JEE Main 29 January 2025 Shift 2 Question Paper

Question 1

If the set of all $a\in R$, for which the equation $2x^2+(a-5)x+15=3a$ has no real root, is the interval $(\alpha,\beta)$, and $X=\{x\in Z:\alpha<x<\beta\}$, then $\displaystyle\sum_{x\in X}x^2$ is equal to

Accepted Answer

(C) 2139

Answer

(A) 2109

Answer

(B) 2129

Answer

(D) 2119

Question 2

If $\sin x+\sin^2 x=1$, $x\in\left(0,\dfrac{\pi}{2}ight)$, then $(\cos^{12}x+	an^{12}x)+3(\cos^{10}x+	an^{10}x+\cos^{8}x+	an^{8}x)+(\cos^{6}x+	an^{6}x)$ is equal to

Accepted Answer

(C) 2

Answer

(A) 4

Answer

(B) 3

Answer

(D) 1

Question 3

Let the area enclosed between the curves $|y|=1-x^2$ and $x^2+y^2=1$ be $\alpha$. If $9\alpha=\beta\pi+\gamma$; $\beta,\gamma$ are integers, then the value of $|\beta-\gamma|$ equals

Accepted Answer

(D) 33

Answer

(A) 27

Answer

(B) 18

Answer

(C) 15

Question 4

If the domain of the function $\log_5(18x-x^2-77)$ is $(\alpha,\beta)$ and the domain of the function $\log_{(x-1)}\left(\dfrac{2x^2+3x-2}{x^2-3x-4}\right)$ is $(\gamma,\delta)$, then $\alpha^2+\beta^2+\gamma^2$ is equal to:

Accepted Answer

(C) 186

Answer

(A) 195

Answer

(B) 174

Answer

(D) 179

Question 5

Let the function $f(x)=(x^2-1)|x^2-ax+2|+\cos|x|$ be not differentiable at the two points $x=\alpha=2$ and $x=\beta$. Then the distance of the point $(\alpha,\beta)$ from the line $12x+5y+10=0$ is equal to:

Accepted Answer

(A) 3

Answer

(B) 4

Answer

(C) 2

Answer

(D) 5

Question 6

Let a straight line L pass through the point $P(2,-1,3)$ and be perpendicular to the lines $\dfrac{x-1}{2}=\dfrac{y+1}{1}=\dfrac{z-3}{-2}$ and $\dfrac{x-3}{1}=\dfrac{y-2}{3}=\dfrac{z+2}{4}$. If the line L intersects the yz-plane at the point Q, then the distance between the points P and Q is:

Accepted Answer

(C) 3

Answer

(A) 2

Answer

(B) $\sqrt{10}$

Answer

(D) $2\sqrt{3}$

Question 7

Let $S=N\cup\{0\}$. Define a relation R from S to R by: $R=\left\{(x,y):\log_e y=x\log_e\left(\dfrac{2}{5}\right),\ x\in S,\ y\in R\right\}$. Then, the sum of all the elements in the range of R is equal to

Accepted Answer

(B) $\dfrac{5}{3}$

Answer

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

Answer

(C) $\dfrac{10}{9}$

Answer

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

Question 8

Let the line $x+y=1$ meet the axes of x and y at A and B, respectively. A right angled triangle AMN is inscribed in the triangle OAB, where O is the origin and the points M and N lie on the lines OB and AB, respectively. If the area of the triangle AMN is $\dfrac{4}{9}$ of the area of the triangle OAB and $AN:NB=\lambda:1$, then the sum of all possible value(s) of $\lambda$ is:

Accepted Answer

(D) 2

Answer

(A) $\dfrac{1}{2}$

Answer

(B) $\dfrac{13}{6}$

Answer

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

Question 9

If $\alpha x+\beta y=109$ is the equation of the chord of the ellipse $\dfrac{x^2}{9}+\dfrac{y^2}{4}=1$, whose mid point is $\left(\dfrac{5}{2},\dfrac{1}{2}\right)$, then $\alpha+\beta$ is equal to

