JEE Main 25 January 2023 Shift 2 Question Paper

Question 1

Let $\Delta, 
abla \in \{\wedge, \vee\}$ be such that $(p 	o q)\,\Delta\,(p\,
abla\,q)$ is a tautology. Then

Accepted Answer

(A) $\Delta = \vee,\ 
abla = \vee$

Answer

(B) $\Delta = \vee,\ 
abla = \wedge$

Answer

(C) $\Delta = \wedge,\ 
abla = \vee$

Answer

(D) $\Delta = \wedge,\ 
abla = \wedge$

Question 2

If the four points, whose position vectors are $3\hat{i} - 4\hat{j} + 2\hat{k}$, $\hat{i} + 2\hat{j} - \hat{k}$, $-2\hat{i} - \hat{j} + 3\hat{k}$ and $5\hat{i} - 2\alpha\hat{j} + 4\hat{k}$ are coplanar, then $\alpha$ is equal to

Accepted Answer

(A) $\dfrac{73}{17}$

Answer

(B) $\dfrac{107}{17}$

Answer

(C) $\dfrac{-73}{17}$

Answer

(D) $\dfrac{-107}{17}$

Question 3

The foot of perpendicular of the point $(2,0,5)$ on the line $\dfrac{x+1}{2} = \dfrac{y-1}{5} = \dfrac{z+1}{-1}$ is $(\alpha, \beta, \gamma)$. Then, which of the following is NOT correct?

Accepted Answer

(A) $\dfrac{\beta}{\gamma} = -5$

Answer

(B) $\dfrac{\gamma}{\alpha} = \dfrac{5}{8}$

Answer

(C) $\dfrac{\alpha}{\beta} = -8$

Answer

(D) $\dfrac{\alpha\beta}{\gamma} = \dfrac{4}{15}$

Question 4

The equations of two sides of a variable triangle are $x = 0$ and $y = 3$, and its third side is a tangent to parabola $y^2 = 6x$. The locus of its circumcentre is:

Accepted Answer

(C) $4y^2 - 18y + 3x + 18 = 0$

Answer

(A) $4y^2 - 18y - 3x - 18 = 0$

Answer

(B) $4y^2 - 18y - 3x + 18 = 0$

Answer

(D) $4y^2 + 18y + 3x + 18 = 0$

Question 5

Let $f(x) = 2x^n + \lambda$, $\lambda \in \mathbb{R}$, $n \in \mathbb{N}$, and $f(4) = 133$, $f(5) = 255$. Then the sum of all the positive integer divisors of $(f(3) - f(2))$ is

Accepted Answer

(A) 60

Answer

(B) 59

Answer

(C) 61

Answer

(D) 58

Question 6

$\displaystyle\sum_{k=0}^{6} {}^{51-k}C_3$ is equal to

Accepted Answer

(C) ${}^{52}C_4 - {}^{45}C_4$

Answer

(A) ${}^{51}C_4 - {}^{45}C_4$

Answer

(B) ${}^{52}C_3 - {}^{45}C_3$

Answer

(D) ${}^{51}C_3 - {}^{45}C_3$

Question 7

Let the function $f(x) = 2x^3 + (2p - 7)x^2 + 3(2p - 9)x - 6$ have a maxima for some value of $x < 0$ and a minima for some value of $x > 0$. Then, the set of all values of $p$ is

Accepted Answer

(B) $\left(-\infty, \dfrac{9}{2}\right)$

Answer

(A) $\left(0, \dfrac{9}{2}\right)$

Answer

(C) $\left(-\dfrac{9}{2}, \dfrac{9}{2}\right)$

Answer

(D) $\left(\dfrac{9}{2}, \infty\right)$

Question 8

Let $A = \begin{bmatrix} \dfrac{1}{\sqrt{10}} & \dfrac{3}{\sqrt{10}} \ \dfrac{-3}{\sqrt{10}} & \dfrac{1}{\sqrt{10}} \end{bmatrix}$ and $B = \begin{bmatrix} 1 & -i \ 0 & 1 \end{bmatrix}$, where $i = \sqrt{-1}$. If $M = A^{T}BA$, then the inverse of the matrix $AM^{2023}A^{T}$ is

