JEE Main 24 January 2025 Shift 2 Question Paper

Question 1

The equation of the chord, of the ellipse $\dfrac{x^2}{25}+\dfrac{y^2}{16}=1$, whose mid-point is $(3,1)$ is :

Accepted Answer

(A) $48x+25y=169$

Answer

(B) $4x+122y=134$

Answer

(C) $25x+101y=176$

Answer

(D) $5x+16y=31$

Question 2

The function $f:(-\infty,\infty)	o(-\infty,1)$, defined by $f(x)=\dfrac{2^x-2^{-x}}{2^x+2^{-x}}$ is :

Accepted Answer

(A) One-one but not onto

Answer

(B) Onto but not one-one

Answer

(C) Both one-one and onto

Answer

(D) Neither one-one nor onto

Question 3

If $\alpha>\beta>\gamma>0$, then the expression $\cot^{-1}\!\left\{\beta+\dfrac{1+\beta^2}{\alpha-\beta}\right\}+\cot^{-1}\!\left\{\gamma+\dfrac{1+\gamma^2}{\beta-\gamma}\right\}+\cot^{-1}\!\left\{\alpha+\dfrac{1+\alpha^2}{\gamma-\alpha}\right\}$ is equal to:

Accepted Answer

(D) $\pi$

Answer

(A) $\dfrac{\pi}{2}-(\alpha+\beta+\gamma)$

Answer

(B) $3\pi$

Answer

(C) $0$

Question 4

Let $f:(0,\infty)	o\mathbb{R}$ be a function differentiable at all points of its domain and satisfies the condition $x^2 f'(x)=2x f(x)+3$, with $f(1)=4$. Then $2f(2)$ is equal to:

Accepted Answer

(C) 39

Answer

(A) 29

Answer

(B) 19

Answer

(D) 23

Question 5

Let $A=\left\{x\in(0,\pi)-\left\{	frac{\pi}{2}ight\}:\log_{(2/\pi)}|\sin x|+\log_{(2/\pi)}|\cos x|=2ight\}$ and $B=\left\{x\ge 0:\sqrt{x}(\sqrt{x}-4)-3|\sqrt{x}-2|+6=0ight\}$. Then $n(A\cup B)$ is equal to:

Accepted Answer

(C) 8

Answer

(A) 4

Answer

(B) 2

Answer

(D) 6

Question 6

Let the position vectors of three vertices of a triangle be $4\vec p+\vec q-3\vec r$, $-5\vec p+\vec q+2\vec r$ and $2\vec p-\vec q+2\vec r$. If the position vectors of the orthocenter and the circumcenter of the triangle are $\dfrac{\vec p+\vec q+\vec r}{4}$ and $\alpha\vec p+\beta\vec q+\gamma\vec r$ respectively, then $\alpha+2\beta+5\gamma$ is equal to:

Accepted Answer

(A) 3

Answer

(B) 1

Answer

(C) 6

Answer

(D) 4

Question 7

Let $[x]$ denote the greatest integer function, and let $m$ and $n$ respectively be the numbers of the points, where the function $f(x)=[x]+|x-2|$, $-2<x<3$, is not continuous and not differentiable. Then $m+n$ is equal to:

Accepted Answer

(C) 8

Answer

(A) 6

Answer

(B) 9

Answer

(D) 7

Question 8

Let the points $\left(\dfrac{11}{2},\alpha\right)$ lie on or inside the triangle with sides $x+y=11$, $x+2y=16$ and $2x+3y=29$. Then the product of the smallest and the largest values of $\alpha$ is equal to:

Accepted Answer

(C) 33

Answer

(A) 22

Answer

(B) 44

Answer

(D) 55

Question 9

In an arithmetic progression, if $S_{40}=1030$ and $S_{12}=57$, then $S_{30}-S_{10}$ is equal to:

Accepted Answer

(B) 515

Answer

(A) 510

Answer

(C) 525

Answer

(D) 505

Question 10

If $7=5+\dfrac{1}{7}(5+\alpha)+\dfrac{1}{7^2}(5+2\alpha)+\dfrac{1}{7^3}(5+3\alpha)+\ldots\infty$, then the value of $\alpha$ is:

Accepted Answer

(C) 6

Answer

(A) 1

Answer

(B) $\dfrac{6}{7}$

Answer

(D) $\dfrac{1}{7}$

Question 11

If the system of equations $x+2y-3z=2,\ 2x+\lambda y+5z=5,\ 14x+3y+\mu z=33$ has infinitely many solutions, then $\lambda+\mu$ is equal to:

Accepted Answer

(D) 12

Answer

(A) 13

Answer

(B) 10

Answer

(C) 11

Question 12

Let $(2,3)$ be the largest open interval in which the function $f(x)=2\log_e(x-2)-x^2+ax+1$ is strictly increasing and $(b,c)$ be the largest open interval, in which the function $g(x)=(x-1)^3(x+2-a)^2$ is strictly decreasing, then $100(a+b-c)$ is equal to:

Accepted Answer

(B) 360

Answer

(A) 280

Answer

(C) 420

Answer

(D) 160

Question 13

Suppose A and B are the coefficients of $30^{	ext{th}}$ and $12^{	ext{th}}$ terms respectively in the binomial expansion of $(1+x)^{2n-1}$. If $2A=5B$, then $n$ is equal to:

Accepted Answer

(B) 21

Answer

(A) 22

Answer

(C) 20

Answer

(D) 19

Question 14

Let $\vec a=3\hat i-\hat j+2\hat k$, $\vec b=\vec a	imes(\hat i-3\hat k)$ and $\vec c=\vec b	imes\hat k$. Then the projection of $\vec c-2\hat j$ on $\vec a$ is:

Accepted Answer

(C) $2\sqrt{14}$

Answer

(A) $3\sqrt7$

Answer

(B) $\sqrt{14}$

Answer

(D) $2\sqrt7$

Question 15

For some $a,b$, let $f(x)=\begin{vmatrix} a+\dfrac{\sin x}{x} & 1 & b \ a & 1+\dfrac{\sin x}{x} & b \ a & 1 & b+\dfrac{\sin x}{x}\end{vmatrix}$, $x
eq 0$, $\displaystyle\lim_{x	o 0}f(x)=\lambda+\mu a+
u b$. Then $(\lambda+\mu+
u)^2$ is equal to:

Accepted Answer

(D) 16

Answer

(A) 25

Answer

(B) 9

Answer

(C) 36

Question 16

Group A consists of 7 boys and 3 girls, while group B consists of 6 boys and 5 girls. The number of ways, 4 boys and 4 girls can be invited for a picnic if 5 of them must be from group A and the remaining 3 from group B, is equal to:

Accepted Answer

(C) 8925

Answer

(A) 8575

Answer

(B) 9100

Answer

(D) 8750

Question 17

The area of the region enclosed by the curves $y=e^x$, $y=|e^x-1|$ and y-axis is:

Accepted Answer

(D) $1-\log_e 2$

Answer

(A) $1+\log_e 2$

Answer

(B) $2\log_e 2$

Answer

(C) $2\log_e 2-1$

Question 18

The number of real solution(s) of the equation $x^2+3x+2=\min\{|x-3|,|x+2|\}$ is :

Accepted Answer

(A) 2

Answer

(B) 0

Answer

(C) 3

Answer

(D) 1

Question 19

Let $A=[a_{ij}]$ be a square matrix of order 2 with entries 0 or 1. Let E be the event that A is an invertible matrix. Then the probability $P(E)$ is :

Accepted Answer

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

Answer

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

Answer

(B) $\dfrac{3}{16}$

Answer

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

Question 20

If the equation of the parabola with vertex $V\left(\dfrac{3}{2},3\right)$ and the directrix $x+2y=0$ is $\alpha x^2+\beta y^2-\gamma xy-30x-60y+225=0$, then $\alpha+\beta+\gamma$ is equal to:

Accepted Answer

(D) 9

Answer

(A) 6

Answer

(B) 8

Answer

(C) 7

Question 21

Number of functions $f:\{1,2,\ldots,100\}	o\{0,1\}$, that assign 1 to exactly one of the positive integers less than or equal to 98, is equal to __________.

