JEE Main 2025 — 22 Jan Shift 2 (Previous Year Paper)

Let E: $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$, $a>b$ and H: $\frac{x^2}{A^2}-\frac{y^2}{B^2}=1$. 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 $\frac{1}{3}$, then the sum of the lengths of their latus rectums is equal to :

1. A.10
2. B.8✓
3. C.9
4. D.7

Correct answer: B

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

1. A.$3\sqrt{5}$✓
2. B.6
3. C.$4\sqrt{3}$
4. D.$5\sqrt{2}$

Correct answer: A

Let $\vec{a}$ and $\vec{b}$ be two unit vectors such that the angle between them is $\frac{\pi}{3}$. 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 :

1. A.0✓
2. B.2
3. C.1
4. D.3

Correct answer: A

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

1. A.2 and 3✓
2. B.1 and 3
3. C.2 and 2
4. D.3 and 2

Correct answer: A

If $\lim_{x\to\infty}\left(\left(\frac{e}{1-e}\right)\left(\frac{1}{e}-\frac{x}{1+x}\right)\right)^x=\alpha$, then the value of $\frac{\log_e\alpha}{1+\log_e\alpha}$ equals :

1. A.$e^{-2}$
2. B.$e^2$
3. C.$e^{-1}$
4. D.$e$✓

Correct answer: D

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 $\triangle PQR$ is equal to :

1. A.136✓
2. B.148
3. C.140
4. D.144

Correct answer: A

Suppose that the number of terms in an A.P. is 2k, $k\in\mathbf{N}$. 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 :

1. A.8
2. B.4
3. C.6
4. D.5✓

Correct answer: D

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

1. A.$\frac{\pi}{6}\sqrt{\frac{e}{3}}$✓
2. B.$\frac{\pi}{6}\sqrt{\frac{e}{2}}$
3. C.$\frac{\pi}{4}\sqrt{\frac{e}{3}}$
4. D.$\frac{\pi}{4}\sqrt{\frac{e}{2}}$

Correct answer: A

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

1. A.163
2. B.151✓
3. C.127
4. D.139

Correct answer: B

For a $3\times3$ matrix M, let trace (M) denote the sum of all the diagonal elements of M. Let A be a $3\times3$ matrix such that $|A|=\frac{1}{2}$ and trace (A) = 3. If B = adj(adj(2A)), then the value of $|B|$ + trace (B) equals :

1. A.174
2. B.56
3. C.132
4. D.280✓

Correct answer: D

Let P$(4, 4\sqrt{3})$ 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 :

1. A.$\frac{263\sqrt{3}}{8}$
2. B.$17\sqrt{3}$
3. C.$\frac{34\sqrt{3}}{3}$
4. D.$\frac{343\sqrt{3}}{8}$✓

Correct answer: D

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 $\frac{P(\bar{A}\cup\bar{B})}{P(\bar{A}\cap\bar{B})}$ is :

1. A.$\frac{7}{4}$
2. B.$\frac{5}{3}$
3. C.$\frac{4}{3}$
4. D.$\frac{9}{4}$✓

Correct answer: D

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 :

1. A.4
2. B.3
3. C.8
4. D.5✓

Correct answer: D

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

1. A.$\frac{\pi}{2}$
2. B.$\pi$✓
3. C.$\frac{5\pi}{6}$
4. D.$4\pi$

Correct answer: B

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 :

1. A.120
2. B.72
3. C.144✓
4. D.96

Correct answer: C

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

1. A.$\frac{8}{3}$✓
2. B.5
3. C.$\frac{4}{3}$
4. D.8

Correct answer: A

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

1. A.$1+\frac{\pi}{4}$
2. B.$1+\frac{\pi}{6}$
3. C.$1+\frac{\pi}{3}$
4. D.$1+\frac{\pi}{2}$✓

Correct answer: D

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

1. A.$e^{\pi/12}$
2. B.$e^{\pi/4}$
3. C.$e^{\pi/3}$
4. D.$e^{\pi/6}$✓

Correct answer: D

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

1. A.16✓
2. B.22
3. C.9
4. D.12

Correct answer: A

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

1. A.27
2. B.25✓
3. C.24
4. D.17

Correct answer: B

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 ______.

