JEE Main 23 January 2025 Shift 2 Question Paper

Question 1

If in the expansion of $(1+x)^p(1-x)^q$, the coefficients of $x$ and $x^2$ are $1$ and $-2$, respectively, then $p^2+q^2$ is equal to :

Accepted Answer

(C) 13

Answer

(A) 8

Answer

(B) 18

Answer

(D) 20

Question 2

Let $A=\{(x,y)\in\mathbb{R}	imes\mathbb{R}:|x+y|\ge 3\}$ and $B=\{(x,y)\in\mathbb{R}	imes\mathbb{R}:|x|+|y|\le 3\}$. If $C=\{(x,y)\in A\cap B: x=0 	ext{ or } y=0\}$, then $\displaystyle\sum_{(x,y)\in C}|x+y|$ is :

Accepted Answer

(D) 12

Answer

(A) 15

Answer

(B) 18

Answer

(C) 24

Question 3

The system of equations $x+y+z=6,\ x+2y+5z=9,\ x+5y+\lambda z=\mu,$ has no solution if :

Accepted Answer

(A) $\lambda=17,\ \mu
eq 18$

Answer

(B) $\lambda
eq 17,\ \mu=18$

Answer

(C) $\lambda=15,\ \mu
eq 18$

Answer

(D) $\lambda=17,\ \mu=18$

Question 4

Let $\displaystyle\int x^3\sin x\,dx=g(x)+C$, where $C$ is the constant of integration. If $8\left[g\!\left(	frac{\pi}{2}ight)+g'\!\left(	frac{\pi}{2}ight)ight]=\alpha\pi^3+\beta\pi^2+\gamma,\ \alpha,\beta,\gamma\in\mathbb{Z}$, then $\alpha+\beta-\gamma$ equals :

Accepted Answer

(A) 55

Answer

(B) 47

Answer

(C) 48

Answer

(D) 62

Question 5

A rod of length eight units moves such that its ends $A$ and $B$ always lie on the lines $x-y+2=0$ and $y+2=0$, respectively. If the locus of the point $P$, that divides the rod $AB$ internally in the ratio $2:1$ is $9(x^2+\alpha y^2+\beta xy+\gamma x+28y)-76=0$, then $\alpha-\beta-\gamma$ is equal to :

Accepted Answer

(B) 23

Answer

(A) 24

Answer

(C) 21

Answer

(D) 22

Question 6

The distance of the line $\dfrac{x-2}{2}=\dfrac{y-6}{3}=\dfrac{z-3}{4}$ from the point $(1,4,0)$ along the line $\dfrac{x}{1}=\dfrac{y-2}{2}=\dfrac{z+3}{3}$ is :

Accepted Answer

(B) $\sqrt{14}$

Answer

(A) $\sqrt{17}$

Answer

(C) $\sqrt{15}$

Answer

(D) $\sqrt{13}$

Question 7

Let the point $A$ divide the line segment joining the points $P(-1,-1,2)$ and $Q(5,5,10)$ internally in the ratio $r:1$ $(r>0)$. If $O$ is the origin and $\left(\overrightarrow{OQ}\cdot\overrightarrow{OA}-	frac{1}{5}\,|\overrightarrow{OP}	imes\overrightarrow{OA}|^2ight)=10$, then the value of $r$ is :

Accepted Answer

(D) 7

Answer

(A) 14

Answer

(B) 3

Answer

(C) $\sqrt{7}$

Question 8

If the area of the region $\{(x,y):-1\le x\le 1,\ 0\le y\le a+e^{|x|}-e^{-x},\ a>0\}$ is $\dfrac{e^2+8e+1}{e}$, then the value of $a$ is :