Accepted Answer

392

Question 22

Let P be the image of the point $Q(7,-2,5)$ in the line $L:\dfrac{x-1}{2}=\dfrac{y+1}{3}=\dfrac{z}{4}$ and $R(5,p,q)$ be a point on L. Then the square of the area of $	riangle PQR$ is __________.

Accepted Answer

957

Question 23

Let $y=y(x)$ be the solution of the differential equation $2\cos x\dfrac{dy}{dx}=\sin 2x-4y\sin x$, $x\in\left(0,\dfrac{\pi}{2}\right)$. If $y\left(\dfrac{\pi}{3}\right)=0$, then $y\left(\dfrac{\pi}{4}\right)+y'\left(\dfrac{\pi}{4}\right)$ is equal to __________.

Accepted Answer

1

Question 24

Let $H_1:\dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1$ and $H_2:-\dfrac{x^2}{A^2}+\dfrac{y^2}{B^2}=1$ be two hyperbolas having length of latus rectums $15\sqrt2$ and $12\sqrt5$ respectively. Let their eccentricities be $e_1=\sqrt{\dfrac{5}{2}}$ and $e_2$ respectively. If the product of the lengths of their transverse axes is $100\sqrt{10}$, then $25e_2^2$ is equal to __________.

Accepted Answer

55

Question 25

If $\displaystyle\int\dfrac{2x^2+5x+9}{\sqrt{x^2+x+1}}\,dx=x\sqrt{x^2+x+1}+\alpha\sqrt{x^2+x+1}+\beta\log_e\left|x+\dfrac12+\sqrt{x^2+x+1}\right|+C$, where C is the constant of integration, then $\alpha+2\beta$ is equal to __________.

Accepted Answer

16

Question 26

Young's double slit interference apparatus is immersed in a liquid of refractive index 1.44. It has slit separation of 1.5 mm. The slits are illuminated by a parallel beam of light whose wavelength in air is 690 nm. The fringe-width recorded behind the plane of slits at a distance of 0.72 m, will be :

Accepted Answer

(A) 0.23 mm

Answer

(B) 0.33 mm

Answer

(C) 0.63 mm

Answer

(D) 0.46 mm

Question 27

Arrange the following in the ascending order of wavelength $(\lambda)$: (A) Microwaves $(\lambda_1)$ (B) Ultraviolet rays $(\lambda_2)$ (C) Infrared rays $(\lambda_3)$ (D) X-rays $(\lambda_4)$. Choose the most appropriate answer from the options given below :

Accepted Answer

(C) $\lambda_4<\lambda_2<\lambda_3<\lambda_1$

Answer

(A) $\lambda_1<\lambda_3<\lambda_2<\lambda_4$

Answer

(B) $\lambda_3<\lambda_4<\lambda_2<\lambda_1$

Answer

(D) $\lambda_4<\lambda_3<\lambda_1<\lambda_2$

Question 28

Given below are two statements.
Assertion (A) : An electron in a certain region of uniform magnetic field is moving with constant velocity in a straight line path.
Reason (R) : The magnetic field in that region is along the direction of velocity of the electron.
In the light of the above statements, choose the correct answer from the options given below :

Accepted Answer

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

Answer

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

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 29

A solid sphere is rolling without slipping on a horizontal plane. The ratio of the linear kinetic energy of the centre of mass of the sphere and rotational kinetic energy is:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 30

A long straight wire of a circular cross-section with radius "a" carries a steady current I. The current I is uniformly distributed across this cross-section. The plot of magnitude of magnetic field B with distance r from the centre of the wire is given by (choose the correct graph):

Accepted Answer

(A) (1)

Answer

(B) (2)

Answer

(C) (3)

Answer

(D) (4)

Question 31

Given below are two statements.
Assertion (A) : In an insulated container, a gas is adiabatically shrunk to half of its initial volume. The temperature of the gas decreases.
Reason (R) : Free expansion of an ideal gas is an irreversible and an adiabatic process. In the light of the above statement, choose the correct answer from the options given below :