Accepted Answer

(D) $\begin{bmatrix} 1 & 2023i \ 0 & 1 \end{bmatrix}$

Answer

(A) $\begin{bmatrix} 1 & 0 \ -2023i & 1 \end{bmatrix}$

Answer

(B) $\begin{bmatrix} 1 & -2023i \ 0 & 1 \end{bmatrix}$

Answer

(C) $\begin{bmatrix} 1 & 0 \ 2023i & 1 \end{bmatrix}$

Question 9

Let $\vec{a} = -\hat{i} - \hat{j} + \hat{k}$, $\vec{a} \cdot \vec{b} = 1$ and $\vec{a} 	imes \vec{b} = \hat{i} - \hat{j}$. Then $\vec{a} - 6\vec{b}$ is equal to

Accepted Answer

(C) $3(\hat{i} + \hat{j} + \hat{k})$

Answer

(A) $3(\hat{i} - \hat{j} + \hat{k})$

Answer

(B) $(\hat{i} + \hat{j} - \hat{k})$

Answer

(D) $3(\hat{i} - \hat{j} - \hat{k})$

Question 10

The integral $16\displaystyle\int_{1}^{2} \dfrac{dx}{x^3 (x^2 + 2)^2}$ is equal to

Accepted Answer

(B) $\dfrac{11}{6} - \log_e 4$

Answer

(A) $\dfrac{11}{12} - \log_e 4$

Answer

(C) $\dfrac{11}{6} + \log_e 4$

Answer

(D) $\dfrac{11}{12} + \log_e 4$

Question 11

Let $T$ and $C$ respectively be the transverse and conjugate axes of the hyperbola $16x^2 - y^2 + 64x + 4y + 44 = 0$. Then the area of the region above the parabola $x^2 = y + 4$, below the transverse axis $T$ and on the right of the conjugate axis $C$ is:

Accepted Answer

(A) $4\sqrt{6} + \dfrac{28}{3}$

Answer

(B) $4\sqrt{6} - \dfrac{44}{3}$

Answer

(C) $4\sqrt{6} + \dfrac{44}{3}$

Answer

(D) $4\sqrt{6} - \dfrac{28}{3}$

Question 12

Let $N$ be the sum of the numbers appeared when two fair dice are rolled and let the probability that $N - 2$, $\sqrt{3N}$, $N + 2$ are in geometric progression be $\dfrac{k}{48}$. Then the value of $k$ is

Accepted Answer

(D) 4

Answer

(A) 8

Answer

(B) 16

Answer

(C) 2

Question 13

If the function $f(x) = \begin{cases} (1 + |\cos x|)^{\frac{\lambda}{|\cos x|}}, & 0 < x < \dfrac{\pi}{2} \ \mu, & x = \dfrac{\pi}{2} \ \dfrac{\cot 6x}{e^{\cot 4x}}, & \dfrac{\pi}{2} < x < \pi \end{cases}$ is continuous at $x = \dfrac{\pi}{2}$, then $9\lambda + 6\log_e \mu + \mu^6 - e^{6\lambda}$ is equal to

Accepted Answer

(A) 10

Answer

(B) $2e^4 + 8$

Answer

(C) 11

Answer

(D) 8

Question 14

The number of functions $f : \{1,2,3,4\} 	o \{a \in \mathbb{Z} : |a| \le 8\}$ satisfying $f(n) + \dfrac{1}{n}f(n+1) = 1$, $\forall n \in \{1,2,3\}$ is

Accepted Answer

(C) 2

Answer

(A) 1

Answer

(B) 4

Answer

(D) 3

Question 15

Let $y = y(t)$ be a solution of the differential equation $\dfrac{dy}{dt} + \alpha y = \gamma e^{-\beta t}$ where $\alpha > 0$, $\beta > 0$ and $\gamma > 0$. Then $\displaystyle\lim_{t 	o \infty} y(t)$