Correct answer: 145

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

Correct answer: 27

If $\sum_{r=1}^{30}\frac{r^2\left({}^{30}C_r\right)^2}{{}^{30}C_{r-1}}=\alpha\times2^{29}$, then $\alpha$ is equal to ______.

Correct answer: 465

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 ______.

Correct answer: 28

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 ______.

Correct answer: 3

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

1. A.$I_0$
2. B.$\frac{I_0}{2}$✓
3. C.$2I_0$
4. D.$\frac{I_0}{\sqrt{2}}$

Correct answer: B

A 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

1. A.4 m/s
2. B.6 m/s
3. C.8 m/s✓
4. D.2 m/s

Correct answer: C

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,

1. A.$[F]=[CM^{-2}L^{-2}T^{-2}]$
2. B.$[F]=[C^2M^{-1}L^{-2}T^2]$✓
3. C.$[F]=[CM^{-1}L^{-2}T^2]$
4. D.$[F]=[C^2M^{-2}L^2T^2]$

Correct answer: B

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)

1. A.$\frac{Mg}{2}$✓
2. B.Mg
3. C.2 Mg
4. D.$\frac{3}{2}$ Mg

Correct answer: A

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

1. A.$\hat{i}-\hat{j}+\hat{k}$
2. B.$\hat{j}+\hat{k}$
3. C.$\hat{i}+\hat{k}$
4. D.$\hat{i}-\hat{k}$✓

Correct answer: D

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.]

1. A.137.5 nm✓
2. B.275 nm
3. C.68.7 nm
4. D.94.8 nm

Correct answer: A

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

1. A.$\sqrt{\frac{h}{\pi eB}}$✓
2. B.$\sqrt{\frac{h}{2\pi eB}}$
3. C.$\sqrt{\frac{4h}{\pi eB}}$
4. D.$\sqrt{\frac{2h}{\pi eB}}$

Correct answer: A

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

1. A.5 J
2. B.zero
3. C.20 J
4. D.15 J✓

Correct answer: D

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.

1. A.$\frac{1}{2}$✓
2. B.$\frac{1}{3}$
3. C.2
4. D.0

Correct answer: A

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)

1. A.$\gamma_2<\gamma_1$✓
2. B.$\gamma_2>\gamma_1$
3. C.$2\gamma_2=\gamma_1$
4. D.$\gamma_2=\gamma_1$

Correct answer: A

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 magnate field, the plot of magnitude of induced emf ($\varepsilon$) with time (t) is given by

1. A.Graph: $\varepsilon$ increases linearly from zero with t
2. B.Graph: $\varepsilon$ decreases (decaying curve) with t
3. C.Graph: $\varepsilon$ constant (horizontal line) with t✓
4. D.Graph: $\varepsilon$ increases non-linearly (upward curving) with t

Correct answer: C

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 at Earth and the other planet. In the light of the above statements, choose the correct answer from the options given below :

1. A.Both (A) and (R) are true and (R) is the correct explanation of (A)
2. B.(A) is false but (R) is true
3. C.Both (A) and (R) are true but (R) is NOT the correct explanation of (A)✓
4. D.(A) is true but (R) is false

Correct answer: C

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

1. A.4D
2. B.2D✓
3. C.D
4. D.8D

Correct answer: B

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

1. A.zero and $\frac{E_0}{8}$
2. B.$\frac{V_0}{2}$ and $\frac{E_0}{16}$
3. C.zero and $\frac{E_0}{16}$✓
4. D.$V_0$ and $\frac{E_0}{4}$

Correct answer: C

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 options given below :

1. A.(D) and (A) Only
2. B.(A) and (B) Only✓
3. C.(C) and (D) Only
4. D.(B) and (C) Only

Correct answer: B

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 the above statements, choose the correct answer from the options given below :