Accepted Answer

(C) 58

Answer

(A) 37

Answer

(B) 46

Answer

(D) 72

Question 10

If all the words with or without meaning made using all the letters of the word “KANPUR” are arranged as in a dictionary, then the word at $440^{	ext{th}}$ position in this arrangement, is:

Accepted Answer

(C) PRKAUN

Answer

(A) PRNAKU

Answer

(B) PRKANU

Answer

(D) PRNAUK

Question 11

Let $\alpha,\beta$ $(\alpha
e\beta)$ be the values of m, for which the equations $x+y+z=1$; $x+2y+4z=m$ and $x+4y+10z=m^2$ have infinitely many solutions. Then the value of $\displaystyle\sum_{n=1}^{10}\left(n^\alpha+n^\betaight)$ is equal to:

Accepted Answer

(A) 440

Answer

(B) 3080

Answer

(C) 3410

Answer

(D) 560

Question 12

Let $A=[a_{ij}]$ be a matrix of order $3	imes 3$, with $a_{ij}=(\sqrt{2})^{i+j}$. If the sum of all the elements in the third row of $A^2$ is $\alpha+\beta\sqrt{2}$, $\alpha,\beta\in Z$, then $\alpha+\beta$ is equal to

Accepted Answer

(D) 224

Answer

(A) 280

Answer

(B) 168

Answer

(C) 210

Question 13

Let P be the foot of the perpendicular from the point $(1, 2, 2)$ on the line $L:\dfrac{x-1}{1}=\dfrac{y+1}{-1}=\dfrac{z-2}{2}$. Let the line $\vec{r}=\left(-\hat{i}-2\hat{k}\right)+\lambda\left(\hat{i}-\hat{j}+\hat{k}\right)$, $\lambda\in R$, intersect the line L at Q. Then $2(PQ)^2$ is equal to:

Accepted Answer

(A) 27

Answer

(B) 25

Answer

(C) 29

Answer

(D) 19

Question 14

Let a circle C pass through the points $(4, 2)$ and $(0, 2)$, and its centre lie on $3x+2y+2=0$. Then the length of the chord, of the circle C, whose mid-point is $(1, 2)$, is:

Accepted Answer

(B) $2\sqrt{3}$

Answer

(A) $\sqrt{3}$

Answer

(C) $4\sqrt{2}$

Answer

(D) $2\sqrt{2}$

Question 15

Let $A=[a_{ij}]$ be a $2	imes 2$ matrix such that $a_{ij}\in\{0, 1\}$ for all i and j. Let the random variable X denote the possible values of the determinant of the matrix A. Then the variance of X is:

Accepted Answer

(B) $\dfrac{3}{8}$

Answer

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

Answer

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

Answer

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

Question 16

Bag 1 contains 4 white balls and 5 black balls, and Bag 2 contains n white balls and 3 black balls. One ball is drawn randomly from Bag 1 and transferred to Bag 2. A ball is then drawn randomly from Bag 2. If the probability, that the ball drawn from Bag 2, is white, is $\dfrac{29}{45}$, then n is equal to:

Accepted Answer

(D) 6

Answer

(A) 3

Answer

(B) 4

Answer

(C) 5

Question 17

The remainder, when $7^{103}$ is divided by 23, is equal to:

Accepted Answer

(A) 14

Answer

(B) 9

Answer

(C) 17

Answer

(D) 6

Question 18

Let $f'(x)=\displaystyle\int_0^x t(t^2-9t+20)\,dt$, $1\le x\le 5$. If the range of f is $[\alpha,\beta]$, then $4(\alpha+\beta)$ equals:

Accepted Answer

(A) 157

Answer

(B) 253

Answer

(C) 125

Answer

(D) 154

Question 19

Let $\hat{a}$ be a unit vector perpendicular to the vectors $\vec{b}=\hat{i}-2\hat{j}+3\hat{k}$ and $\vec{c}=2\hat{i}+3\hat{j}-\hat{k}$, and makes an angle of $\cos^{-1}\left(-\dfrac{1}{3}\right)$ with the vector $\hat{i}+\hat{j}+\hat{k}$. If $\hat{a}$ makes an angle of $\dfrac{\pi}{3}$ with the vector $\hat{i}+\alpha\hat{j}+\hat{k}$, then the value of $\alpha$ is:

Accepted Answer

(C) $-\sqrt{6}$

Answer

(A) $-\sqrt{3}$

Answer

(B) $\sqrt{6}$

Answer

(D) $\sqrt{3}$

Question 20

If for the solution curve $y=f(x)$ of the differential equation $\dfrac{dy}{dx}+(	an x)y=\dfrac{2+\sec x}{(1+2\sec x)^2}$, $x\in\left(-\dfrac{\pi}{2},\dfrac{\pi}{2}ight)$, $f\left(\dfrac{\pi}{3}ight)=\dfrac{\sqrt{3}}{10}$, then $f\left(\dfrac{\pi}{4}ight)$ is equal to:

Accepted Answer

(D) $\dfrac{4-\sqrt{2}}{14}$

Answer

(A) $\dfrac{9\sqrt{3}+3}{10(4+\sqrt{3})}$

Answer

(B) $\dfrac{\sqrt{3}+1}{10(4+\sqrt{3})}$

Answer

(C) $\dfrac{5-\sqrt{3}}{2\sqrt{2}}$

Question 21

If $24\displaystyle\int_0^{\pi/4}\left(\sin\left|4x-\dfrac{\pi}{12}\right|+[2\sin x]\right)dx=2\pi+\alpha$, where $[\cdot]$ denotes the greatest integer function, then $\alpha$ is equal to ______.

Accepted Answer

12

Question 22

If $\displaystyle\lim_{t	o 0}\left(\int_0^1 (3x+5)^t\,dxight)^{\frac{1}{t}}=\dfrac{\alpha}{5e}\left(\dfrac{8}{5}ight)^{\frac{2}{3}}$, then $\alpha$ is equal to ______.

Accepted Answer

64

Question 23

Let $a_1, a_2,\ldots,a_{2024}$ be an Arithmetic Progression such that $a_1+(a_5+a_{10}+a_{15}+\cdots+a_{2020})+a_{2024}=2233$. Then $a_1+a_2+a_3+\cdots+a_{2024}$ is equal to ______.

Accepted Answer

11132

Question 24

Let integers $a, b\in[-3, 3]$ be such that $a+b
e 0$. Then the number of all possible ordered pairs $(a, b)$, for which $\left|\dfrac{z-a}{z+b}ight|=1$ and $\begin{vmatrix}z+1 & \omega & \omega^2\ \omega & z+\omega^2 & 1\ \omega^2 & 1 & z+\omega\end{vmatrix}=1$, $z\in C$, where $\omega$ and $\omega^2$ are the roots of $x^2+x+1=0$, is equal to ______.

Accepted Answer

10

Question 25

Let $y^2=12x$ be the parabola and S be its focus. Let PQ be a focal chord of the parabola such that $(SP)(SQ)=\dfrac{147}{4}$. Let C be the circle described taking PQ as a diameter. If the equation of a circle C is $64x^2+64y^2-\alpha x-64\sqrt{3}\,y=\beta$, then $\beta-\alpha$ is equal to ______.

Accepted Answer

1328

Question 26

The difference of temperature in a material can convert heat energy into electrical energy. To harvest the heat energy, the material should have

Accepted Answer

(C) low thermal conductivity and high electrical conductivity

Answer

(A) high thermal conductivity and low electrical conductivity

Answer

(B) high thermal conductivity and high electrical conductivity

Answer

(D) low thermal conductivity and low electrical conductivity

Question 27

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): With the increase in the pressure of an ideal gas, the volume falls off more rapidly in an isothermal process in comparison to the adiabatic process.
Reason (R): In isothermal process, PV = constant, while in adiabatic process $PV^{\gamma}$ = constant. Here $\gamma$ is the ratio of specific heats, P is the pressure and V is the volume of the ideal gas.
In the light of the above statements, choose the correct answer from the options given below:

Accepted Answer

(C) 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

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

Answer

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

Question 28

An electric dipole is placed at a distance of 2 cm from an infinite plane sheet having positive charge density $\sigma_0$ (orientation as shown in the figure). Choose the correct option from the following.

Accepted Answer

(C) Potential energy of dipole is minimum and torque is zero.

