JEE Main 2026 — 28 Jan Shift 2 (3:00 PM - 6:00 PM) (Previous Year

The sum of all the elements in the range of $f(x)=\text{Sgn}(\sin x)+\text{Sgn}(\cos x)+\text{Sgn}(\tan x)+\text{Sgn}(\cot x)$, $x\ne\frac{n\pi}{2}$, $n\in\mathbb{Z}$, where $\text{Sgn}(t)=\begin{cases}1, & \text{if } t>0\\ -1, & \text{if } t<0\end{cases}$, is :

1. A.0
2. B.2✓
3. C.-2
4. D.4

Correct answer: B

Given below are two statements : Statement I : The function $f:\mathbb{R}\to\mathbb{R}$ defined by $f(x)=\frac{x}{1+|x|}$ is one-one. Statement II : The function $f:\mathbb{R}\to\mathbb{R}$ defined by $f(x)=\frac{x^2+4x-30}{x^2-8x+18}$ is many-one. 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.Statement I is false but Statement II is true
4. D.Both Statement I and Statement II are false

Correct answer: B

Let $A=\{z\in\mathbb{C}: |z-2|\le4\}$ and $B=\{z\in\mathbb{C}: |z-2|+|z+2|=5\}$. Then the max $\{|z_1-z_2|: z_1\in A\text{ and }z_2\in B\}$ is :

1. A.8
2. B.$\frac{15}{2}$
3. C.9
4. D.$\frac{17}{2}$✓

Correct answer: D

Let the arithmetic mean of $\frac{1}{a}$ and $\frac{1}{b}$ be $\frac{5}{16}$, $a>2$. If $\alpha$ is such that $a, 4, \alpha, b$ are in A.P., then the equation $\alpha x^2-ax+2(\alpha-2b)=0$ has :

1. A.one root in (1, 4) and another in (-2, 0)✓
2. B.complex roots of magnitude less than 2
3. C.both roots in the interval (-2, 0)
4. D.one root in (0, 2) and another in (-4, -2)

Correct answer: A

$\frac{6}{3^{26}}+\frac{10\cdot1}{3^{25}}+\frac{10\cdot2}{3^{24}}+\frac{10\cdot2^2}{3^{23}}+\ldots+\frac{10\cdot2^{24}}{3}$ is equal to :

1. A.$3^{25}$
2. B.$2^{25}$
3. C.$3^{26}$
4. D.$2^{26}$✓

Correct answer: D

The sum of the coefficients of $x^{499}$ and $x^{500}$ in $(1+x)^{1000}+x(1+x)^{999}+x^2(1+x)^{998}+\ldots+x^{1000}$ is :

1. A.${}^{1000}C_{501}$
2. B.${}^{1002}C_{500}$✓
3. C.${}^{1001}C_{501}$
4. D.${}^{1002}C_{501}$

Correct answer: B

Given below are two statements : Statement I : $25^{13}+20^{13}+8^{13}+3^{13}$ is divisible by 7. Statement II : The integral part of $(7+4\sqrt{3})^{25}$ is an odd number. In the light of the above statements, choose the correct answer from the options given below :

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

Correct answer: D

The probability distribution of a random variable X is given below : X: $4k$, $\frac{30}{7}k$, $\frac{32}{7}k$, $\frac{34}{7}k$, $\frac{36}{7}k$, $\frac{38}{7}k$, $\frac{40}{7}k$, $6k$ with P(X): $\frac{2}{15}$, $\frac{1}{15}$, $\frac{2}{15}$, $\frac{1}{5}$, $\frac{1}{15}$, $\frac{2}{15}$, $\frac{1}{5}$, $\frac{1}{15}$. If $E(X)=\frac{263}{15}$, then $P(X<20)$ is equal to :

1. A.$\frac{3}{5}$
2. B.$\frac{14}{15}$
3. C.$\frac{8}{15}$
4. D.$\frac{11}{15}$✓

Correct answer: D

An ellipse has its center at (1, $-$2), one focus at (3, $-$2) and one vertex at (5, $-$2). Then the length of its latus rectum is :

1. A.$\frac{16}{\sqrt{3}}$
2. B.6✓
3. C.$4\sqrt{3}$
4. D.$6\sqrt{3}$

Correct answer: B

Let the circle $x^2+y^2=4$ intersect $x$-axis at the points A(a, 0), $a>0$ and B(b, 0). Let P($2\cos\alpha$, $2\sin\alpha$), $0<\alpha<\frac{\pi}{2}$ and Q($2\cos\beta$, $2\sin\beta$) be two points such that $(\alpha-\beta)=\frac{\pi}{2}$. Then the point of intersection of AQ and BP lies on :

1. A.$x^2+y^2-4x-4y-4=0$
2. B.$x^2+y^2-4x-4=0$
3. C.$x^2+y^2-4y-4=0$✓
4. D.$x^2+y^2-4x-4y=0$

Correct answer: C

Considering the principal values of inverse trigonometric functions, the value of the expression $\tan\left(2\sin^{-1}\left(\frac{2}{\sqrt{13}}\right)-2\cos^{-1}\left(\frac{3}{\sqrt{10}}\right)\right)$ is equal to :