1. A.Both (A) and (R) are true but (R) is NOT the correct explanation of (A)
2. B.(A) is true but (R) is false
3. C.Both (A) and (R) are true and (R) is the correct explanation of (A)
4. D.(A) is false but (R) is true✓

Correct answer: D

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 $m/s^2$)

1. A.$\frac{2+\sqrt{2}}{3}$
2. B.$\frac{3+\sqrt{3}}{2}$✓
3. C.$\frac{2+\sqrt{3}}{3}$
4. D.$\frac{3-\sqrt{2}}{2}$

Correct answer: B

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)

1. A.3 eV
2. B.2 eV
3. C.5 eV✓
4. D.6 eV

Correct answer: C

The maximum percentage error in the measurment 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]

1. A.7
2. B.4
3. C.8
4. D.5✓

Correct answer: D

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 ______.

Correct answer: 1

The net current flowing in the given circuit is ______ A.

Correct answer: 1

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 $x\times10^{-5}$ T. The value of x is ______. Take permeability of free space as $\mu_0=4\pi\times10^{-7}$ SI units.

Correct answer: 1

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 $A_0=3.2\ cm^2$ 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 $A_0$ is ______ mA.

Correct answer: 1200

A proton is moving undeflected in a region of crossed electric and magnetic fields at a constant speed of $2\times10^5\ ms^{-1}$. When the electric field is switched off, the proton moves along a circular path of radius 2 cm. The magnitude of electric field is $x\times10^4$ N/C. The value of x is ______. Take the mass of the proton = $1.6\times10^{-27}$ kg.

Correct answer: 2

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

1. A.5
2. B.4✓
3. C.3
4. D.6

Correct answer: B

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 :

1. A.Statement I is true but Statement II is false
2. B.Both Statement I and Statement II are true
3. C.Both Statement I and Statement II are false
4. D.Statement I is false but Statement II is true✓

Correct answer: D

Identify the number of structure/s from the following which can be correlated to D-glyceraldehyde. (A) Fischer chain: CHO / C–OH (right) / C–OH (right) / $CH_2$OH. (B) CHO / C–OH (right) / HO–C (left) / C–OH (right) / $CH_2$OH. (C) CHO / C–OH (right) / HO–C (left) / HO–C (left) / $CH_2$OH. (D) drawn upside down: $CH_2$OH (top) / HO–C (left) / C–OH (right) / HO–C (left) / CHO (bottom).

1. A.four
2. B.two
3. C.three✓
4. D.one

Correct answer: C

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 :

1. A.Statement I is true but Statement II is false✓
2. B.Statement I is false but Statement II is true
3. C.Both Statement I and Statement II are true
4. D.Both Statement I and Statement II are false

Correct answer: A

Given below are two statements : Statement (I) : A spectral line will be observed for a $2p_x\to2p_y$ 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 :

1. A.Statement I is true but Statement II is false
2. B.Statement I is false but Statement II is true✓
3. C.Both Statement I and Statement II are false
4. D.Both Statement I and Statement II are true

Correct answer: B

Consider the given figure and choose the correct option :

1. A.Activation energy of backward reaction is $E_1$ and product is more stable than reactant.
2. B.Activation energy of both forward and backward reaction is $E_1+E_2$ and reactant is more stable than product.
3. C.Activation energy of forward reaction is $E_1+E_2$ and product is more stable than reactant.
4. D.Activation energy of forward reaction is $E_1+E_2$ and product is less stable than reactant.✓

Correct answer: D

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

1. A.$\left(\frac{K_{sp}}{9612}\right)^{1/3}$
2. B.$\left(\frac{K_{sp}}{8435}\right)^{1/7}$
3. C.$\left(\frac{K_{sp}}{5348}\right)^{1/6}$
4. D.$\left(\frac{K_{sp}}{6912}\right)^{1/7}$✓

Correct answer: D

The most stable carbocation from the following is :