Answer

(A) Torque on dipole is zero and net force is directed away from the sheet.

Answer

(B) Torque on dipole is zero and net force acts towards the sheet.

Answer

(D) Potential energy and torque both are maximum.

Question 29

In an experiment with photoelectric effect, the stopping potential,

Accepted Answer

(C) is $\left(\dfrac{1}{e}\right)$ times the maximum kinetic energy of the emitted photoelectrons

Answer

(A) increases with increase in the wavelength of the incident light

Answer

(B) increases with increase in the intensity of the incident light

Answer

(D) decreases with increase in the intensity of the incident light

Question 30

A point charge causes an electric flux of $-2	imes 10^4$ Nm²C⁻¹ to pass through a spherical Gaussian surface of 8.0 cm radius, centred on the charge. The value of the point charge is: (Given $\varepsilon_0=8.85	imes 10^{-12}$ C²N⁻¹m⁻²)

Accepted Answer

(A) $-17.7	imes 10^{-8}$ C

Answer

(B) $-15.7	imes 10^{-8}$ C

Answer

(C) $17.7	imes 10^{-8}$ C

Answer

(D) $15.7	imes 10^{-8}$ C

Question 31

Two identical symmetric double convex lenses of focal length f are cut into two equal parts $L_1, L_2$ by AB plane and $L_3, L_4$ by XY plane as shown in figure. The ratio of focal lengths of lenses $L_1$ and $L_3$ is

Accepted Answer

(D) 1 : 2

Answer

(A) 1 : 4

Answer

(B) 1 : 1

Answer

(C) 2 : 1

Question 32

A plane electromagnetic wave propagates along the + x direction in free space. The components of the electric field, $\vec{E}$ and magnetic field, $\vec{B}$ vectors associated with the wave in Cartesian frame are:

Accepted Answer

(B) $E_y, B_z$

Answer

(A) $E_y, B_x$

Answer

(C) $E_x, B_y$

Answer

(D) $E_z, B_y$

Question 33

Two concave refracting surfaces of equal radii of curvature and refractive index 1.5 face each other in air as shown in figure. A point object O is placed midway, between P and B. The separation between the images of O, formed by each refracting surface is:

Accepted Answer

(B) 0.114R

Answer

(A) 0.214R

Answer

(C) 0.411R

Answer

(D) 0.124R

Question 34

Two bodies A and B of equal mass are suspended from two massless springs of spring constant $k_1$ and $k_2$, respectively. If the bodies oscillate vertically such that their amplitudes are equal, the ratio of the maximum velocity of A to the maximum velocity of B is

Accepted Answer

(A) $\sqrt{\dfrac{k_1}{k_2}}$

Answer

(B) $\dfrac{k_1}{k_2}$

Answer

(C) $\dfrac{k_2}{k_1}$

Answer

(D) $\sqrt{\dfrac{k_2}{k_1}}$

Question 35

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Three identical spheres of same mass undergo one dimensional motion as shown in figure with initial velocities $v_A=5$ m/s, $v_B=2$ m/s, $v_C=4$ m/s (arranged A, B, C from left to right and all moving in the +x direction). If we wait sufficiently long for elastic collisions to happen, then $v_A=4$ m/s, $v_B=2$ m/s, $v_C=5$ m/s will be the final velocities.
Reason (R): In an elastic collision between identical masses, two objects exchange their velocities.
In the light of the above statements, choose the correct answer from the options given below:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 36

A sand dropper drops sand of mass m(t) on a conveyer belt at a rate proportional to the square root of speed (v) of the belt, i.e. $\dfrac{dm}{dt}\propto\sqrt{v}$. If P is the power delivered to run the belt at constant speed then which of the following relationship is true?

