JEE Main 22 January 2025 Shift 2 Question Paper

Question 1

Let $\alpha,\beta,\gamma$ and $\delta$ be the coefficients of $x^7,x^5,x^3$ and $x$ respectively in the expansion of $\left(x+\sqrt{x^3-1}\right)^5+\left(x-\sqrt{x^3-1}\right)^5$, $x>1$. If $u$ and $v$ satisfy the equations $\alpha u+\beta v=18$, $\gamma u+\delta v=20$, then $u+v$ equals:

Accepted Answer

(A) 5

Answer

(B) 4

Answer

(C) 3

Answer

(D) 8

Question 2

In a group of 3 girls and 4 boys, there are two boys $B_1$ and $B_2$. The number of ways, in which these girls and boys can stand in a queue such that all the girls stand together, all the boys stand together, but $B_1$ and $B_2$ are not adjacent to each other, is:

Accepted Answer

(A) 144

Answer

(B) 72

Answer

(C) 96

Answer

(D) 120

Question 3

Let $P\left(4,4\sqrt{3}\right)$ be a point on the parabola $y^2=4ax$ and $PQ$ be a focal chord of the parabola. If $M$ and $N$ are the foot of perpendiculars drawn from $P$ and $Q$ respectively on the directrix of the parabola, then the area of the quadrilateral $PQMN$ is equal to:

Accepted Answer

(C) $\dfrac{343\sqrt{3}}{8}$

Answer

(A) $\dfrac{263\sqrt{3}}{8}$

Answer

(B) $17\sqrt{3}$

Answer

(D) $\dfrac{34\sqrt{3}}{3}$

Question 4

For a $3	imes3$ matrix $M$, let trace $(M)$ denote the sum of all the diagonal elements of $M$. Let $A$ be a $3	imes3$ matrix such that $|A|=\dfrac{1}{2}$ and trace $(A)=3$. If $B=\operatorname{adj}(\operatorname{adj}(2A))$, then the value of $|B|+\operatorname{trace}(B)$ equals:

Accepted Answer

(D) 280

Answer

(A) 56

Answer

(B) 132

Answer

(C) 174

Question 5

Suppose that the number of terms in an A.P. is $2k$, $k\in\mathbb{N}$. If the sum of all odd terms of the A.P. is 40, the sum of all even terms is 55 and the last term of the A.P. exceeds the first term by 27, then $k$ is equal to

Accepted Answer

(A) 5

Answer

(B) 8

Answer

(C) 6

Answer

(D) 4

Question 6

Let a line pass through two distinct points $P(-2,-1,3)$ and $Q$, and be parallel to the vector $3\hat{i}+2\hat{j}+2\hat{k}$. If the distance of the point $Q$ from the point $R(1,3,3)$ is 5, then the square of the area of $	riangle PQR$ is equal to:

Accepted Answer

(A) 136

Answer

(B) 140

Answer

(C) 144

Answer

(D) 148

Question 7

If $\displaystyle\lim_{x	o\infty}\left(\dfrac{e}{1-e}\left(\dfrac{1}{e}-\dfrac{x}{1+x}ight)ight)^x=\alpha$, then the value of $\dfrac{\log_e\alpha}{1+\log_e\alpha}$ equals:

Accepted Answer

(A) e

Answer

(B) $e^{-2}$

Answer

(C) $e^{2}$

Answer

(D) $e^{-1}$

Question 8

Let $f(x)=\displaystyle\int_0^{x^2}\dfrac{t^2-8t+15}{e^t}\,dt$, $x\in\mathbb{R}$. Then the numbers of local maximum and local minimum points of $f$, respectively, are:

Accepted Answer

(A) 2 and 3

Answer

(B) 3 and 2

Answer

(C) 1 and 3

Answer

(D) 2 and 2

Question 9

The perpendicular distance, of the line $\dfrac{x-1}{2}=\dfrac{y+2}{-1}=\dfrac{z+3}{2}$ from the point $P(2,-10,1)$, is:

Accepted Answer

(C) $3\sqrt{5}$

Answer

(A) 6

Answer

(B) $5\sqrt{2}$

Answer

(D) $4\sqrt{3}$

Question 10

If $x=f(y)$ is the solution of the differential equation $(1+y^2)+\left(x-2e^{	an^{-1}y}ight)\dfrac{dy}{dx}=0$, $y\in\left(-\dfrac{\pi}{2},\dfrac{\pi}{2}ight)$ with $f(0)=1$, then $f\left(\dfrac{1}{\sqrt{3}}ight)$ is equal to:

Accepted Answer

(D) $e^{\pi/6}$

Answer

(A) $e^{\pi/4}$

Answer

(B) $e^{\pi/12}$

Answer

(C) $e^{\pi/3}$

Question 11

If $\displaystyle\int e^x\left(\dfrac{x\sin^{-1}x}{\sqrt{1-x^2}}+\dfrac{\sin^{-1}x}{\left(1-x^2\right)^{3/2}}+\dfrac{x}{1-x^2}\right)dx=g(x)+C$, where $C$ is the constant of integration, then $g\left(\dfrac{1}{2}\right)$ equals:

Accepted Answer

(C) $\dfrac{\pi}{6}\sqrt{\dfrac{e}{3}}$

Answer

(A) $\dfrac{\pi}{6}\sqrt{\dfrac{e}{2}}$

Answer

(B) $\dfrac{\pi}{4}\sqrt{\dfrac{e}{2}}$

Answer

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

Question 12

Let $\alpha_0$ and $\beta_0$ be the distinct roots of $2x^2+(\cos	heta)x-1=0$, $	heta\in(0,2\pi)$. If $m$ and $M$ are the minimum and the maximum values of $\alpha_0^4+\beta_0^4$, then $16(M+m)$ equals:

Accepted Answer

(B) 25

Answer

(A) 24

Answer

(C) 27

Answer

(D) 17

Question 13

Let $A=\{1,2,3,4\}$ and $B=\{1,4,9,16\}$. Then the number of many-one functions $f:A	o B$ such that $1\in f(A)$ is equal to:

Accepted Answer

(B) 151

Answer

(A) 127

Answer

(C) 163

Answer

(D) 139

Question 14

If the system of linear equations: $x+y+2z=6$, $2x+3y+az=a+1$, $-x-3y+bz=2b$, where $a,b\in\mathbb{R}$, has infinitely many solutions, then $7a+3b$ is equal to:

Accepted Answer

(C) 16

Answer

(A) 9

Answer

(B) 12

Answer

(D) 22

Question 15

Let $\vec{a}$ and $\vec{b}$ be two unit vectors such that the angle between them is $\dfrac{\pi}{3}$. If $\lambda\vec{a}+2\vec{b}$ and $3\vec{a}-\lambda\vec{b}$ are perpendicular to each other, then the number of values of $\lambda$ in $[-1,3]$ is:

Accepted Answer

(D) 0

Answer

(A) 3

Answer

(B) 2

Answer

(C) 1

Question 16

Let $E:\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1$, $a>b$ and $H:\dfrac{x^2}{A^2}-\dfrac{y^2}{B^2}=1$. Let the distance between the foci of $E$ and the foci of $H$ be $2\sqrt{3}$. If $a-A=2$, and the ratio of the eccentricities of $E$ and $H$ is $\dfrac{1}{3}$, then the sum of the lengths of their latus rectums is equal to:

Accepted Answer

(C) 8

Answer

(A) 10

Answer

(B) 7

Answer

(D) 9

Question 17

If $A$ and $B$ are two events such that $P(A\cap B)=0.1$, and $P(A|B)$ and $P(B|A)$ are the roots of the equation $12x^2-7x+1=0$, then the value of $\dfrac{P\left(\bar{A}\cup\bar{B}\right)}{P\left(\bar{A}\cap\bar{B}\right)}$ is:

Accepted Answer

(C) $\dfrac{9}{4}$

Answer

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

Answer

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

Answer

(D) $\dfrac{7}{4}$

Question 18

The sum of all values of $	heta\in[0,2\pi]$ satisfying $2\sin^2	heta=\cos2	heta$ and $2\cos^2	heta=3\sin	heta$ is

Accepted Answer

(D) \pi

Answer

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

Answer

(B) 4\pi

Answer

(C) $\dfrac{5\pi}{6}$

Question 19

Let the curve $z(1+i)+\bar{z}(1-i)=4$, $z\in\mathbb{C}$, divide the region $|z-3|\le1$ into two parts of areas $\alpha$ and $\beta$. Then $|\alpha-\beta|$ equals:

Accepted Answer

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

Answer

(B) $1+\dfrac{\pi}{3}$

Answer

(C) $1+\dfrac{\pi}{4}$

Answer

(D) $1+\dfrac{\pi}{6}$

Question 20

The area of the region enclosed by the curves $y=x^2-4x+4$ and $y^2=16-8x$ is:

Accepted Answer

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

Answer

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

Answer

(C) 5

Answer

(D) 8

Question 21

Let $y=f(x)$ be the solution of the differential equation $\dfrac{dy}{dx}+\dfrac{xy}{x^2-1}=\dfrac{x^6+4x}{\sqrt{1-x^2}}$, $-1<x<1$ such that $f(0)=0$. If $6\displaystyle\int_{-1/2}^{1/2}f(x)\,dx=2\pi-\alpha$ then $\alpha^2$ is equal to ______.

Accepted Answer

27

Question 22

Let $A(6,8)$, $B(10\cos\alpha,-10\sin\alpha)$ and $C(-10\sin\alpha,10\cos\alpha)$ be the vertices of a triangle. If $L(a,9)$ and $G(h,k)$ be its orthocenter and centroid respectively, then $(5a-3h+6k+100\sin2\alpha)$ is equal to ______.

Accepted Answer

145

Question 23

Let the distance between two parallel lines be 5 units and a point $P$ lie between the lines at a unit distance from one of them. An equilateral triangle $PQR$ is formed such that $Q$ lies on one of the parallel lines, while $R$ lies on the other. Then $(QR)^2$ is equal to ______.

Accepted Answer

28

Question 24

If $\displaystyle\sum_{r=1}^{30}\dfrac{r^2\left(^{30}C_right)^2}{^{30}C_{r-1}}=\alpha	imes2^{29}$, then $\alpha$ is equal to ______.

Accepted Answer

465

Question 25

Let $A=\{1,2,3\}$. The number of relations on $A$, containing $(1,2)$ and $(2,3)$, which are reflexive and transitive but not symmetric, is ______.

Accepted Answer

3

Question 26

A symmetric thin biconvex lens is cut into four equal parts by two planes AB and CD as shown in figure. If the power of original lens is 4D then the power of a part of the divided lens is

Accepted Answer

(D) 2D

Answer

(A) 8D

Answer

(B) 4D

Answer

(C) D

Question 27

A small rigid spherical ball of mass M is dropped in a long vertical tube containing glycerine. The velocity of the ball becomes constant after some time. If the density of glycerine is half of the density of the ball, then the viscous force acting on the ball will be (consider g as acceleration due to gravity)

Accepted Answer

(B) $\frac{Mg}{2}$

Answer

(A) $\frac{3}{2}Mg$

Answer

(C) $Mg$

Answer

(D) $2Mg$

Question 28

The maximum percentage error in the measurement of density of a wire is [Given, mass of wire $=(0.60\pm0.003)$ g, radius of wire $=(0.50\pm0.01)$ cm, length of wire $=(10.00\pm0.05)$ cm]

Accepted Answer

(B) 5

Answer

(A) 4

Answer

(C) 8

Answer

(D) 7

Question 29

A series LCR circuit is connected to an alternating source of emf E. The current amplitude at resonant frequency is $I_0$. If the value of resistance R becomes twice of its initial value then amplitude of current at resonance will be

Accepted Answer

(B) $\frac{I_0}{2}$

Answer

(A) $I_0$

Answer

(C) $\frac{I_0}{\sqrt{2}}$

Answer

(D) $2I_0$

Question 30

For a short dipole placed at origin O, the dipole moment P is along x-axis, as shown in the figure. If the electric potential and electric field at A are $V_0$ and $E_0$, respectively, then the correct combination of the electric potential and electric field, respectively, at point B on the y-axis is given by

Accepted Answer

(C) zero and $\frac{E_0}{16}$

Answer

(A) $\frac{V_0}{2}$ and $\frac{E_0}{16}$

Answer

(B) zero and $\frac{E_0}{8}$

Answer

(D) $V_0$ and $\frac{E_0}{4}$

Question 31

Which one of the following is the correct dimensional formula for the capacitance in F? M, L, T and C stand for unit of mass, length, time and charge,

Accepted Answer

(D) $[F]=[C^{2}M^{-1}L^{-2}T^{2}]$

Answer

(A) $[F]=[C^{2}M^{-2}L^{2}T^{2}]$

Answer

(B) $[F]=[CM^{-2}L^{-2}T^{-2}]$

Answer

(C) $[F]=[CM^{-1}L^{-2}T^{2}]$

Question 32

An electron projected perpendicular to a uniform magnetic field B moves in a circle. If Bohr's quantization is applicable, then the radius of electronic orbit in the first excited state is:

Accepted Answer

(D) $\sqrt{\frac{h}{\pi eB}}$

Answer

(A) $\sqrt{\frac{2h}{\pi eB}}$

Answer

(B) $\sqrt{\frac{4h}{\pi eB}}$

Answer

(C) $\sqrt{\frac{h}{2\pi eB}}$

Question 33

For a diatomic gas, if $\gamma_1=\left(\frac{C_p}{C_v}\right)$ for rigid molecules and $\gamma_2=\left(\frac{C_p}{C_v}\right)$ for another diatomic molecules, but also having vibrational modes. Then, which one of the following options is correct? ($C_p$ and $C_v$ are specific heats of the gas at constant pressure and volume)

Accepted Answer

(D) $\gamma_2<\gamma_1$

Answer

(A) $\gamma_2>\gamma_1$

Answer

(B) $\gamma_2=\gamma_1$

Answer

(C) $2\gamma_2=\gamma_1$

Question 34

A rectangular metallic loop is moving out of a uniform magnetic field region to a field free region with a constant speed. When the loop is partially inside the magnetic field, the plot of magnitude of induced emf ($\varepsilon$) with time (t) is given by

Accepted Answer

(D) (4)

Answer

(A) (1)

Answer

(B) (2)

Answer

(C) (3)

Question 35

A light source of wavelength $\lambda$ illuminates a metal surface and electrons are ejected with maximum kinetic energy of 2 eV. If the same surface is illuminated by a light source of wavelength $\frac{\lambda}{2}$, then the maximum kinetic energy of ejected electrons will be (The work function of metal is 1 eV)

Accepted Answer

(C) 5 eV

Answer

(A) 2 eV

Answer

(B) 6 eV

Answer

(D) 4 eV

Question 36

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): A simple pendulum is taken to a planet of mass and radius, 4 times and 2 times, respectively, than the earth. The time period of the pendulum remains same on earth and the planet.
Reason (R): The mass of the pendulum remains unchanged on earth and the other planet.
In the light of the above statements, choose the correct answer from the options given below:

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

Answer

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

Question 37

The torque due to the force $\left(2\hat{i}+\hat{j}+2\hat{k}\right)$ about the origin, acting on a particle whose position vector is $\left(\hat{i}+\hat{j}+\hat{k}\right)$, would be

Accepted Answer

(C) $\hat{i}-\hat{k}$

Answer

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

Answer

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

Answer

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

Question 38

A force $\vec{F}=2\hat{i}+b\hat{j}+\hat{k}$ is applied on a particle and it undergoes a displacement $\hat{i}-2\hat{j}-\hat{k}$. What will be the value of b, if work done on the particle is zero.

Accepted Answer

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

Answer

(A) 0

Answer

(C) $\frac{1}{3}$

Answer

(D) 2

Question 39

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): In Young's double slit experiment, the fringes produced by red light are closer as compared to those produced by blue light.
Reason (R): The fringe width is directly proportional to the wavelength of light. In the light of above statements, choose the correct answer from the options given below:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 40

A ball of mass 100 g is projected with velocity 20 m/s at $60^\circ$ with horizontal. The decrease in kinetic energy of the ball during the motion from point of projection to highest point is:

Accepted Answer

(B) 15 J

Answer

(A) 20 J

Answer

(C) zero

Answer

(D) 5 J

Question 41

A transparent film of refractive index, 2.0 is coated on a glass slab of refractive index, 1.45. What is the minimum thickness of transparent film to be coated for the maximum transmission of Green light of wavelength 550 nm. [Assume that the light is incident nearly perpendicular to the glass surface.]