1. A.p-Methoxybenzyl cation ($p$-MeO–$C_6H_4$–$\overset{+}{C}H_2$)✓
2. B.m-Methoxybenzyl cation ($m$-MeO–$C_6H_4$–$\overset{+}{C}H_2$)
3. C.Benzyl cation ($C_6H_5$–$\overset{+}{C}H_2$)
4. D.p-Methylbenzyl cation ($p$-$H_3C$–$C_6H_4$–$\overset{+}{C}H_2$)

Correct answer: A

Arrange the following compounds in increasing order of their dipole moment : HBr, $H_2S$, $NF_3$ and $CHCl_3$

1. A.$HBr<H_2S<NF_3<CHCl_3$
2. B.$NF_3<HBr<H_2S<CHCl_3$✓
3. C.$CHCl_3<NF_3<HBr<H_2S$
4. D.$H_2S<HBr<NF_3<CHCl_3$

Correct answer: B

Identify the homoleptic complex(es) that is/are low spin. (A) $[Fe(CN)_5NO]^{2-}$ (B) $[CoF_6]^{3-}$ (C) $[Fe(CN)_6]^{4-}$ (D) $[Co(NH_3)_6]^{3+}$ (E) $[Cr(H_2O)_6]^{2+}$. Choose the correct answer from the options given below :

1. A.(C) and (D) only✓
2. B.(C) only
3. C.(A) and (C) only
4. D.(B) and (E) only

Correct answer: A

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

1. A.$[Co(NH_3)_4]^{2+}<[Co(NH_3)_6]^{2+}<[Co(NH_3)_6]^{3+}<[Co(en)_3]^{3+}$✓
2. B.$[Co(NH_3)_4]^{2+}<[Co(NH_3)_6]^{2+}<[Co(en)_3]^{3+}<[Co(NH_3)_6]^{3+}$
3. C.$[Co(NH_3)_6]^{2+}<[Co(NH_3)_6]^{3+}<[Co(NH_3)_4]^{2+}<[Co(en)_3]^{3+}$
4. D.$[Co(en)_3]^{3+}<[Co(NH_3)_6]^{3+}<[Co(NH_3)_6]^{2+}<[Co(NH_3)_4]^{2+}$

Correct answer: A

Match List - I with List - II. List - I (Partial Derivatives): (A) $\left(\frac{\partial G}{\partial T}\right)_P$ (B) $\left(\frac{\partial H}{\partial T}\right)_P$ (C) $\left(\frac{\partial G}{\partial P}\right)_T$ (D) $\left(\frac{\partial U}{\partial T}\right)_V$. List - II (Thermodynamic Quantity): (I) $C_p$ (II) $-S$ (III) $C_v$ (IV) V. Choose the correct answer from the options given below :

1. A.(A)-(I), (B)-(II), (C)-(IV), (D)-(III)
2. B.(A)-(II), (B)-(I), (C)-(IV), (D)-(III)✓
3. C.(A)-(II), (B)-(III), (C)-(I), (D)-(IV)
4. D.(A)-(II), (B)-(I), (C)-(III), (D)-(IV)

Correct answer: B

Given below are two statements : Statement (I) : Corrosion is an electrochemical phenomenon in which pure metal acts as an anode and impure metal as a cathode. Statement (II) : The rate of corrosion is more in alkaline medium than in acidic medium. In the light of the above statements, choose the correct answer from the options given below :

1. A.Both Statement I and Statement II are false
2. B.Statement I is true but Statement II is false✓
3. C.Both Statement I and Statement II are true
4. D.Statement I is false but Statement II is true

Correct answer: B

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

1. A.2 m
2. B.3 m
3. C.1.79 m
4. D.2.79 m✓

Correct answer: D

Match the Compounds (List - I) with the appropriate Catalyst/Reagents (List - II) for their reduction into corresponding amines. List - I (Compounds): (A) $R-CO-NH_2$ (B) Nitrobenzene (C) $R-C\equiv N$ (D) N-alkylphthalimide. List - II (Catalyst/Reagents): (I) NaOH (aqueous) (II) $H_2$/Ni (III) $LiAlH_4$, $H_2O$ (IV) Sn, HCl. Choose the correct answer from the options given below :