Accepted Answer

(D) 5

Answer

(A) 7

Answer

(B) 6

Answer

(C) 8

Question 9

A spherical chocolate ball has a layer of ice-cream of uniform thickness around it. When the thickness of the ice-cream layer is $1$ cm, the ice-cream melts at the rate of $81\,	ext{cm}^3/	ext{min}$ and the thickness of the ice-cream layer decreases at the rate of $\dfrac{1}{4\pi}$ cm/min. The surface area (in $	ext{cm}^2$) of the chocolate ball (without the ice-cream layer) is :

Accepted Answer

(D) $256\pi$

Answer

(A) $225\pi$

Answer

(B) $128\pi$

Answer

(C) $196\pi$

Question 10

A board has 16 squares as shown in the figure : Out of these 16 squares, two squares are chosen at random. The probability that they have no side in common is :

Accepted Answer

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

Answer

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

Answer

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

Answer

(D) $\dfrac{23}{30}$

Question 11

Let $x=x(y)$ be the solution of the differential equation $y=\left(x-y\dfrac{dx}{dy}\right)\sin\!\left(\dfrac{x}{y}\right),\ y>0$ and $x(1)=\dfrac{\pi}{2}$. Then $\cos\big(x(2)\big)$ is equal to :

Accepted Answer

(B) $2(\log_e 2)^2-1$

Answer

(A) $1-2(\log_e 2)^2$

Answer

(C) $2(\log_e 2)-1$

Answer

(D) $1-2(\log_e 2)$

Question 12

Let the range of the function $f(x)=6+16\cos x\cdot\cos\!\left(\dfrac{\pi}{3}-x\right)\cdot\cos\!\left(\dfrac{\pi}{3}+x\right)\cdot\sin 3x\cdot\cos 6x,\ x\in\mathbb{R}$ be $[\alpha,\beta]$. Then the distance of the point $(\alpha,\beta)$ from the line $3x+4y+12=0$ is :

Accepted Answer

(A) 11

Answer

(B) 8

Answer

(C) 10

Answer

(D) 9

Question 13

Let the shortest distance from $(a,0),\ a>0,$ to the parabola $y^2=4x$ be $4$. Then the equation of the circle passing through the point $(a,0)$ and the focus of the parabola, and having its centre on the axis of the parabola is :

Accepted Answer

(A) $x^2+y^2-6x+5=0$

Answer

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

Answer

(C) $x^2+y^2-10x+9=0$

Answer

(D) $x^2+y^2-8x+7=0$

Question 14

Let $X=\mathbb{R}	imes\mathbb{R}$. Define a relation $R$ on $X$ as: $(a_1,b_1)\,R\,(a_2,b_2)\Leftrightarrow b_1=b_2$.
Statement-I: $R$ is an equivalence relation.
Statement-II: For some $(a,b)\in X$, the set $S=\{(x,y)\in X:(x,y)\,R\,(a,b)\}$ represents a line parallel to $y=x$.
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 15

The length of the chord of the ellipse $\dfrac{x^2}{4}+\dfrac{y^2}{2}=1$, whose mid-point is $\left(1,\dfrac{1}{2}\right)$, is :

Accepted Answer

(A) $\dfrac{2}{3}\sqrt{15}$

Answer

(B) $\dfrac{5}{3}\sqrt{15}$

Answer

(C) $\dfrac{1}{3}\sqrt{15}$

Answer

(D) $\sqrt{15}$

Question 16

Let $A=[a_{ij}]$ be a $3	imes 3$ matrix such that $A\begin{bmatrix}0\1\0\end{bmatrix}=\begin{bmatrix}0\0\1\end{bmatrix},\ A\begin{bmatrix}4\1\3\end{bmatrix}=\begin{bmatrix}1\1\0\end{bmatrix}$ and $A\begin{bmatrix}2\1\2\end{bmatrix}=\begin{bmatrix}1\0\0\end{bmatrix}$, then $a_{23}$ equals :

Accepted Answer

(A) $-1$

Answer

(B) $0$

Answer

(C) $2$

Answer

(D) $1$

Question 17

The number of complex numbers $z$, satisfying $|z|=1$ and $\left|\dfrac{z}{\bar z}+\dfrac{\bar z}{z}\right|=1$, is :

