer

(B) $30$

Answer

(C) $-30$

Answer

(D) $-25$

Question 9

Let $\left(5,\dfrac{a}{4}\right)$ be the circumcenter of a triangle with vertices $A(a,-2)$, $B(a,6)$ and $C\left(\dfrac{a}{4},-2\right)$. Let $\alpha$ denote the circumradius, $\beta$ denote the area and $\gamma$ denote the perimeter of the triangle. Then $\alpha+\beta+\gamma$ is

Accepted Answer

(B) $53$

Answer

(A) $60$

Answer

(C) $62$

Answer

(D) $30$

Question 10

For $x\in\left(-\dfrac{\pi}{2},\dfrac{\pi}{2}ight)$, if $y(x)=\displaystyle\int\dfrac{\operatorname{cosec}x+\sin x}{\operatorname{cosec}x\sec x+	an x\sin^2 x}dx$ and $\displaystyle\lim_{x	o\left(\frac{\pi}{2}ight)^-}y(x)=0$ then $y\left(\dfrac{\pi}{4}ight)$ is equal to

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 11

If $\alpha$, $-\dfrac{\pi}{2}<\alpha<\dfrac{\pi}{2}$ is the solution of $4\cos	heta+5\sin	heta=1$, then the value of $	an\alpha$ is

Accepted Answer

(C) $\dfrac{\sqrt{10}-10}{12}$

Answer

(A) $\dfrac{10-\sqrt{10}}{6}$

Answer

(B) $\dfrac{10-\sqrt{10}}{12}$

Answer

(D) $\dfrac{\sqrt{10}-10}{6}$

Question 12

A function $y=f(x)$ satisfies $f(x)\sin 2x+\sin x-(1+\cos^2 x)f'(x)=0$ with condition $f(0)=0$. Then $f\left(\dfrac{\pi}{2}\right)$ is equal to

Accepted Answer

(A) $1$

Answer

(B) $0$

Answer

(C) $-1$

Answer

(D) $2$

Question 13

Let O be the origin and the position vector of A and B be $2\hat{i}+2\hat{j}+\hat{k}$ and $2\hat{i}+4\hat{j}+4\hat{k}$ respectively. If the internal bisector of $\angle AOB$ meets the line AB at C, then the length of OC is

Accepted Answer

(B) $\dfrac{2}{3}\sqrt{34}$

Answer

(A) $\dfrac{2}{3}\sqrt{31}$

Answer

(C) $\dfrac{3}{4}\sqrt{34}$

Answer

(D) $\dfrac{3}{2}\sqrt{31}$

Question 14

Consider the function $f:\left[\dfrac{1}{2},1ight]	o R$ defined by $f(x)=4\sqrt{2}x^3-3\sqrt{2}x-1$. Consider the statements (I) The curve $y=f(x)$ intersects the x-axis exactly at one point (II) The curve $y=f(x)$ intersects the x-axis at $x=\cos\dfrac{\pi}{12}$. Then

Accepted Answer

(D) Both (I) and (II) are correct

Answer

(A) Only (II) is correct

Answer

(B) Both (I) and (II) are incorrect

Answer

(C) Only (I) is correct

Question 15

Let $A=\begin{bmatrix}1 & 0 & 0\ 0 & \alpha & \beta\ 0 & \beta & \alpha\end{bmatrix}$ and $|2A|^3=2^{21}$ where $\alpha,\beta\in Z$. Then a value of $\alpha$ is

Accepted Answer

(B) $5$

Answer

(A) $3$

Answer

(C) $17$

Answer

(D) $9$

Question 16

Let PQR be a triangle with $R(-1,4,2)$. Suppose $M(2,1,2)$ is the mid point of PQ. The distance of the centroid of $	riangle PQR$ from the point of intersection of the line $\dfrac{x-2}{0}=\dfrac{y}{2}=\dfrac{z+3}{-1}$ and $\dfrac{x-1}{1}=\dfrac{y+3}{-3}=\dfrac{z+1}{1}$ is

Accepted Answer

(C) $\sqrt{69}$

Answer

(A) $69$

Answer

(B) $9$

Answer

(D) $\sqrt{99}$

Question 17

Let R be a relation on $Z	imes Z$ defined by $(a,b)R(c,d)$ if and only if $ad-bc$ is divisible by 5. Then R is