Accepted Answer

(D) $P^2\propto v^5$

Answer

(A) $P^2\propto v^3$

Answer

(B) $P\propto\sqrt{v}$

Answer

(C) $P\propto v$

Question 37

A convex lens made of glass (refractive index = 1.5) has focal length 24 cm in air. When it is totally immersed in water (refractive index = 1.33), its focal length changes to

Accepted Answer

(B) 96 cm

Answer

(A) 72 cm

Answer

(C) 24 cm

Answer

(D) 48 cm

Question 38

A capacitor, $C_1=6\ \mu F$ is charged to a potential difference of $V_0=5$ V using a 5 V battery. The battery is removed and another capacitor, $C_2=12\ \mu F$ is inserted in place of the battery. When the switch ‘S’ is closed, the charge flows between the capacitors for some time until equilibrium condition is reached. What are the charges ($q_1$ and $q_2$) on the capacitors $C_1$ and $C_2$ when equilibrium condition is reached.

Accepted Answer

(C) $q_1=10\ \mu C, q_2=20\ \mu C$

Answer

(A) $q_1=15\ \mu C, q_2=30\ \mu C$

Answer

(B) $q_1=30\ \mu C, q_2=15\ \mu C$

Answer

(D) $q_1=20\ \mu C, q_2=10\ \mu C$

Question 39

Three equal masses m are kept at vertices (A, B, C) of an equilateral triangle of side a in free space. At t = 0, they are given an initial velocity $\vec{V}_A=V_0\,\hat{AC}$, $\vec{V}_B=V_0\,\hat{BA}$ and $\vec{V}_C=V_0\,\hat{CB}$. Here, $\hat{AC}, \hat{CB}$ and $\hat{BA}$ are unit vectors along the edges of the triangle. If the three masses interact gravitationally, then the magnitude of the net angular momentum of the system at the point of collision is:

Accepted Answer

(C) $\dfrac{\sqrt{3}}{2}a m V_0$

Answer

(A) $\dfrac{1}{2}a m V_0$

Answer

(B) $3 a m V_0$

Answer

(D) $\dfrac{3}{2}a m V_0$

Question 40

Match List-I (Mechanical Quantity) with List-II (Dimensional Formula). Choose the correct answer from the options given below:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 41

The truth table for the logic circuit given in the figure (inputs A, B; output Y) is:

Accepted Answer

(A) A,B→Y: (0,0)→0, (0,1)→1, (1,0)→1, (1,1)→0

Answer

(B) A,B→Y: (0,0)→0, (1,0)→0, (1,1)→1, (0,1)→1

Answer

(C) A,B→Y: (0,0)→0, (1,0)→1, (0,1)→0, (1,1)→0

Answer

(D) A,B→Y: (0,0)→0, (1,1)→1, (1,0)→1, (0,1)→1

Question 42

A cup of coffee cools from 90°C to 80°C in t minutes when the room temperature is 20°C. The time taken by the similar cup of coffee to cool from 80°C to 60°C at the same room temperature is:

Accepted Answer

(A) $\dfrac{13}{5}t$

Answer

(B) $\dfrac{10}{13}t$

Answer

(C) $\dfrac{13}{10}t$

Answer

(D) $\dfrac{5}{13}t$

Question 43

The number of spectral lines emitted by atomic hydrogen that is in the $4^{	ext{th}}$ energy level, is

Accepted Answer

(A) 6

Answer

(B) 0

Answer

(C) 3

Answer

(D) 1

Question 44

The magnetic field inside a 200 turns solenoid of radius 10 cm is $2.9	imes 10^{-4}$ Tesla. If the solenoid carries a current of 0.29 A, then the length of the solenoid is ______ $\pi$ cm.

Accepted Answer

8

Question 45

A parallel plate capacitor consisting of two circular plates of radius 10 cm is being charged by a constant current of 0.15 A. If the rate of change of potential difference between the plates is $7	imes 10^8$ V/s then the integer value of the distance between the parallel plates is ______ μm. (Take $\varepsilon_0=9	imes 10^{-12}$ F/m, $\pi=\dfrac{22}{7}$.)

Accepted Answer

1320

Question 46

A physical quantity Q is related to four observables a, b, c, d as follows: $Q=\dfrac{ab^4}{cd}$, where $a=(60\pm 3)$ Pa; $b=(20\pm 0.1)$ m; $c=(40\pm 0.2)$ Nsm⁻² and $d=(50\pm 0.1)$ m, then the percentage error in Q is $\dfrac{x}{1000}$, where $x=$ ______.