Accepted Answer

(D) 8

Answer

(A) 6

Answer

(B) 4

Answer

(C) 10

Question 18

If the square of the shortest distance between the lines $\dfrac{x-2}{1}=\dfrac{y-1}{2}=\dfrac{z+3}{-3}$ and $\dfrac{x+1}{2}=\dfrac{y+3}{4}=\dfrac{z+5}{-5}$ is $\dfrac{m}{n}$, where $m,n$ are coprime numbers, then $m+n$ is equal to :

Accepted Answer

(B) 9

Answer

(A) 6

Answer

(C) 21

Answer

(D) 14

Question 19

If $I=\displaystyle\int_0^{\pi/2}\dfrac{\sin^2 x}{\sin^4 x+\cos^4 x}\,dx$, then $\displaystyle\int_0^{\pi/2}\dfrac{x\sin x\cos x}{\sin^4 x+\cos^4 x}\,dx$ equals :

Accepted Answer

(A) $\dfrac{\pi^2}{16}$

Answer

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

Answer

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

Answer

(D) $\dfrac{\pi^2}{12}$

Question 20

$\displaystyle\lim_{x	o\infty}\dfrac{\left(2x^2-3x+5ight)\left(3x-1ight)^{x/2}}{\left(3x^2+5x+4ight)\sqrt{\left(3x+2ight)^x}}$ is equal to :

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 21

The number of ways, $5$ boys and $4$ girls can sit in a row so that either all the boys sit together or no two boys sit together, is __________.

Accepted Answer

17280

Question 22

Let $\alpha,\beta$ be the roots of the equation $x^2-ax-b=0$ with $\operatorname{Im}(\alpha)<\operatorname{Im}(\beta)$. Let $P_n=\alpha^n-\beta^n$. If $P_3=-5\sqrt7\,i,\ P_4=-3\sqrt7\,i,\ P_5=11\sqrt7\,i$ and $P_6=45\sqrt7\,i$, then $|\alpha^4+\beta^4|$ is equal to __________.

Accepted Answer

31

Question 23

The focus of the parabola $y^2=4x+16$ is the centre of the circle $C$ of radius $5$. If the values of $\lambda$, for which $C$ passes through the point of intersection of the lines $3x-y=0$ and $x+\lambda y=4$, are $\lambda_1$ and $\lambda_2,\ \lambda_1<\lambda_2$, then $12\lambda_1+29\lambda_2$ is equal to __________.

Accepted Answer

15

Question 24

The variance of the numbers $8,\ 21,\ 34,\ 47,\ \ldots,\ 320$, is __________.

Accepted Answer

8788

Question 25

The roots of the quadratic equation $3x^2-px+q=0$ are $10^{	ext{th}}$ and $11^{	ext{th}}$ terms of an arithmetic progression with common difference $\dfrac{3}{2}$. If the sum of the first $11$ terms of this arithmetic progression is $88$, then $q-2p$ is equal to __________.

Accepted Answer

474

Question 26

A ball having kinetic energy KE, is projected at an angle of $60^\circ$ from the horizontal. What will be the kinetic energy of ball at the highest point of its flight?

Accepted Answer

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

Answer

(A) $\dfrac{KE}{8}$

Answer

(C) $\dfrac{KE}{16}$

Answer

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

Question 27

Two charges $7\,\mu c$ and $-4\,\mu c$ are placed at $(-7	ext{ cm}, 0, 0)$ and $(7	ext{ cm}, 0, 0)$ respectively. Given, $\varepsilon_0=8.85	imes10^{-12}\ \mathrm{C^2\,N^{-1}\,m^{-2}}$, the electrostatic potential energy of the charge configuration is :

Accepted Answer

(D) $-1.8$ J

Answer

(A) $-1.5$ J

Answer

(B) $-2.0$ J

Answer

(C) $-1.2$ J

Question 28

The refractive index of the material of a glass prism is $\sqrt3$. The angle of minimum deviation is equal to the angle of the prism. What is the angle of the prism?