Accepted Answer

(C) 137.5 nm

Answer

(A) 94.8 nm

Answer

(B) 68.7 nm

Answer

(D) 275 nm

Question 42

The tube of length L is shown in the figure. The radius of cross section at the point (1) is 2 cm and at the point (2) is 1 cm, respectively. If the velocity of water entering at point (1) is 2 m/s, then velocity of water leaving the point (2) will be:

Accepted Answer

(D) 8 m/s

Answer

(A) 2 m/s

Answer

(B) 4 m/s

Answer

(C) 6 m/s

Question 43

Given are statements for certain thermodynamic variables, (A) Internal energy, volume (V) and mass (M) are extensive variables. (B) Pressure (P), temperature (T) and density ($\rho$) are intensive variables. (C) Volume (V), temperature (T) and density ($\rho$) are intensive variables. (D) Mass (M), temperature (T) and internal energy are extensive variables. Choose the correct answer from the points given below:

Accepted Answer

(C) (A) and (B) only

Answer

(A) (C) and (D) only

Answer

(B) (D) and (A) only

Answer

(D) (B) and (C) only

Question 44

A body of mass 100 g is moving in circular path of radius 2 m on vertical plane as shown in figure. The velocity of the body at point A is 10 m/s. The ratio of its kinetic energies at point B and C is: (Take acceleration due to gravity as 10 m/s$^2$)

Accepted Answer

(C) $\frac{3+\sqrt{3}}{2}$

Answer

(A) $\frac{2+\sqrt{3}}{3}$

Answer

(B) $\frac{2+\sqrt{2}}{3}$

Answer

(D) $\frac{3-\sqrt{2}}{2}$

Question 45

A proton is moving undeflected in a region of crossed electric and magnetic fields at a constant speed of $2	imes10^5$ ms$^{-1}$. When the electric field is switched off, the proton moves along a circular path of radius 2 cm. The magnitude of electric field is $x	imes10^4$ N/C, the value of x is ______. Take the mass of the proton $=1.6	imes10^{-27}$ kg.

Accepted Answer

2

Question 46

Two long parallel wires X and Y, separated by a distance of 6 cm, carry currents of 5A and 4A, respectively, in opposite directions as shown in the figure. Magnitude of the resultant magnetic field at point P at a distance of 4 cm from wire Y is $x	imes10^{-5}$ T. The value of x is ______. Take permeability of free space as $\mu_0=4\pi	imes10^{-7}$ SI units.

Accepted Answer

1

Question 47

A parallel plate capacitor of area A = 16 cm$^2$ and separation between the plates 10 cm, is charged by a DC current. Consider a hypothetical plane surface of area $A_s=3.2$ cm$^2$ inside the capacitor and parallel to the plates. At an instant, the current through the circuit is 6A. At the same instant the displacement current through $A_s$ is ______ mA.

Accepted Answer

1200

Question 48

A tube of length 1m is filled completely with an ideal liquid of mass 2M, and closed at both ends. The tube is rotated uniformly in horizontal plane about one of its ends. If the force exerted by the liquid at the other end is F then angular velocity of the tube is $\sqrt{\frac{F}{\alpha M}}$ in SI unit. The value of $\alpha$ is ______.

Accepted Answer

1

Question 49

Arrange the following compounds in increasing order of their dipole moment: HBr, H$_2$S, NF$_3$ and CHCl$_3$

Accepted Answer

(A) $NF_3 < HBr < H_2S < CHCl_3$

Answer

(B) $HBr < H_2S < NF_3 < CHCl_3$

Answer

(C) $H_2S < HBr < NF_3 < CHCl_3$

Answer

(D) $CHCl_3 < NF_3 < HBr < H_2S$

Question 50

Identify the number of structure/s from the following which can be correlated to D-glyceraldehyde.

Accepted Answer

(A) three

Answer

(B) two

Answer

(C) four

Answer

(D) one

Question 51

The maximum covalency of a non-metallic group 15 element 'E' with weakest E$-$E bond is:

Accepted Answer

(D) 4

Answer

(A) 5

Answer

(B) 3

Answer

(C) 6

Question 52

Consider the given figure and choose the correct option:

Accepted Answer

(C) Activation energy of forward reaction is $E_1+E_2$ and product is less stable than reactant.

Answer

(A) Activation energy of backward reaction is $E_1$ and product is more stable than reactant.

Answer

(B) Activation energy of forward reaction is $E_1+E_2$ and product is more stable than reactant.

Answer

(D) Activation energy of both forward and backward reaction is $E_1+E_2$ and reactant is more stable than product.