1. A.(A)-(III), (B)-(II), (C)-(IV), (D)-(I)
2. B.(A)-(II), (B)-(I), (C)-(III), (D)-(IV)
3. C.(A)-(III), (B)-(IV), (C)-(II), (D)-(I)✓
4. D.(A)-(II), (B)-(IV), (C)-(III), (D)-(I)

Correct answer: C

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

1. A.1
2. B.4✓
3. C.5
4. D.3

Correct answer: B

The species which does not undergo disproportionation reaction is :

1. A.$ClO_2^-$
2. B.$ClO^-$
3. C.$ClO_3^-$
4. D.$ClO_4^-$✓

Correct answer: D

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

1. A.1-Bromo-2-(sec-butyl)cyclohexane (Br on the ring carbon adjacent to the substituent)
2. B.2-Bromo-3-cyclohexylbutane (Br on the side-chain CH next to the branching CH)
3. C.1-Bromo-1-(sec-butyl)cyclohexane (Br on the ring carbon bearing the side chain)
4. D.2-Bromo-2-cyclohexylbutane (Br on the side-chain tertiary carbon)✓

Correct answer: D

The alkane from below having two secondary hydrogens is :

1. A.2,2,4,5-Tetramethylheptane
2. B.4-Ethyl-3,4-dimethyloctane
3. C.2,2,3,3-Tetramethylpentane✓
4. D.2,2,4,4-Tetramethylhexane

Correct answer: C

Toluene (excess) $\xrightarrow{\text{(i) } CrO_2Cl_2, CS_2;\ \text{(ii) } H_3O^+;\ \text{(iii) } NaHSO_3}$ Filter $\to$ Residue (A). Residue (A) + HCl(dil) $\to$ Compound (B). Structure of residue (A) and compound (B) formed respectively is :

1. A.A = benzaldehyde ($C_6H_5CHO$); B = benzoic acid ($C_6H_5COOH$)
2. B.A = benzaldehyde ($C_6H_5CHO$); B = sodium benzoate ($C_6H_5COONa$)
3. C.A = bisulphite adduct $C_6H_5CH(OH)SO_3Na$; B = benzaldehyde ($C_6H_5CHO$)✓
4. D.A = chromium complex $C_6H_5CH(OCrOHCl_2)_2$; B = benzaldehyde ($C_6H_5CHO$)

Correct answer: C

The complex of $Ni^{2+}$ ion and dimethyl glyoxime contains ______ number of Hydrogen (H) atoms.

Correct answer: 14

Niobium (Nb) and ruthenium (Ru) have "x" and "y" number of electrons in their respective 4d orbitals. The value of x + y is ______.

Correct answer: 11

The compound with molecular formula $C_6H_6$, which gives only one monobromo derivative and takes up four moles of hydrogen per mole for complete hydrogenation has ______ $\pi$ electrons.

Correct answer: 8

20 mL of 2 M NaOH solution is added to 400 mL of 0.5 M NaOH solution. The final concentration of the solution is ______ $\times10^{-2}$ M. (Nearest integer)

Correct answer: 57

Consider the following cases of standard enthalpy of reaction ($\Delta H_r^\circ$ in kJ $mol^{-1}$): $C_2H_6(g)+\frac{7}{2}O_2(g)\to2CO_2(g)+3H_2O(l)$ $\Delta H_1^\circ=-1550$; C(graphite) + $O_2(g)\to CO_2(g)$ $\Delta H_2^\circ=-393.5$; $H_2(g)+\frac{1}{2}O_2(g)\to H_2O(l)$ $\Delta H_3^\circ=-286$. The magnitude of $\Delta H_f^\circ$ $C_2H_6(g)$ is ______ kJ $mol^{-1}$ (Nearest integer).

Correct answer: 95