Accepted Answer

(B) $60^\circ$

Answer

(A) $50^\circ$

Answer

(C) $58^\circ$

Answer

(D) $48^\circ$

Question 29

The equation of a transverse wave travelling along a string is $y(x,t)=4.0\sin[20	imes10^{-3}x+600t]$ mm, where $x$ is in the mm and $t$ is in second. The velocity of the wave is :

Accepted Answer

(C) $-30$ m/s

Answer

(A) $+30$ m/s

Answer

(B) $-60$ m/s

Answer

(D) $+60$ m/s

Question 30

The energy of a system is given as $E(t)=\alpha^3 e^{-\beta t}$, where $t$ is the time and $\beta=0.3\ \mathrm{s^{-1}}$. The errors in the measurement of $\alpha$ and $t$ are $1.2\%$ and $1.6\%$, respectively. At $t=5$ s, maximum percentage error in the energy is :

Accepted Answer

(C) $6\%$

Answer

(A) $4\%$

Answer

(B) $11.6\%$

Answer

(D) $8.4\%$

Question 31

In photoelectric effect an em-wave is incident on a metal surface and electrons are ejected from the surface. If the work function of the metal is $2.14$ eV and stopping potential is $2$V, what is the wavelength of the em-wave? (Given $hc=1242$ eVnm where $h$ is the Planck's constant and $c$ is the speed of light in vacuum.)

Accepted Answer

(D) $300$ nm

Answer

(A) $400$ nm

Answer

(B) $600$ nm

Answer

(C) $200$ nm

Question 32

A circular disk of radius R meter and mass M kg is rotating about the axis perpendicular to the disk. An external torque is applied to the disk such that $	heta(t)=5t^2-8t$, where $	heta(t)$ is the angular position of the rotating disc as a function of time t. How much power is delivered by the applied torque, when $t=2$s?

Accepted Answer

(A) $60\,MR^2$

Answer

(B) $72\,MR^2$

Answer

(C) $108\,MR^2$

Answer

(D) $8\,MR^2$

Question 33

Water flows in a horizontal pipe whose one end is closed with a valve. The reading of the pressure gauge attached to the pipe is $P_1$. The reading of the pressure gauge falls to $P_2$ when the valve is opened. The speed of water flowing in the pipe is proportional to :

Accepted Answer

(A) $\sqrt{P_1-P_2}$

Answer

(B) $(P_1-P_2)^2$

Answer

(C) $(P_1-P_2)^4$

Answer

(D) $P_1-P_2$

Question 34

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 35

If a satellite orbiting the Earth is $9$ times closer to the Earth than the Moon, what is the time period of rotation of the satellite? Given rotational time period of Moon $=27$ days and gravitational attraction between the satellite and the moon is neglected.

Accepted Answer

(A) $1$ day

Answer

(B) $81$ days

Answer

(C) $27$ days

Answer

(D) $3$ days

Question 36

Two point charges $-4\,\mu c$ and $4\,\mu c$, constituting an electric dipole, are placed at $(-9, 0, 0)$ cm and $(9, 0, 0)$ cm in a uniform electric field of strength $10^4\ \mathrm{NC^{-1}}$. The work done on the dipole in rotating it from the equilibrium through $180^\circ$ is :

Accepted Answer

(A) $14.4$ mJ

Answer

(B) $18.4$ mJ

Answer

(C) $12.4$ mJ

Answer

(D) $16.4$ mJ

Question 37

A galvanometer having a coil of resistance $30\ \Omega$ need $20$ mA of current for full-scale deflection. If a maximum current of $3$ A is to be measured using this galvanometer, the resistance of the shunt to be added to the galvanometer should be $\dfrac{30}{X}\ \Omega$, where $X$ is :

Accepted Answer

(C) $149$

Answer

(A) $447$

Answer

(B) $298$

Answer

(D) $596$

Question 38

The width of one of the two slits in Young's double slit experiment is $d$ while that of the other slit is $xd$. If the ratio of the maximum to the minimum intensity in the interference pattern on the screen is $9:4$ what is the value of $x$? (Assume that the field strength varies according to the slit width.)