Question 53

When sec-butylcyclohexane reacts with bromine in the presence of sunlight, the major product is:

Accepted Answer

(D) (4)

Answer

(A) (1)

Answer

(B) (2)

Answer

(C) (3)

Question 54

The species which does not undergo disproportionation reaction is:

Accepted Answer

(B) $ClO_4^-$

Answer

(A) $ClO_2^-$

Answer

(C) $ClO^-$

Answer

(D) $ClO_3^-$

Question 55

Match List-I (Compound) with List-II (Catalyst/Reagents). Choose the correct answer from the options given below:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 56

RBr $\xrightarrow{	ext{(i) Mg, dry ether (ii) }H_2O}$ 2-Methylbutane. The maximum number of RBr producing 2-Methylbutane by above sequence of reactions is ______. (Consider the structural isomers only)

Accepted Answer

(A) 4

Answer

(B) 5

Answer

(C) 3

Answer

(D) 1

Question 57

Match List-I (Partial Derivative) with List-II (Thermodynamic Quantity). Choose the correct answer from the options given below:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 58

The correct order of the following complexes in terms of their crystal field stabilization energies is:

Accepted Answer

(B) $[Co(NH_3)_4]^{2+} < [Co(NH_3)_6]^{2+} < [Co(NH_3)_6]^{3+} < [Co(en)_3]^{3+}$

Answer

(A) $[Co(NH_3)_4]^{2+} < [Co(NH_3)_6]^{2+} < [Co(en)_3]^{3+} < [Co(NH_3)_6]^{3+}$

Answer

(C) $[Co(NH_3)_6]^{2+} < [Co(NH_3)_6]^{3+} < [Co(NH_3)_4]^{2+} < [Co(en)_3]^{3+}$

Answer

(D) $[Co(en)_3]^{3+} < [Co(NH_3)_6]^{3+} < [Co(NH_3)_6]^{2+} < [Co(NH_3)_4]^{2+}$

Question 59

Density of 3 M NaCl solution is 1.25 g/mL. The molality of the solution is:

Accepted Answer

(D) 2.79 m

Answer

(A) 1.79 m

Answer

(B) 2 m

Answer

(C) 3 m

Question 60

The molar solubility(s) of zirconium phosphate with molecular formula $(Zr^{4+})_3(PO_4^{3-})_4$ is given by relation:

Accepted Answer

(A) $\left(\frac{K_{sp}}{6912}\right)^{1/7}$

Answer

(B) $\left(\frac{K_{sp}}{5348}\right)^{1/6}$

Answer

(C) $\left(\frac{K_{sp}}{8435}\right)^{1/7}$

Answer

(D) $\left(\frac{K_{sp}}{9612}\right)^{1/3}$

Question 61

The most stable carbocation from the following is:

Accepted Answer

(A) (1)

Answer

(B) (2)

Answer

(C) (3)

Answer

(D) (4)

Question 62

Given below are two statements: Statement (I): An element in the extreme left of the periodic table forms acidic oxides. Statement (II): Acid is formed during the reaction between water and oxide of a reactive element present in the extreme right of the periodic table. In the light of the above statements, choose the correct answer from the options given below:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 63

Given below are two statements: Statement (I): A spectral line will be observed for a $2p_x 	o 2p_y$ transition. Statement (II): $2p_x$ and $2p_y$ are degenerate orbitals. In the light of the above statements, choose the correct answer from the options given below:

Accepted Answer

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

Answer

(A) Both Statement-I and Statement-II are true.

Answer

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

Answer

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

Question 64

Given below are two statements: Statement (I): Nitrogen, sulphur, halogen and phosphorus present in an organic compound are detected by Lassaigne's Test. Statement (II): The elements present in the compound are converted from covalent form into ionic form by fusing the compound with Magnesium in Lassaigne's test. In the light of the above statements, choose the correct answer 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

List-I (Compound)	List-II (Catalyst/Reagents)
A.see figure	I.NaOH (aqueous)
B.see figure	II. $H_2$ /Ni
C.see figure	III. $LiAlH_4$ , $H_2O$
D.see figure	IV.Sn, HCl

List-I (Partial Derivative)	List-II (Thermodynamic Quantity)
A. $\left(\frac{\partial G}{\partial T}\right)_P$	I. $C_P$
B. $\left(\frac{\partial H}{\partial T}\right)_P$	II. $-S$
C. $\left(\frac{\partial G}{\partial P}\right)_T$	III. $C_V$
D. $\left(\frac{\partial U}{\partial T}\right)_V$	IV.V

JEE Main 22 January 2025 Shift 2 Question Paper with Answers

Physics — JEE Main 22 January 2025 Shift 2

Chemistry — JEE Main 22 January 2025 Shift 2

Mathematics — JEE Main 22 January 2025 Shift 2

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