Accepted Answer

7700

Question 47

Two planets, A and B are orbiting a common star in circular orbits of radii $R_A$ and $R_B$, respectively, with $R_B=2R_A$. The planet B is $4\sqrt{2}$ times more massive than planet A. The ratio $\left(\dfrac{L_B}{L_A}\right)$ of angular momentum ($L_B$) of planet B to that of planet $A(L_A)$ is closest to integer ______.

Accepted Answer

8

Question 48

Two cars P and Q are moving on a road in the same direction. Acceleration of car P increases linearly with time whereas car Q moves with a constant acceleration. Both cars cross each other at time t = 0, for the first time. The maximum possible number of crossing(s) (including the crossing at t = 0) is ______.

Accepted Answer

3

Question 49

The calculated spin-only magnetic moments of $K_3[Fe(OH)_6]$ and $K_4[Fe(OH)_6]$ respectively are:

Accepted Answer

(B) 5.92 and 4.90 B.M.

Answer

(A) 4.90 and 4.90 B.M.

Answer

(C) 3.87 and 4.90 B.M.

Answer

(D) 4.90 and 5.92 B.M.

Question 50

For hydrogen like species, which of the following graphs provides the most appropriate representation of E vs Z plot for a constant a? [E: Energy of the stationary state, Z: atomic number, n = principal quantum number] (graphs shown in the figure)

Accepted Answer

(A) (1)

Answer

(B) (2)

Answer

(C) (3)

Answer

(D) (4)

Question 51

Given below are two statements: Statement (I): In partition chromatography, stationary phase is thin film of liquid present in the inert support. Statement (II): In paper chromatography, paper acts as a stationary phase. In the light of the above statements, choose the correct answer from the options given below:

Accepted Answer

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

Answer

(A) Both Statement I and Statement II are false

Answer

(C) Both Statement I and Statement II are true

Answer

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

Question 52

Identify the essential amino acids from below: (A) Valine  (B) Proline  (C) Lysine  (D) Threonine  (E) Tyrosine. Choose the correct answer from the options given below:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 53

Which among the following halides (shown in the figure) will generate the most stable carbocation in a nucleophilic substitution reaction?

Accepted Answer

(D) (4)

Answer

(A) (1)

Answer

(B) (2)

Answer

(C) (3)

Question 54

Consider the equilibrium $CO(g)+3H_2(g)\rightleftharpoons CH_4(g)+H_2O(g)$. If the pressure applied over the system increases by two fold at constant temperature then (A) Concentration of reactants and products increases. (B) Equilibrium will shift in forward direction. (C) Equilibrium constant increases since concentration of products increases. (D) Equilibrium constant remains unchanged as concentration of reactants and products remain same. Choose the correct answer from the options given below:

Accepted Answer

(A) (A) and (B) only

Answer

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

Answer

(C) (B) and (C) only

Answer

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

Question 55

Given below are two statements: Statement (I): NaCl is added to the ice at 0°C, present in the ice cream box to prevent the melting of ice cream. Statement (II): On addition of NaCl to ice at 0°C, there is a depression in freezing point. In the light of the above statements, choose the correct answer from the options given below:

Accepted Answer

(B) Both Statement I and Statement II are true

Answer

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

Answer

(C) Both Statement I and Statement II are false

Answer

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

Question 56

Given below are two statements: Statement (I): On nitration of m-xylene with $HNO_3$, $H_2SO_4$ followed by oxidation, 4-nitrobenzene-1,3-dicarboxylic acid is obtained as the major product. Statement (II): $-CH_3$ group is o/p-directing while $-NO_2$ group is m-directing group. In the light of the above statements, choose the correct answer from the options given below:

Accepted Answer

(C) Both Statement I and Statement II are true

Answer

(A) Both Statement I and Statement II are false

Answer

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

Answer

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

Question 57

0.1 M solution of KI reacts with excess of $H_2SO_4$ and $KIO_3$ solution. According to the equation $5I^-+IO_3^-+6H^+ightarrow 3I_2+3H_2O$. Identify the correct statements: (A) 200 mL of KI solution reacts with 0.004 mol of $KIO_3$. (B) 200 mL of KI solution reacts with 0.006 mol of $H_2SO_4$. (C) 0.5 L of KI solution produced 0.005 mol of $I_2$. (D) Equivalent weight of $KIO_3$ is equal to $\dfrac{	ext{Molecular weight}}{5}$. Choose the correct answer from the options given below:

Accepted Answer

(A) (A) and (D) only

Answer

(B) (B) and (C) only

Answer

(C) (A) and (B) only

Answer

(D) (C) and (D) only

Question 58

Match List-I (Applications) with List-II (Batteries/Cell). Choose the correct answer from the options given below:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 59

$O_2$ gas will be evolved as a product of electrolysis of: (A) an aqueous solution of $AgNO_3$ using silver electrodes. (B) an aqueous solution of $AgNO_3$ using platinum electrodes. (C) a dilute solution of $H_2SO_4$ using platinum electrodes. (D) a high concentration solution of $H_2SO_4$ using platinum electrodes. Choose the correct answer from the options given below:

Accepted Answer

(A) (B) and (C) only

Answer

(B) (A) and (D) only

Answer

(C) (B) and (D) only

Answer

(D) (A) and (C) only

Question 60

Identify the homoleptic complexes with odd number of d electrons in the central metal. (A) $[FeO_4]^{2-}$  (B) $[Fe(CN)_6]^{3-}$  (C) $[Fe(CN)_5NO]^{2-}$  (D) $[CoCl_4]^{2-}$  (E) $[Co(H_2O)_3F_3]$. Choose the correct answer from the options given below:

Accepted Answer

(A) (B) and (D) only

Answer

(B) (C) and (E) only

Answer

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

Answer

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

Question 61

Total number of sigma ($\sigma$) ______ and pi ($\pi$) ______ bonds respectively present in the hex-1-en-4-yne are:

Accepted Answer

(A) 13 and 3

Answer

(B) 11 and 3

Answer

(C) 13 and 5

Answer

(D) 14 and 3

Question 62

If $C(	ext{diamond})ightarrow C(	ext{graphite})+X$ kJ mol⁻¹; $C(	ext{diamond})+O_2(g)ightarrow CO_2(g)+Y$ kJ mol⁻¹; $C(	ext{graphite})+O_2(g)ightarrow CO_2(g)+Z$ kJ mol⁻¹. At constant temperature, then

Accepted Answer

(B) X = Y − Z

Answer

(A) X = Y + Z

Answer

(C) X = Z − Y

Answer

(D) X = Y = Z

Question 63

Given below are two statements: Statement (I): It is impossible to specify simultaneously with arbitrary precision, both the linear momentum and the position of a particle. Statement (II): If the uncertainty in the measurement of position and uncertainty in measurement of momentum are equal for an electron, then the uncertainty in the measurement of velocity is $\ge\dfrac{1}{2m}\sqrt{\dfrac{h}{\pi}}$. In the light of the above statements, choose the correct answer from the options given below:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 64

Which one of the following reaction sequences (shown in the figure) will give an azo dye?

Accepted Answer

(A) (1)

Answer

(B) (2)

Answer

(C) (3)

Answer

(D) (4)

List-I (Mechanical Quantity)	List-II (Dimensional Formula)
A.Young’s Modulus	I. $ML^{-1}T^{-1}$
B.Torque	II. $ML^{-1}T^{-2}$
C.Coefficient of Viscosity	III. $M^{-1}L^{3}T^{-2}$
D.Gravitational Constant	IV. $ML^{2}T^{-2}$

List-I (Applications)	List-II (Batteries/Cell)
A.Transistors	I.Anode – Zn/Hg ; Cathode – HgO + C
B.Hearing aids	II.Hydrogen fuel cell
C.Invertors	III.Anode – Zn ; Cathode – Carbon
D.Apollo space ship	IV.Anode – Pb ; Cathode – Pb \| PbO₂

JEE Main 29 January 2025 Shift 2 Question Paper with Answers

Physics — JEE Main 29 January 2025 Shift 2

Chemistry — JEE Main 29 January 2025 Shift 2

Mathematics — JEE Main 29 January 2025 Shift 2

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