Accepted Answer

(C) $5$

Answer

(A) $2$

Answer

(B) $3$

Answer

(D) $4$

Question 39

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : The binding energy per nucleon is found to be practically independent of the atomic number A, for nuclei with mass numbers between 30 and 170.
Reason (R) : Nuclear force is long range.
In the light of the above statements, choose the correct answer from the options given below :

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 40

Water of mass m gram is slowly heated to increase the temperature from $T_1$ to $T_2$. The change in entropy of the water, given specific heat of water is $1\ \mathrm{Jkg^{-1}K^{-1}}$, is :

Accepted Answer

(D) $m\ln\!\left(\dfrac{T_2}{T_1}\right)$

Answer

(A) zero

Answer

(B) $m(T_2-T_1)$

Answer

(C) $m\ln\!\left(\dfrac{T_1}{T_2}\right)$

Question 41

What is the current through the battery in the circuit shown below?

Accepted Answer

(C) $0.5$ A

Answer

(A) $1.0$ A

Answer

(B) $1.5$ A

Answer

(D) $0.25$ A

Question 42

A plane electromagnetic wave of frequency 20 MHz travels in free space along the $+x$ direction. At a particular point in space and time, the electric field vector of the wave is $E_y=9.3\ \mathrm{V\,m^{-1}}$. Then, the magnetic field vector of the wave at that point is :

Accepted Answer

(D) $B_z=3.1	imes10^{-8}$ T

Answer

(A) $B_z=9.3	imes10^{-8}$ T

Answer

(B) $B_z=1.55	imes10^{-8}$ T

Answer

(C) $B_z=6.2	imes10^{-8}$ T

Question 43

Using the given P-V diagram, the work done by an ideal gas along the path ABCD is :

Accepted Answer

(D) $-3\,P_0V_0$

Answer

(A) $4\,P_0V_0$

Answer

(B) $3\,P_0V_0$

Answer

(C) $-4\,P_0V_0$

Question 44

A concave mirror of focal length $f$ in air is dipped in a liquid of refractive index $\mu$. Its focal length in the liquid is :

Accepted Answer

(D) $f$

Answer

(A) $\dfrac{f}{\mu}$

Answer

(B) $\dfrac{f}{\mu-1}$

Answer

(C) $\mu f$

Question 45

A massless spring gets elongated by amount $x_1$ under a tension of 5N. Its elongation is $x_2$ under the tension of 7N. For the elongation of $(5x_1-2x_2)$, the tension in the spring will be :

Accepted Answer

(C) $11$ N

Answer

(A) $15$ N

Answer

(B) $20$ N

Answer

(D) $39$ N

Question 46

An air bubble of radius 1.0 mm is observed at a depth of 20 cm below the free surface of a liquid having surface tension $0.095\ \mathrm{J/m^2}$ and density $10^3\ \mathrm{kg/m^3}$. The difference between pressure inside the bubble and atmospheric pressure is __________ $\mathrm{N/m^2}$. (Take $g=10\ \mathrm{m/s^2}$)

Accepted Answer

2190

Question 47

A satellite of mass $\dfrac{M}{2}$ is revolving around earth in a circular orbit at a height of $\dfrac{R}{3}$ from earth surface. The angular momentum of the satellite is $M\sqrt{\dfrac{GMR}{x}}$. The value of $x$ is __________, where $M$ and $R$ are the mass and radius of earth, respectively. ($G$ is the gravitational constant)

Accepted Answer

3

Question 48

At steady state the charge on the capacitor, as shown in the circuit below, is __________ $\mu$C.