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 32

In the first configuration (1) as shown in the figure, four identical charges $(q_0)$ are kept at the corners A, B, C and D of a square of side length "a". In the second configuration (2), the same charges are shifted to mid points G, E, F and H, of the sides of the square. If $K=\dfrac{1}{4\pi\varepsilon_0}$, the difference between the potential energy of configuration (2) and (1) is given by:

Accepted Answer

(D) $\dfrac{Kq_0^2}{a}\left(3\sqrt2-2\right)$

Answer

(A) $\dfrac{Kq_0^2}{a}\left(4\sqrt2-2\right)$

Answer

(B) $\dfrac{Kq_0^2}{a}\left(3-\sqrt2\right)$

Answer

(C) $\dfrac{Kq_0^2}{a}\left(4-2\sqrt2\right)$

Question 33

The position vector of a moving body at any instant of time is given as $\vec r=(5t^2\hat i-5t\hat j)$ m. The magnitude and direction of velocity at $t=2$ s, is,

Accepted Answer

(C) $5\sqrt{17}$ m/s, making an angle of $	an^{-1}4$ with $-$ve Y axis

Answer

(A) $5\sqrt{15}$ m/s, making an angle of $	an^{-1}4$ with $-$ve Y axis

Answer

(B) $5\sqrt{15}$ m/s, making an angle of $	an^{-1}4$ with $+$ve X axis

Answer

(D) $5\sqrt{17}$ m/s, making an angle of $	an^{-1}4$ with $+$ve X axis

Question 34

A solid sphere and a hollow sphere of the same mass and of same radius are rolled on an inclined plane. Let the time taken to reach the bottom by the solid sphere and the hollow sphere be $t_1$ and $t_2$, respectively, then

Accepted Answer

(A) $t_1<t_2$

Answer

(B) $t_1=t_2$

Answer

(C) $t_1=2t_2$

Answer

(D) $t_1>t_2$

Question 35

Which of the following figure represents the relation between Celsius and Fahrenheit temperatures? (Choose the correct C vs F graph.)

Accepted Answer

(B) (2)

Answer

(A) (1)

Answer

(C) (3)

Answer

(D) (4)

Question 36

N equally spaced charges each of value q, are placed on a circle of radius R. The circle rotates about its axis with an angular velocity $\omega$ as shown in the figure. A bigger Amperian loop B encloses the whole circle where as a smaller Amperian loop A encloses a small segment. The difference between enclosed currents, $I_A-I_B$, for the given Amperian loops is :

Accepted Answer

(C) $\dfrac{N}{2\pi}q\omega$

Answer

(A) $\dfrac{N^2}{2\pi}q\omega$

Answer

(B) $\dfrac{2\pi}{N}q\omega$

Answer

(D) $\dfrac{N}{\pi}q\omega$

Question 37

In photoelectric effect, the stopping potential $(V_0)$ v/s frequency $(
u)$ curve is plotted. ($h$ is the Planck's constant and $\phi_0$ is work function of metal) (A) $V_0$ v/s $
u$ is linear. (B) The slope of $V_0$ v/s $
u$ curve $=\dfrac{\phi_0}{h}$. (C) $h$ is constant is related to the slope of $V_0$ v/s $
u$ line. (D) The value of electric charge of electron is not required to determine $h$ using the $V_0$ v/s $
u$ curve. (E) The work function can be estimated without knowing the value of $h$. Choose the correct answer from the options given below :

Accepted Answer

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

Answer

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

Answer

(B) (C) and (D) only

Answer

(D) (D) and (E) only

Question 38

The magnitude of heat exchanged by a system for the given cyclic process ABCA (as shown in figure, a semicircular loop in the P-V plane with P in kPa and V in cc) is (in SI unit):

Accepted Answer

(B) $5\pi$

Answer

(A) $10\pi$

Answer

(C) zero

Answer

(D) $40\pi$

Question 39

A photograph of a landscape is captured by a drone camera at a height of 18 km. The size of the camera film is 2 cm $	imes$ 2 cm and the area of the landscape photographed is 400 km$^2$. The focal length of the lens in the drone camera is :