Accepted Answer

(D) is 0

Answer

(A) is $-1$

Answer

(B) is 1

Answer

(C) does not exist

Question 16

Let $z$ be a complex number such that $\left|\dfrac{z-2i}{z+i}ight|=2$, $z
eq -i$. Then $z$ lies on the circle of radius $2$ and centre

Accepted Answer

(C) $(0,-2)$

Answer

(A) $(2,0)$

Answer

(B) $(0,2)$

Answer

(D) $(0,0)$

Question 17

Let $A, B, C$ be $3	imes 3$ matrices such that $A$ is symmetric and $B$ and $C$ are skew-symmetric. Consider the statements
(S1) $A^{13}B^{26}-B^{26}A^{13}$ is symmetric
(S2) $A^{26}C^{13}-C^{13}A^{26}$ is symmetric
Then,

Accepted Answer

(A) Only S2 is true

Answer

(B) Both S1 and S2 are false

Answer

(C) Only S1 is true

Answer

(D) Both S1 and S2 are true

Question 18

The number of numbers, strictly between $5000$ and $10000$ that can be formed using the digits $1,3,5,7,9$ without repetition, is

Accepted Answer

(C) $72$

Answer

(A) $12$

Answer

(B) $120$

Answer

(D) $6$

Question 19

Let $f:\mathbb{R}	o\mathbb{R}$ be a function defined by $f(x)=\log_{\sqrt{m}}\{\sqrt{2}(\sin x-\cos x)+m-2\}$, for some $m$, such that the range of $f$ is $[0,2]$. Then the value of $m$ is

Accepted Answer

(A) $5$

Answer

(B) $4$

Answer

(C) $3$

Answer

(D) $2$

Question 20

The shortest distance between the lines $x+1=2y=-12z$ and $x=y+2=6z-6$ is

Accepted Answer

(B) $2$

Answer

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

Answer

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

Answer

(D) $3$

Question 21

$25\%$ of the population are smokers. A smoker has $27$ times more chances to develop lung cancer than a non smoker. A person is diagnosed with lung cancer and the probability that this person is a smoker is $\dfrac{k}{10}$. Then the value of $k$ is.

Accepted Answer

9

Question 22

The remainder when $(2023)^{2023}$ is divided by $35$ is

Accepted Answer

7

Question 23

Let $a\in\mathbb{R}$ and let $\alpha,\beta$ be the roots of the equation $x^{2}+60^{\frac{1}{4}}x+a=0$. If $\alpha^{4}+\beta^{4}=-30$, then the product of all possible values of $a$ is

Accepted Answer

45

Question 24

For two positive numbers $a,b$ such that $a,b$ and $\dfrac{1}{18}$ are in a geometric progression, while $\dfrac{1}{a},10$ and $\dfrac{1}{b}$ are in an arithmetic progression, then $16a+b$ is equal to

Accepted Answer

3

Question 25

If $m$ and $n$ respectively are the numbers of positive and negative values of $	heta$ in the interval $[-\pi,\pi]$ that satisfy the equation $\cos 2	heta\cos\dfrac{	heta}{2}=\cos 3	heta\cos\dfrac{9	heta}{2}$, then $mn$ is equal to

Accepted Answer

25

Question 26

If the shortest distance between the line joining the points $(1,2,3)$ and $(2,3,4)$, and the line $\dfrac{x-1}{2}=\dfrac{y+1}{-1}=\dfrac{z-2}{0}$ is $a$, then $28a^{2}$ is equal to

Accepted Answer

18

Question 27

Points $P(-3,2)$, $Q(9,10)$ and $R(a,4)$ lie on a circle $C$ with $PR$ as its diameter. The tangents to $C$ at the points $Q$ and $R$ intersect at the point $S$. If $S$ lies on the line $2x-ky=1$, then $k$ is equal to

Accepted Answer

3

Question 28

Suppose Anil's mother wants to give $5$ whole fruits to Anil from a basket of $7$ red apples, $5$ white apples and $8$ oranges. If in the selected $5$ fruits, at least $2$ oranges, at least one red apple and at least one white apple must be given, then the number of ways Anil's mother can offer $5$ fruits to Anil is