Accepted Answer

16

Question 49

A time varying potential difference is applied between the plates of a parallel plate capacitor of capacitance $2.5\ \mu$F. The dielectric constant of the medium between the capacitor plates is 1. It produces an instantaneous displacement current of $0.25$ mA in the intervening space between the capacitor plates, the magnitude of the rate of change of the potential difference will be __________ $\mathrm{Vs^{-1}}$.

Accepted Answer

100

Question 50

In a series LCR circuit, a resistor of $300\ \Omega$, a capacitor of $25$ nF and an inductor of $100$ mH are used. For maximum current in the circuit, the angular frequency of the ac source is __________ $	imes10^4$ radians $\mathrm{s^{-1}}$.

Accepted Answer

2

Question 51

The effect of temperature on spontaneity of reactions are represented as: (A) $\Delta H=+,\ \Delta S=-$, any T $	o$ Non-spontaneous; (B) $\Delta H=+,\ \Delta S=+$, low T $	o$ spontaneous; (C) $\Delta H=-,\ \Delta S=-$, low T $	o$ Non-spontaneous; (D) $\Delta H=-,\ \Delta S=+$, any T $	o$ spontaneous.

Accepted Answer

(C) (B) and (C) only

Answer

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

Answer

(B) (A) and (D) only

Answer

(D) (D) and (C) only

Question 52

Standard electrode potentials for a few half cells are mentioned below: $E^\circ_{Cu^{2+}/Cu}=0.34$ V, $E^\circ_{Zn^{2+}/Zn}=-0.76$ V, $E^\circ_{Ag^+/Ag}=0.80$ V, $E^\circ_{Mg^{2+}/Mg}=-2.37$ V. Which one of the following cells gives the most negative value of $\Delta G^\circ$?

Accepted Answer

(A) $Zn\,|\,Zn^{2+}(1M)\,||\,Ag^+(1M)\,|\,Ag$

Answer

(B) $Zn\,|\,Zn^{2+}(1M)\,||\,Mg^{2+}(1M)\,|\,Mg$

Answer

(C) $Ag\,|\,Ag^+(1M)\,||\,Mg^{2+}(1M)\,|\,Mg$

Answer

(D) $Cu\,|\,Cu^{2+}(1M)\,||\,Ag^+(1M)\,|\,Ag$

Question 53

The $\alpha$-Helix and $\beta$-Pleated sheet structures of protein are associated with its:

Accepted Answer

(C) secondary structure

Answer

(A) quaternary structure

Answer

(B) primary structure

Answer

(D) tertiary structure

Question 54

Given below are two statements. Consider the following reaction: $R	ext{-CHO}+H_2O\xrightleftharpoons{K}R	ext{-CH(OH)}_2$. Statement (I): In the case of formaldehyde (HCHO), K is about 2280, due to small substituents, hydration is faster. Statement (II): In the case of trichloro acetaldehyde (CCl$_3$CHO), K is about 2000 due to $-I$ effect of $-$Cl. 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 true but Statement II is false

Answer

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

Answer

(D) Both Statement I and Statement II are false

Question 55

Consider the reaction $X_2Y(g)ightleftharpoons X_2(g)+	frac12 Y_2(g)$. The equation representing correct relationship between the degree of dissociation $(x)$ of $X_2Y(g)$ with its equilibrium constant $K_p$ is __________. Assume $x$ to be very very small.

Accepted Answer

(B) $x=\sqrt[3]{\dfrac{2K_p^2}{p}}$

Answer

(A) $x=\sqrt{\dfrac{2K_p}{p}}$

Answer

(C) $x=\sqrt{\dfrac{K_p}{2p}}$

Answer

(D) $x=\sqrt[3]{\dfrac{K_p}{p}}$

Question 56

Identify A, B and C in the given below reaction sequence: $A\xrightarrow{HNO_3}Pb(NO_3)_2\xrightarrow{H_2SO_4}B\xrightarrow{	ext{(1) ammonium acetate, (2) acetic acid, (3) }K_2CrO_4}C$ (Yellow ppt).