Accepted Answer

(A) Reflexive and symmetric but not transitive

Answer

(B) Reflexive but neither symmetric not transitive

Answer

(C) Reflexive, symmetric and transitive

Answer

(D) Reflexive and transitive but not symmetric

Question 18

If the value of the integral $\displaystyle\int_{-\pi/2}^{\pi/2}\left(\dfrac{x^2\cos x}{1+\pi^x}+\dfrac{1+\sin^2 x}{1+e^{\sin x^{2023}}}\right)dx=\dfrac{\pi}{4}(\pi+a)-2$, then the value of a is

Accepted Answer

(A) $3$

Answer

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

Answer

(C) $2$

Answer

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

Question 19

Suppose $f(x)=\dfrac{\left(2^x+2^{-x}ight)	an x\sqrt{	an^{-1}\left(x^2-x+1ight)}}{\left(7x^2+3x+1ight)^3}$. Then the value of $f'(0)$ is equal to

Accepted Answer

(C) $\sqrt{\pi}$

Answer

(A) $\pi$

Answer

(B) $0$

Answer

(D) $\dfrac{\pi}{2}$

Question 20

Let A be a square matrix such that $AA^T=I$. Then $\dfrac{1}{2}A\left[\left(A+A^T\right)^2+\left(A-A^T\right)^2\right]$ is equal to

Accepted Answer

(D) $A^3+A^T$

Answer

(A) $A^2+I$

Answer

(B) $A^3+I$

Answer

(C) $A^2+A^T$

Question 21

Equation of two diameters of a circle are $2x-3y=5$ and $3x-4y=7$. The line joining the points $\left(-\dfrac{22}{7},-4\right)$ and $\left(-\dfrac{1}{7},3\right)$ intersects the circle at only one point $P(\alpha,\beta)$. Then $17\beta-\alpha$ is equal to ______.

Accepted Answer

2

Question 22

All the letters of the word "GTWENTY" are written in all possible ways with or without meaning and these words are written as in a dictionary. The serial number of the word "GTWENTY" is ______.

Accepted Answer

553

Question 23

Let $\alpha,\beta$ be the roots of the equation $x^2-x+2=0$ with $\operatorname{Im}(\alpha)>\operatorname{Im}(\beta)$. Then $\alpha^6+\alpha^4+\beta^4-5\alpha^2$ is equal to ______.

Accepted Answer

13

Question 24

Let $f(x)=2^x-x^2$, $x\in R$. If m and n are respectively the number of points at which the curves $y=f(x)$ and $y=f'(x)$ intersects the x-axis, then the value of $m+n$ is ______.

Accepted Answer

5

Question 25

If the points of intersection of two distinct conics $x^2+y^2=4b$ and $\dfrac{x^2}{16}+\dfrac{y^2}{b^2}=1$ lie on the curve $y^2=3x^2$, then $3\sqrt{3}$ times the area of the rectangle formed by the intersection points is ______.

Accepted Answer

432

Question 26

If the solution curve $y=y(x)$ of the differential equation $\left(1+y^2ight)\left(1+\log_e xight)dx+x\,dy=0$, $x>0$ passes through the point $(1,1)$ and $y(e)=\dfrac{\alpha-	an\left(\frac{3}{2}ight)}{\beta+	an\left(\frac{3}{2}ight)}$, then $\alpha+2\beta$ is ______.

Accepted Answer

3

Question 27

If the mean and variance of the data $65,68,58,44,48,45,60,\alpha,\beta,60$ where $\alpha>\beta$ are 56 and 66.2 respectively, then $\alpha^2+\beta^2$ is equal to ______.

Accepted Answer

6344

Question 28

The area (in sq. units) of the part of circle $x^2+y^2=169$ which is below the line $5x-y=13$ is $\dfrac{\pi\alpha}{2\beta}-\dfrac{65}{2}+\dfrac{\alpha}{\beta}\sin^{-1}\left(\dfrac{12}{13}\right)$ where $\alpha,\beta$ are coprime numbers. Then $\alpha+\beta$ is equal to ______.

Accepted Answer

171

Question 29

If $\dfrac{^{11}C_1}{2}+\dfrac{^{11}C_2}{3}+\cdots+\dfrac{^{11}C_9}{10}=\dfrac{n}{m}$ with $\gcd(n,m)=1$, then $n+m$ is equal to ______.