Accepted Answer

(A) 1.8 cm

Answer

(B) 2.8 cm

Answer

(C) 2.5 cm

Answer

(D) 0.9 cm

Question 40

The output of the circuit (shown in the figure) is low (zero) for : (A) X=0, Y=0 (B) X=0, Y=1 (C) X=1, Y=0 (D) X=1, Y=1. Choose the correct answer from the options given below :

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 41

The temperature of a body in air falls from $40^\circ$C to $24^\circ$C in 4 minutes. The temperature of the air is $16^\circ$C. The temperature of the body in the next 4 minutes will be :

Accepted Answer

(C) $\dfrac{56}{3}\,^\circ$C

Answer

(A) $\dfrac{14}{3}\,^\circ$C

Answer

(B) $\dfrac{28}{3}\,^\circ$C

Answer

(D) $\dfrac{42}{3}\,^\circ$C

Question 42

The energy E and momentum p of a moving body of mass m are related by some equation. Given that c represents the speed of light, identify the correct equation.

Accepted Answer

(D) $E^2=p^2c^2+m^2c^4$

Answer

(A) $E^2=pc^2+m^2c^4$

Answer

(B) $E^2=pc^2+m^2c^2$

Answer

(C) $E^2=p^2c^2+m^2c^2$

Question 43

A small uncharged conducting sphere is placed in contact with an identical sphere but having $4	imes10^{-8}$ C charge and then removed to a distance such that the force of repulsion between them is $9	imes10^{-3}$ N. The distance between them is (Take $\dfrac{1}{4\pi\varepsilon_0}$ as $9	imes10^9$ in SI units):

Accepted Answer

(A) 2 cm

Answer

(B) 3 cm

Answer

(C) 4 cm

Answer

(D) 1 cm

Question 44

A particle oscillates along the x-axis according to the law, $x(t)=x_0\sin^2\left(\dfrac{t}{2}\right)$ where $x_0=1$ m. The kinetic energy (K) of the particle as a function of x is correctly represented by the graph:

Accepted Answer

(A) (1)

Answer

(B) (2)

Answer

(C) (3)

Answer

(D) (4)

Question 45

In a Young's double slit experiment, three polarizers are kept as shown in the figure. The transmission axes of $P_1$ and $P_2$ are orthogonal to each other. The polarizer $P_3$ covers both the slits with its transmission axis at $45^\circ$ to those of $P_1$ and $P_2$. An unpolarized light of wavelength $\lambda$ and intensity $I_0$ is incident on $P_1$ and $P_2$. The intensity at a point after $P_3$ where the path difference between the light waves from $s_1$ and $s_2$ is $\dfrac{\lambda}{3}$, is

Accepted Answer

(B) $\dfrac{I_0}{4}$

Answer

(A) $\dfrac{I_0}{2}$

Answer

(C) $I_0$

Answer

(D) $\dfrac{I_0}{3}$

Question 46

A tightly wound long solenoid carries a current of 1.5 A. An electron is executing uniform circular motion inside the solenoid with a time period of 75 ns. The number of turns per metre in the solenoid is __________. [Take mass of electron $=9	imes10^{-31}$ kg, charge of electron $|q_e|=1.6	imes10^{-19}$ C, $\mu_0=4\pi	imes10^{-7}\ \mathrm{N/A^2}$, $1$ ns $=10^{-9}$ s]

Accepted Answer

250

Question 47

A string of length L is fixed at one end and carries a mass of M at the other end. The mass makes $\left(\dfrac{3}{\pi}\right)$ rotations per second about the vertical axis passing through end of the string as shown. The tension in the string is __________ ML.

Accepted Answer

36

Question 48

The ratio of the power of a light source $S_1$ to the light source $S_2$ is 2. $S_1$ is emitting $2	imes10^{15}$ photons per second at 600 nm. If the wavelength of the source $S_2$ is 300 nm, then the number of photons per second emitted by $S_2$ is __________ $	imes10^{14}$.