Accepted Answer

6860

Question 29

If $\displaystyle\int_{1/3}^{3}|\log_{e}x|\,dx=\dfrac{m}{n}\log_{e}\left(\dfrac{n^{2}}{e}\right)$, where $m$ and $n$ are coprime natural numbers, then $m^{2}+n^{2}-5$ is equal to

Accepted Answer

20

Question 30

A triangle is formed by the X-axis, the Y-axis and the line $3x+4y=60$. Then the number of points $P(a,b)$ which lie strictly inside the triangle, where $a$ is an integer and $b$ is a multiple of $a$, is

Accepted Answer

31

Question 31

According to law of equipartition of energy the molar specific heat of a diatomic gas at constant volume where the molecule has one additional vibrational mode is:

Accepted Answer

(C) $\frac{7}{2}R$

Answer

(A) $\frac{5}{2}R$

Answer

(B) $\frac{9}{2}R$

Answer

(D) $\frac{3}{2}R$

Question 32

A wire of length $1$ m moving with velocity $8$ m/s at right angles to a magnetic field of $2$ T. The magnitude of induced emf, between the ends of wire will be

Accepted Answer

(D) $16$ V

Answer

(A) $20$ V

Answer

(B) $8$ V

Answer

(C) $12$ V

Question 33

The energy levels of an atom is shown in figure. Which one of these transitions will result in the emission of a photon of wavelength $124.1$ nm? Given $h = 6.62	imes10^{-34}$ Js.

Accepted Answer

(A) D

Answer

(B) B

Answer

(C) C

Answer

(D) A

Question 34

Given below are two statements:
Statement I: Stopping potential in photoelectric effect does not depend on the power of the light source.
Statement II: For a given metal, the maximum kinetic energy of the photoelectron depends on the wavelength of the incident light.
In the light of above statements, choose the most appropriate answer from the options given below

Accepted Answer

(C) Both Statement I and Statement II are correct

Answer

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

Answer

(B) Statement I is incorrect but statement II is correct

Answer

(D) Both Statement I and Statement II are incorrect

Question 35

The distance travelled by a particle is related to time t as $x = 4t^2$. The velocity of the particle at $t = 5$ s is:

Accepted Answer

(A) $40$ ms$^{-1}$

Answer

(B) $20$ ms$^{-1}$

Answer

(C) $8$ ms$^{-1}$

Answer

(D) $25$ ms$^{-1}$

Question 36

Match List I (physical quantities) with List II (their dimensional formulae) and choose the correct answer.

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 37

Match List I (layers of the atmosphere / ionosphere) with List II (their approximate heights over Earth's surface) and choose the correct answer.

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 38

The light rays from an object have been reflected towards an observer from a standard flat mirror, the image observed by the observer are:
A. Real
B. Erect
C. Smaller in size then object
D. Laterally inverted
Choose the most appropriate answer from the options given below:

Accepted Answer

(B) B and D Only

Answer

(A) A, C, and D Only

Answer

(C) A and D Only

Answer

(D) B and C Only

Question 39

The graph between two temperature scales $P$ and $Q$ is shown in the figure. Between upper fixed point and lower fixed point there are $150$ equal divisions of scale P and $100$ divisions on scale Q. The relationship for conversion between the two scales is given by:

Accepted Answer

(D) $\frac{t_Q}{100} = \frac{t_P - 30}{150}$

Answer

(A) $\frac{t_P}{100} = \frac{t_Q - 180}{150}$

Answer

(B) $\frac{t_Q}{150} = \frac{t_P - 180}{100}$

Answer

(C) $\frac{t_P}{180} - \frac{t_Q - 40}{100}$

Question 40

Consider a block kept on an inclined plane (inclined at $45^\circ$) as shown in the figure. If the force required to just push it up the incline is $2$ times the force required to just prevent it from sliding down, the coefficient of friction between the block and inclined plane ($\mu$) is equal to:

Accepted Answer

(D) $0.33$

Answer

(A) $0.25$

Answer

(B) $0.50$

Answer

(C) $0.60$

Question 41

Every planet revolves around the sun in an elliptical orbit:
A. The force acting on a planet is inversely proportional to square of distance from sun.
B. Force acting on planet is inversely proportional to product of the masses of the planet and the sun.
C. The Centripetal force acting on the planet is directed away from the sun.
D. The square of time period of revolution of planet around sun is directly proportional to cube of semi-major axis of elliptical orbit.
Choose the correct answer from the options given below:

Accepted Answer

(C) A and D only

Answer

(A) B and C only

Answer

(B) A and C Only

Answer

(D) C and D only

Question 42

For a moving coil galvanometer, the deflection in the coil is $0.05$ rad when a current of $10$ mA is passed through it. If the torsional constant of suspension wire is $4.0	imes10^{-5}$ N m rad$^{-1}$, the magnetic field is $0.01$ T and the number of turns in the coil is $200$, the area of each turn (in cm$^2$) is:

Accepted Answer

(A) $1.0$

Answer

(B) $2.0$

Answer

(C) $1.5$

Answer

(D) $0.5$

Question 43

Match List I (fundamental laws of electromagnetism) with List II (their integral form expressions) and choose the correct answer.

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 44

Two objects are projected with same velocity 'u' however at different angles $\alpha$ and $\beta$ with the horizontal. If $\alpha + \beta = 90^\circ$, the ratio of horizontal range of the first object to the 2nd object will be:

Accepted Answer

(C) $1:1$

Answer

(A) $2:1$

Answer

(B) $1:2$

Answer

(D) $4:1$

Question 45

A particle executes simple harmonic motion between $x = -A$ and $x = +A$. If time taken by particle to go from $x = 0$ to $\frac{A}{2}$ is $2$ s; then time taken by particle in going from $x = \frac{A}{2}$ to A is

Accepted Answer

(A) $4$ S

Answer

(B) $1.5$ S

Answer

(C) $2$ S

Answer

(D) $3$ S

Question 46

Match List I with List II:
LIST I: (A) Isothermal Process, (B) Adiabatic Process, (C) Isochoric Process, (D) Isobaric Process.
LIST II: (I) Work done by the gas decreases internal energy, (II) No change in internal energy, (III) The heat absorbed goes partly to increase internal energy and partly to do work, (IV) No work is done on or by the gas.
Choose the correct answer from the options given below:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 47

Statement I: When a Si sample is doped with Boron, it becomes P type and when doped by Arsenic it becomes N-type semi conductor such that P-type has excess holes and N-type has excess electrons.
Statement II: When such P-type and N-type semi-conductors, are fused to make a junction, a current will automatically flow which can be detected with an externally connected ammeter.
In the light of above statements, choose the most appropriate answer from the options given below:

Accepted Answer

(D) Statement I is correct but statement II is incorrect

Answer

(A) Both Statement I and statement II are correct

Answer

(B) Statement I is incorrect but statement II is correct

Answer

(C) Both Statement I and Statement II are incorrect

Question 48

A point charge of $10\,\mu C$ is placed at the origin. At what location on the X-axis should a point charge of $40\,\mu C$ be placed so that the net electric field is zero at $x = 2$ cm on the X-axis?

Accepted Answer

(B) $x = 6$ cm

Answer

(A) $x = -4$ cm

Answer

(C) $x = 4$ cm

Answer

(D) $x = 8$ cm

Question 49

The resistance of a wire is $5\,\Omega$. Its new resistance in ohm if stretched to 5 times of its original length will be:

Accepted Answer

(B) 125

Answer

(A) 25

Answer

(C) 5

Answer

(D) 625

Question 50

A body of mass is taken from earth surface to the height $h$ equal to twice the radius of earth ($R_e$), the increase in potential energy will be: ( $g$ = acceleration due to gravity on the surface of Earth)