Accepted Answer

2041

Question 30

A line with direction ratios $2,1,2$ meets the lines $x=y+2=z$ and $x+2=2y=2z$ respectively at the point P and Q. If the length of the perpendicular from the point $(1,2,12)$ to the line PQ is $l$, then $l^2$ is ______.

Accepted Answer

65

Question 31

In the given circuit, the breakdown voltage of the Zener diode is 3.0 V. What is the value of $I_z$?

Accepted Answer

(B) 5.5 mA

Answer

(A) 3.3 mA

Answer

(C) 10 mA

Answer

(D) 7 mA

Question 32

The electric current through a wire varies with time as $I=I_0+\beta t$ where $I_0=20$ A and $\beta=3$ A/s. The amount of electric charge crossed through a section of the wire in 20 s is:

Accepted Answer

(B) 1000 C

Answer

(A) 80 C

Answer

(C) 800 C

Answer

(D) 1600 C

Question 33

Given below are two statements:
Statement I : If a capillary tube is immersed first in cold water and then in hot water, the height of capillary rise will be smaller in hot water.
Statement II : If a capillary tube is immersed first in cold water and then in hot water, the height of capillary rise will be smaller in cold water.
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 true

Answer

(B) Both Statement I and Statement II are false

Answer

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

Question 34

A convex mirror of radius of curvature 30 cm forms an image that is half the size of the object. The object distance is :

Accepted Answer

(A) $-15$ cm

Answer

(B) $45$ cm

Answer

(C) $-45$ cm

Answer

(D) $15$ cm

Question 35

Two charges of $5Q$ and $-2Q$ are situated at the points $(3a,0)$ and $(-5a,0)$ respectively. The electric flux through a sphere of radius $4a$ having center at origin is :

Accepted Answer

(B) $\dfrac{5Q}{\epsilon_0}$

Answer

(A) $\dfrac{2Q}{\epsilon_0}$

Answer

(C) $\dfrac{7Q}{\epsilon_0}$

Answer

(D) $\dfrac{3Q}{\epsilon_0}$

Question 36

A body starts moving from rest with constant acceleration covers displacement $S_1$ in first $(p-1)$ seconds and $S_2$ in first $p$ seconds. The displacement $S_1+S_2$ will be made in time :

Accepted Answer

(B) $\sqrt{2p^2-2p+1}$ s

Answer

(A) $(2p+1)$ s

Answer

(C) $(2p-1)$ s

Answer

(D) $(2p^2-2p+1)$ s

Question 37

The potential energy function (in J) of a particle in a region of space is given as $U=(2x^2+3y^3+2z)$. Here x, y and z are in meter. The magnitude of x-component of force (in N) acting on the particle at point $P(1,2,3)$ m is :

Accepted Answer

(C) $4$

Answer

(A) $2$

Answer

(B) $6$

Answer

(D) $8$

Question 38

The resistance $R=\dfrac{V}{I}$ where $V=(200\pm5)$ V and $I=(20\pm0.2)$ A, the percentage error in the measurement of R is :

Accepted Answer

(A) $3.5\%$

Answer

(B) $7\%$

Answer

(C) $3\%$

Answer

(D) $5.5\%$

Question 39

A block of mass 100 kg slides over a distance of 10 m on a horizontal surface. If the co-efficient of friction between the surfaces is 0.4, then the work done against friction (in J) is :

Accepted Answer

(C) $4000$

Answer

(A) $4200$

Answer

(B) $3900$

Answer

(D) $4500$

Question 40

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 41

If the radius of curvature of the path of two particles of same mass are in the ratio 3:4, in order to have constant centripetal force, their velocities will be in the ratio of

Accepted Answer

(A) $\sqrt{3}:2$

Answer

(B) $1:\sqrt{3}$

Answer

(C) $\sqrt{3}:1$

Answer

(D) $2:\sqrt{3}$

Question 42

A galvanometer having coil resistance $10\,\Omega$ shows a full scale deflection for a current of 3 mA. If it to measure a current of 8 A, the value of the shunt should be:

Accepted Answer

(C) $3.75	imes10^{-3}\,\Omega$

Answer

(A) $3	imes10^{-3}\,\Omega$

Answer

(B) $4.85	imes10^{-3}\,\Omega$

Answer

(D) $2.75	imes10^{-3}\,\Omega$

Question 43

The de-Broglie wavelength of an electron is the same as that of a photon. If velocity of electron is 25% of the velocity of light, then the ratio of K.E. of electron and K.E. of photon will be:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 44

The deflection in moving coil galvanometer falls from 25 divisions to 5 division when a shunt of $24\,\Omega$ is applied. The resistance of galvanometer coil will be:

Accepted Answer

(B) $96\,\Omega$

Answer

(A) $12\,\Omega$

Answer

(C) $48\,\Omega$

Answer

(D) $100\,\Omega$

Question 45

A biconvex lens of refractive index 1.5 has a focal length of 20 cm in air. Its focal length when immersed in a liquid of refractive index 1.6 will be:

Accepted Answer

(B) $-160$ cm

Answer

(A) $-16$ cm

Answer

(C) $+160$ cm

Answer

(D) $+16$ cm

Question 46

At what distance above and below the surface of the earth a body will have same weight, (take radius of earth as R.)

Accepted Answer

(D) $\dfrac{\sqrt{5}R-R}{2}$

Answer

(A) $\sqrt{5}R-R$

Answer

(B) $\dfrac{\sqrt{3}R-R}{2}$

Answer

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

Question 47

A capacitor of capacitance $100\,\mu$F is charged to a potential of 12 V and connected to a 6.4 mH inductor to produce oscillations. The maximum current in the circuit would be :

Accepted Answer

(B) $1.5$ A

Answer

(A) $3.2$ A

Answer

(C) $2.0$ A

Answer

(D) $1.2$ A

Question 48

The explosive in a Hydrogen bomb is a mixture of $_1H^2$, $_1H^3$ and $_3Li^6$ in some condensed form. The chain reaction is given by $_3Li^6+_0n^1	o{}_2He^4+_1H^3$ ; $_1H^2+_1H^3	o{}_2He^4+_0n^1$. During the explosion the energy released is approximately [Given : M($_3Li^6$) = 6.01690 amu. M($_1H^2$) = 2.01471 amu. M($_2He^4$) = 4.00388 amu, and 1 amu = 931.5 MeV]

Accepted Answer

(D) $22.22$ MeV

Answer

(A) $28.12$ MeV

Answer

(B) $12.64$ MeV

Answer

(C) $16.48$ MeV

Question 49

Two vessels A and B are of the same size and are at same temperature. A contains 1 g of hydrogen and B contains 1 g of oxygen. $P_A$ and $P_B$ are the pressures of the gases in A and B respectively, then $\dfrac{P_A}{P_B}$ is :

Accepted Answer

(A) $16$

Answer

(B) $8$

Answer

(C) $4$

Answer

(D) $32$

Question 50

When a hydrogen atom going from $n=2$ to $n=1$ emits a photon, its recoil speed is $\dfrac{x}{5}$ m/s. Where $x=$ ______ . (Use : mass of hydrogen atom $=1.6	imes10^{-27}$ kg)

Accepted Answer

17

Question 51

A ball rolls off the top of a stairway with horizontal velocity u. The steps are 0.1 m high and 0.1 m wide. The minimum velocity u with which that ball just hits the step 5 of the stairway will be $\sqrt{x}$ ms$^{-1}$ where $x=$ ______ [use $g=10$ m/s$^2$].

Accepted Answer

2

Question 52

A square loop of side 10 cm and resistance $0.7\,\Omega$ is placed vertically in east-west plane. A uniform magnetic field of 0.20 T is set up across the plane in north east direction. The magnetic field is decreased to zero in 1 s at a steady rate. Then, magnitude of induced emf is $\sqrt{x}	imes10^{-3}$ V. The value of x is ______ .

Accepted Answer

2

Question 53

A cylinder is rolling down on an inclined plane of inclination $60^\circ$. It’s acceleration during rolling down will be $\dfrac{x}{\sqrt{3}}$ m/s$^2$, where $x=$ ______ . (use $g=10$ m/s$^2$).