Accepted Answer

(B) $PbS,\ PbSO_4,\ PbCrO_4$

Answer

(A) $PbCl_2,\ PbSO_4,\ PbCrO_4$

Answer

(C) $PbS,\ PbSO_4,\ Pb(CH_3COO)_2$

Answer

(D) $PbCl_2,\ Pb(SO_4)_2,\ PbCrO_4$

Question 57

Given below are two statements: Statement (I): The boiling points of alcohols and phenols increase with increase in the number of C-atoms. Statement (II): The boiling points of alcohols and phenols are higher in comparison to other class of compounds such as ethers, haloalkanes. 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) Both Statement I and Statement II are false

Answer

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

Answer

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

Question 58

When a non-volatile solute is added to the solvent, the vapour pressure of the solvent decreases by 10 mm of Hg. The mole fraction of the solute in the solution is 0.2. What would be the mole fraction of the solvent if decrease in vapour pressure is 20 mm of Hg ?

Accepted Answer

(A) 0.6

Answer

(B) 0.4

Answer

(C) 0.2

Answer

(D) 0.8

Question 59

Given below are two statements: Statement (I): For a given shell, the total number of allowed orbitals is given by $n^2$. Statement (II): For any subshell, the spatial orientation of the orbitals is given by $-l$ to $+l$ values including zero. 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) Statement I is true but Statement II is false

Answer

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

Answer

(D) Both Statement I and Statement II are false

Question 60

The ascending order of relative rate of solvolysis of following compounds (A), (B), (C) and (D) (shown in the figure) is :

Accepted Answer

(C) (D) < (B) < (A) < (C)

Answer

(A) (D) < (A) < (B) < (C)

Answer

(B) (C) < (B) < (A) < (D)

Answer

(D) (C) < (D) < (B) < (A)

Question 61

Match List-I (Isomers of $C_{10}H_{14}$) with List-II (Ozonolysis product). Choose the correct answer from the options given below:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 62

Which of the following graphs most appropriately represents a zero order reaction?

Accepted Answer

(B) (2)

Answer

(A) (1)

Answer

(C) (3)

Answer

(D) (4)

Question 63

Match List-I (Alloy) with List-II (Constituent Metals). Choose the correct answer from the options given below:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 64

Identify the coordination complexes in which the central metal ion has $d^4$ configuration. (A) $[FeO_4]^{2-}$ (B) $[Mn(CN)_6]^{3-}$ (C) $[Fe(CN)_6]^{3-}$ (D) $Cr_2(	ext{O–CO–Me})_4(H_2O)_2$ (E) $[NiF_6]^{2-}$. Choose the correct answer from the options given below:

Accepted Answer

(C) (B) and (D) only

Answer

(A) (C) and (E) only

Answer

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

Answer

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

List-I (Electromagnetic Quantity)	List-II (Dimensional Formula)
A.Permeability of free space	I. $[\mathrm{M\,L^2\,T^{-2}}]$
B.Magnetic field	II. $[\mathrm{M\,T^{-2}\,A^{-1}}]$
C.Magnetic moment	III. $[\mathrm{M\,L\,T^{-2}\,A^{-2}}]$
D.Torsional constant	IV. $[\mathrm{L^2\,A}]$

List-I (Isomers of $C_{10}H_{14}$)	List-II (Ozonolysis product)
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 (Alloy)	List-II (Constituent Metals)
A.Bronze	I.Cu, Ni
B.Brass	II.Fe, Cr, Ni, C
C.UK silver coin	III.Cu, Zn
D.Stainless Steel	IV.Cu, Sn

JEE Main 23 January 2025 Shift 2 Question Paper with Answers

Physics — JEE Main 23 January 2025 Shift 2

Chemistry — JEE Main 23 January 2025 Shift 2

Mathematics — JEE Main 23 January 2025 Shift 2

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