Accepted Answer

(C) $\frac{2}{3}mgR_e$

Answer

(A) $3\,mgR_e$

Answer

(B) $\frac{1}{3}mgR_e$

Answer

(D) $\frac{1}{2}mgR_e$

Question 51

Two long parallel wires carrying currents 8 A and 15 A in opposite directions are placed at a distance of 7 cm from each other. A point $P$ is at equidistant from both the wires such that the lines joining the point $P$ to the wires are perpendicular to each other. The magnitude of magnetic field at $P$ is ______ $	imes 10^{-6}$ T (Given: $\sqrt{2} = 1.4$)

Accepted Answer

68

Question 52

A spherical drop of liquid splits into 1000 identical spherical drops. If $u_i$ is the surface energy of the original drop and $u_f$ is the total surface energy of the resulting drops, then (ignoring evaporation), $\frac{u_f}{u_i} = \left(\frac{10}{x}\right)$. Then value of $x$ is ______.

Accepted Answer

1

Question 53

A nucleus disintegrates into two smaller parts, which have their velocities in the ratio $3:2$. The ratio of their nuclear sizes will be $\left(\frac{x}{3}\right)^{\frac{1}{3}}$. The value of '$x$' is:

Accepted Answer

2

Question 54

A train blowing a whistle of frequency 320 Hz approaches an observer standing on the platform at a speed of 66 m/s. The frequency observed by the observer will be (given speed of sound $= 330\,	ext{ms}^{-1}$) ______ Hz.

Accepted Answer

400

Question 55

A body of mass 1 kg collides head on elastically with a stationary body of mass 3 kg. After collision, the smaller body reverses its direction of motion and moves with a speed of 2 m/s. The initial speed of the smaller body before collision is ______ $	ext{ms}^{-1}$

Accepted Answer

4

Question 56

A series LCR circuit is connected to an AC source of 220 V, 50 Hz. The circuit contains a resistance $R = 80\,\Omega$, an inductor of inductive reactance $X_L = 70\,\Omega$, and a capacitor of capacitive reactance $X_C = 130\,\Omega$. The power factor of circuit is $\frac{x}{10}$. The value of $x$ is:

Accepted Answer

8

Question 57

If a solid sphere of mass 5 kg and a disc of mass 4 kg have the same radius. Then the ratio of moment of inertia of the disc about a tangent in its plane to the moment of inertia of the sphere about its tangent will be $\frac{x}{7}$. The value of $x$ is ______.

Accepted Answer

5

Question 58

An object is placed on the principal axis of convex lens of focal length 10 cm as shown. A plane mirror is placed on the other side of lens at a distance of 20 cm. The image produced by the plane mirror is 5 cm inside the mirror. The distance of the object from the lens is ______ cm.

Accepted Answer

30

Question 59

A capacitor has capacitance $5\,\mu F$ when its parallel plates are separated by air medium of thickness $d$. A slab of material of dielectric constant 1.5 having area equal to that of plates but thickness $\frac{d}{2}$ is inserted between the plates. Capacitance of the capacitor in the presence of slab will be ______ $\mu F$.

Accepted Answer

6

Question 60

Two cells are connected between points A and B as shown. Cell 1 has emf of 12 V and internal resistance of $3\,\Omega$. Cell 2 has emf of 6 V and internal resistance of $6\,\Omega$. An external resistor R of $4\,\Omega$ is connected across A and B. The current flowing through R will be ______ A.

Accepted Answer

1

Question 61

When the hydrogen ion concentration $[H^+]$ changes by a factor of $1000$, the value of pH of the solution

Accepted Answer

(D) decreases by 3 units

Answer

(A) increases by 2 units

Answer

(B) increases by 1000 units

Answer

(C) decreases by 2 units

Question 62

Find out the major product from the following reaction.