Accepted Answer

5

Question 49

The increase in pressure required to decrease the volume of a water sample by 0.2% is $P	imes10^5\ \mathrm{Nm^{-2}}$. Bulk modulus of water is $2.15	imes10^9\ \mathrm{Nm^{-2}}$. The value of P is __________.

Accepted Answer

43

Question 50

Acceleration due to gravity on the surface of earth is "g". If the diameter of earth is reduced to one third of its original value and mass remains unchanged, then the acceleration due to gravity on the surface of the earth is __________ g.

Accepted Answer

9

Question 51

Based on the data given below: $E^0_{Cr_2O_7^{2-}/Cr^{3+}}=1.33$ V, $E^0_{Cl_2/Cl^-}=1.36$ V, $E^0_{MnO_4^-/Mn^{2+}}=1.51$ V, $E^0_{Cr^{3+}/Cr}=-0.74$ V. The strongest reducing agent is :

Accepted Answer

(B) $Cr$

Answer

(A) $Mn^{2+}$

Answer

(C) $MnO_4^-$

Answer

(D) $Cl^-$

Question 52

Given below are two statements: Statement (I): A plot of half-life $t_{1/2}$ versus initial concentration $[R]_0$ is a horizontal straight line — is valid for first order reaction. Statement (II): A plot of $\log\dfrac{[R]}{[R]_0}$ versus time is a straight line with slope $\dfrac{k}{2.303}$ — is valid for first order reaction. In the light of the above statements, choose the correct answer from the options given below :

Accepted Answer

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

Answer

(A) Both Statement I and Statement II are false

Answer

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

Answer

(C) Both Statement I and Statement II are true

Question 53

For the reaction in which aniline is converted to o-bromoaniline (2-bromoaniline) as the major product, the correct order of set of reagents for the above conversion is :

Accepted Answer

(B) $H_2SO_4,\ Ac_2O,\ Br_2,\ H_2O(\Delta),\ NaOH$

Answer

(A) $Br_2\,|\,FeBr_3,\ H_2O(\Delta),\ NaOH$

Answer

(C) $Ac_2O,\ Br_2,\ H_2O(\Delta),\ NaOH$

Answer

(D) $Ac_2O,\ H_2SO_4,\ Br_2,\ NaOH$

Question 54

For hydrogen atom, the orbital/s with lowest energy is/are : (A) $4s$ (B) $3p_x$ (C) $3d_{x^2-y^2}$ (D) $3d_{z^2}$ (E) $4p_z$. Choose the correct answer from the options given below :

Accepted Answer

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

Answer

(A) (A) and (E) only

Answer

(B) (B) only

Answer

(C) (A) only

Question 55

In the given structure $CH_3	ext{-}CO	ext{-}CH{=}CH	ext{-}CH_2	ext{-}C{\equiv}C	ext{-}CH{=}CH	ext{-}C{\equiv}N$, the number of sp and sp$^2$ hybridized carbon atoms present respectively are :

Accepted Answer

(B) 3 and 5

Answer

(A) 3 and 6

Answer

(C) 4 and 6

Answer

(D) 4 and 5

Question 56

Which of the following mixing of 1M base and 1M acid leads to the largest increase in temperature?

Accepted Answer

(A) 30 mL HCl and 30 mL NaOH

Answer

(B) 30 mL $CH_3COOH$ and 30 mL NaOH

Answer

(C) 50 mL HCl and 20 mL NaOH

Answer

(D) 45 mL $CH_3COOH$ and 25 mL NaOH

Question 57

Given below are two statements: Statement (I): Experimentally determined oxygen-oxygen bond lengths in O$_3$ are found to be same and the bond length is greater than that of a O=O (double bond) but less than that of a single bond (O–O). Statement (II): The strong lone pair-lone pair repulsion between oxygen atoms is solely responsible for the fact about the bond length in ozone. In the light of the above statements, choose the correct answer from the options given below :

Accepted Answer

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

Answer

(B) Statement I is true and Statement II is true

Answer

(C) Both Statement I and Statement II are false

Answer

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

Question 58

Find the compound "A" from the following reaction sequences. $A\xrightarrow{	ext{aqua-regia}}B\xrightarrow{	ext{(1) }KNO_3/NH_4OH,\ 	ext{(2) AcOH}}$ yellow ppt ($K_3[Co(NO_2)_6]\downarrow$ yellow).