Accepted Answer

10

Question 54

The magnetic potential due to a magnetic dipole at a point on its axis situated at a distance of 20 cm from its center is $1.5	imes10^{-5}$ Tm. The magnetic moment of the dipole is ______ Am$^2$. (Given : $\dfrac{\mu_0}{4\pi}=10^{-7}$ TmA$^{-1}$)

Accepted Answer

6

Question 55

In a double slit experiment shown in figure, when light of wavelength 400 nm is used, dark fringe is observed at P. If $D=0.2$ m the minimum distance between the slits $S_1$ and $S_2$ is ______ mm.

Accepted Answer

0.20

Question 56

A $16\,\Omega$ wire is bend to form a square loop. A 9V battery with internal resistance $1\,\Omega$ is connected across one of its sides. If a $4\,\mu$F capacitor is connected across one of its diagonals, the energy stored by the capacitor will be $\dfrac{x}{2}\,\mu$J. where $x=$ ______ .

Accepted Answer

81

Question 57

When the displacement of a simple harmonic oscillator is one third of its amplitude, the ratio of total energy to the kinetic energy is $\dfrac{x}{8}$, where $x=$ ______ .

Accepted Answer

9

Question 58

An electron is moving under the influence of the electric field of a uniformly charged infinite plane sheet S having surface charge density $+\sigma$. The electron at $t=0$ is at a distance of 1 m from S and has a speed of 1 m/s. The maximum value of $\sigma$ if the electron strikes S at $t=1$ s is $\alpha\left[\dfrac{m\epsilon_0}{e}\right]\dfrac{C}{m^2}$ the value of $\alpha$ is ______ .

Accepted Answer

8

Question 59

In a test experiment on a model aeroplane in wind tunnel, the flow speeds on the upper and lower surfaces of the wings are 70 ms$^{-1}$ and 65 ms$^{-1}$ respectively. If the wing area is 2 m$^2$ the lift of the wing is ______ N. (Given density of air $=1.2$ kg m$^{-3}$)

Accepted Answer

810

Question 60

Given below are two statements : one is labelled as Assertion A and the other is labelled as
Reason R :
Assertion A : The first ionisation enthalpy decreases across a period.
Reason R : The increasing nuclear charge outweighs the shielding across the period.
In the light of the above statements, choose the most appropriate from the options given below :

Accepted Answer

(C) A is false but R is true

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

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

Question 61

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 62

In chromyl chloride test for confirmation of $Cl^-$ ion, a yellow solution is obtained. Acidification of the solution and addition of amyl alcohol and 10% $H_2O_2$ turns organic layer blue indicating formation of chromium pentoxide. The oxidation state of chromium in that is

Accepted Answer

(A) $+6$

Answer

(B) $+5$

Answer

(C) $+10$

Answer

(D) $+3$

Question 63

The difference in energy between the actual structure and the lowest energy resonance structure for the given compound is

Accepted Answer

(B) resonance energy

Answer

(A) electromeric energy

Answer

(C) ionization energy

Answer

(D) hyperconjugation energy

Question 64

Given below are two statements :
Statement I : The electronegativity of group 14 elements from Si to Pb gradually decreases.
Statement II : Group 14 contains non-metallic, metallic, as well as metalloid elements.
In the light of the above statements, choose the most appropriate from the options given below :

Accepted 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 true

Answer

(D) Both Statement I and Statement II are false

List I (Equation)	List II (Law)
A. $\oint\vec{B}\cdot\vec{dl}=\mu_0 i_c+\mu_0\epsilon_0\dfrac{d\phi_E}{dt}$	I.Gauss’ law for electricity
B. $\oint\vec{E}\cdot\vec{dl}=\dfrac{d\phi_B}{dt}$	II.Gauss’ law for magnetism
C. $\oint\vec{E}\cdot\vec{dA}=\dfrac{Q}{\epsilon_0}$	III.Faraday law
D. $\oint\vec{B}\cdot\vec{dA}=0$	IV.Ampere – Maxwell law

List-I (Substances)	List-II (Element Present)
A.Ziegler catalyst	I.Rhodium
B.Blood Pigment	II.Cobalt
C.Wilkinson catalyst	III.Iron
D.Vitamin $B_{12}$	IV.Titanium

JEE Main 29 January 2024 Shift 1 Question Paper with Answers

Physics — JEE Main 29 January 2024 Shift 1

Chemistry — JEE Main 29 January 2024 Shift 1

Mathematics — JEE Main 29 January 2024 Shift 1

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