Accepted Answer

(D) (4)

Answer

(A) (1)

Answer

(B) (2)

Answer

(C) (3)

Question 63

Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : Carbon forms two important oxides - CO and $CO_2$. CO is neutral whereas $CO_2$ is acidic in nature.
Reason R : $CO_2$ can combine with water in a limited way to form carbonic acid, while CO is sparingly soluble in water.
In the light of the above statements, choose the most appropriate answer from the options given below

Accepted Answer

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

Answer

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

Answer

(B) A is correct but R is not correct

Answer

(D) A is not correct but R is correct

Question 64

Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : The alkali metals and their salts impart characteristic colour to reducing flame.
Reason R : Alkali metals can be detected using flame tests.
In the light of the above statements, choose the most appropriate answer from the options given below

Accepted Answer

(A) A is not correct but R is correct

Answer

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

Answer

(C) A is correct but R is not correct

Answer

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

List-I	List-II
A.Young's Modulus (Y)	I. $[M\,L^{-1}\,T^{-1}]$
B.Co-efficient of Viscosity ( $\eta$ )	II. $[M\,L^2\,T^{-1}]$
C.Planck's Constant (h)	IV. $[M\,L^2\,T^{-2}]$
D.Work Function ( $\varphi$ )	III. $[M\,L^{-1}\,T^{-2}]$

List-I	List-II
A.Troposphere	I.Approximate $65 - 75$ km over Earth's surface
B.E- Part of Stratosphere	II.Approximate $300$ km over Earth's surface
C.F2- Part of Thermosphere	IV.Approximate $100$ km over Earth's surface
D.D- Part of Stratosphere	III.Approximate $10$ km over Earth's surface

List-I	List-II
A.Gauss's Law in Electrostatics	I. $\oint \vec{E}\cdot d\vec{l} = -\frac{d\phi_B}{dt}$
B.Faraday's Law	II. $\oint \vec{B}\cdot d\vec{A} = 0$
C.Gauss's Law in Magnetism	IV. $\oint \vec{E}\cdot d\vec{s} = \frac{q}{\epsilon_0}$
D.Ampere-Maxwell Law	III. $\oint \vec{B}\cdot d\vec{l} = \mu_0 i_c + \mu_0 \epsilon_0 \frac{d\phi_E}{dt}$

List-I	List-II
A.Isothermal Process	I.Work done by the gas decreases internal energy
B.Adiabatic Process	II.No change in internal energy
C.Isochoric Process	III.The heat absorbed goes partly to increase internal energy and partly to do work
D.Isobaric Process	IV.No work is done on or by the gas

LIST I (Name of polymer)	LIST II (Uses)
A.Glyptal	I.Flexible pipes
B.Neoprene	II.Synthetic wool
C.Acrilan	III.Paints and Lacquers
D.LDP	IV.Gaskets

JEE Main 25 January 2023 Shift 2 Question Paper with Answers

Physics — JEE Main 25 January 2023 Shift 2

Chemistry — JEE Main 25 January 2023 Shift 2

Mathematics — JEE Main 25 January 2023 Shift 2

Chapters tested in this paper

Attempt this paper under exam timing.

LIST I	LIST II
A.Cobalt catalyst	I. $(H_2 + Cl_2)$ production
B.Syngas	II.Water gas production
C.Nickel catalyst	III.Coal gasification
D.Brine solution	IV.Methanol production

LIST I (Amines)	LIST II ($pK_b$)
A.Aniline	I.3.25
B.Ethanamine	II.3.00
C.N-Ethylethanamine	III.9.38
D.N,N-Diethylethanamine	IV.3.29

LIST I (Isomeric pairs)	LIST II (Type of isomers)
A.Propanamine and N-Methylethanamine	I.Metamers
B.Hexan-2-one and Hexan-3-one	II.Positional isomers
C.Ethanamide and Hydroxyethanimine	III.Functional isomers
D.o-nitrophenol and p-nitrophenol	IV.Tautomers

LIST I (Coordination entity)	LIST II (Wavelength of light absorbed in nm)
A. $[CoCl(NH_3)_5]^{2+}$	I.310
B. $[Co(NH_3)_6]^{3+}$	II.475
C. $[Co(CN)_6]^{3-}$	III.535
D. $[Cu(H_2O)_4]^{2+}$	IV.600