Accepted Answer

(B) CoS

Answer

(A) ZnS

Answer

(C) MnS

Answer

(D) NiS

Question 59

For the reaction, $H_2(g) + I_2(g) \rightleftharpoons 2HI(g)$, the attainment of equilibrium is predicted correctly by:

Accepted Answer

(B) (2)

Answer

(A) (1)

Answer

(C) (3)

Answer

(D) (4)

Question 60

Match List-I (Transition metal ion) with List-II (Spin only magnetic moment B.M.). Choose the correct answer from the options given below:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 61

The elemental composition of a compound is 54.2% C, 9.2% H and 36.6% O. If the molar mass of the compound is 132 g mol$^{-1}$, the molecular formula of the compound is : [Given : The relative atomic mass of C : H : O = 12 : 1 : 16]

Accepted Answer

(C) $C_6H_{12}O_3$

Answer

(A) $C_4H_9O_3$

Answer

(B) $C_6H_{12}O_6$

Answer

(D) $C_4H_8O_2$

Question 62

When Ethane-1,2-diamine is added progressively to an aqueous solution of Nickel (II) chloride, the sequence of colour change observed will be :

Accepted Answer

(C) Green $	o$ Pale Blue $	o$ Violet

Answer

(A) Pale Blue $	o$ Blue $	o$ Green $	o$ Violet

Answer

(B) Pale Blue $	o$ Violet $	o$ Violet $	o$ Green

Answer

(D) Violet $	o$ Blue $	o$ Pale Blue $	o$ Green

Question 63

The conditions and consequence that favours the $t_{2g}^4\,e_g^0$ configuration in a metal complex are :

Accepted Answer

(C) strong field ligand, low spin complex

Answer

(A) weak field ligand, high spin complex

Answer

(B) strong field ligand, high spin complex

Answer

(D) weak field ligand, low spin complex

Question 64

Identify correct statement/s : (A) $-OCH_3$ and $-NHCOCH_3$ are activating group (B) $-CN$ and $-OH$ are meta directing group (C) $-CN$ and $-SO_3H$ are meta directing group (D) Activating groups act as ortho- and para- directing groups (E) Halides are activating groups. Choose the correct answer from the options given below :

Accepted Answer

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

Answer

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

Answer

(C) (A) only

Answer

(D) (A) and (C) only

List-I (Transition metal ion)	List-II (Spin only magnetic moment B.M.)
A. $Ti^{3+}$	I.3.87
B. $V^{2+}$	II.0.00
C. $Ni^{2+}$	III.1.73
D. $Sc^{3+}$	IV.2.84

List-I (Aldehyde Synthesis)	List-II (Name Reaction)
A. $RCN\xrightarrow{\text{(i) }SnCl_2,3HCl\ \text{(ii) }H_2O}RCHO$	I.Etard reaction
B. $C_6H_5COCl\xrightarrow{H_2,\ Pd\text{-}BaSO_4}C_6H_5CHO$	II.Gattermann-Koch reaction
C. $C_6H_5CH_3\xrightarrow{\text{(i) }CrO_2Cl_2,CS_2\ \text{(ii) }H_2O}C_6H_5CHO$	III.Rosenmund reduction
D. $C_6H_6\xrightarrow{\text{(i) }CO,HCl\ \text{(ii) anhydrous }AlCl_3/CuCl}C_6H_5CHO$	IV.Stephen reaction

List-I (Nucleobase)	List-II (Structure)
A.Adenine	I.see figure
B.Cytosine	II.see figure
C.Thymine	III.see figure
D.Uracil	IV.see figure

JEE Main 24 January 2025 Shift 2 Question Paper with Answers

Physics — JEE Main 24 January 2025 Shift 2

Chemistry — JEE Main 24 January 2025 Shift 2

Mathematics — JEE Main 24 January 2025 Shift 2

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