1. A.$\frac{33}{56}$✓
2. B.$-\frac{33}{56}$
3. C.$\frac{16}{63}$
4. D.$-\frac{16}{63}$

Correct answer: A

Let the ellipse $E: \frac{x^2}{144}+\frac{y^2}{169}=1$ and the hyperbola $H: \frac{x^2}{16}-\frac{y^2}{\lambda^2}=-1$ have the same foci. If e and L respectively denote the eccentricity and the length of the latus rectum of H, then the value of $24(e+L)$ is :

1. A.67
2. B.296✓
3. C.148
4. D.126

Correct answer: B

Let A be the focus of the parabola $y^2=8x$. Let the line $y=mx+c$ intersect the parabola at two distinct points B and C. If the centroid of the triangle ABC is $\left(\frac{7}{3}, \frac{4}{3}\right)$, then $(BC)^2$ is equal to :

1. A.41
2. B.89
3. C.32
4. D.80✓

Correct answer: D

Let P be a point in the plane of the vectors $\overrightarrow{AB}=3\hat{i}+\hat{j}-\hat{k}$ and $\overrightarrow{AC}=\hat{i}-\hat{j}+3\hat{k}$ such that P is equidistant from the lines AB and AC. If $|\overrightarrow{AP}|=\frac{\sqrt{5}}{2}$, then the area of the triangle ABP is :

1. A.2
2. B.$\frac{3}{2}$
3. C.$\frac{\sqrt{26}}{4}$
4. D.$\frac{\sqrt{30}}{4}$✓

Correct answer: D

Let Q(a, b, c) be the image of the point P(3, 2, 1) in the line $\frac{x-1}{1}=\frac{y}{2}=\frac{z-1}{1}$. Then the distance of Q from the line $\frac{x-9}{3}=\frac{y-9}{2}=\frac{z-5}{-2}$ is

1. A.8
2. B.7✓
3. C.6
4. D.5

Correct answer: B

Let $f(x)=\lim_{\theta\to0}\left(\frac{\cos\pi x-x^{\left(\frac{2}{\theta}\right)}\sin(x-1)}{1+x^{\left(\frac{2}{\theta}\right)}(x-1)}\right)$, $x\in\mathbb{R}$. Consider the following two statements : (I) f(x) is discontinous at $x=1$. (II) f(x) is continous at $x=-1$. Then,

1. A.Only (I) is True
2. B.Neither (I) nor (II) is True✓
3. C.Both (I) and (II) are True
4. D.Only (II) is True

Correct answer: B

Let $[\cdot]$ denote the greatest integer function. Then $\int_{-\pi/2}^{\pi/2}\left(\frac{12(3+[x])}{3+[\sin x]+[\cos x]}\right)dx$ is equal to :

1. A.$13\pi+1$
2. B.$12\pi+5$
3. C.$11\pi+2$✓
4. D.$15\pi+4$

Correct answer: C

Let $f(x)=\int\frac{dx}{x^{\left(\frac{2}{3}\right)}+2x^{\left(\frac{1}{2}\right)}}$ be such that $f(0)=-26+24\log_e(2)$. If $f(1)=a+b\log_e(3)$, where $a, b\in\mathbb{Z}$, then $a+b$ is equal to :

1. A.-11✓
2. B.-5
3. C.-26
4. D.-18

Correct answer: A

Let $y=y(x)$ be the solution of the differential equation $x\frac{dy}{dx}-y=x^2\cot x$, $x\in(0, \pi)$. If $y\left(\frac{\pi}{2}\right)=\frac{\pi}{2}$, then $6y\left(\frac{\pi}{6}\right)-8y\left(\frac{\pi}{4}\right)$ is equal to :

1. A.$3\pi$
2. B.$-3\pi$
3. C.$\pi$
4. D.$-\pi$✓

Correct answer: D

Let $P_1: y=4x^2$ and $P_2: y=x^2+27$ be two parabolas. If the area of the bounded region enclosed between $P_1$ and $P_2$ is six times the area of the bounded region enclosed between the line $y=\alpha x$, $\alpha>0$ and $P_1$, then $\alpha$ is equal to :

1. A.8
2. B.15
3. C.6
4. D.12✓

Correct answer: D

Let $A=\begin{bmatrix}3 & -4\\ 1 & -1\end{bmatrix}$ and B be two matrices such that $A^{100}=100B+I$. Then the sum of all the elements of $B^{100}$ is ______

Correct answer: 0

If $\sum_{r=1}^{25}\left(\frac{r}{r^4+r^2+1}\right)=\frac{p}{q}$, where p and q are positive integers such that $\gcd(p, q)=1$, then $p+q$ is equal to ______.

Correct answer: 976

Three persons enter in a lift at the ground floor. The lift will go upto 10$^{th}$ floor. The number of ways, in which the three persons can exit the lift at three different floors, if the lift does not stop at first, second and third floors, is equal to ______.

Correct answer: 210

If the distance of the point P(43, $\alpha$, $\beta$), $\beta<0$, from the line $\vec{r}=4\hat{i}-\hat{k}+\mu(2\hat{i}+3\hat{k})$, $\mu\in\mathbb{R}$ along a line with direction ratios 3, $-$1, 0 is $13\sqrt{10}$, then $\alpha^2+\beta^2$ is equal to ______

Correct answer: 170

Let f be a differentiable function satisfying $f(x)=1-2x+\int_0^xe^{(x-t)}f(t)dt$, $x\in\mathbb{R}$ and let $g(x)=\int_0^x(f(t)+2)^{15}(t-4)^6(t+12)^{17}dt$, $x\in\mathbb{R}$. If p and q are respectively the points of local minima and local maxima of g, then the value of $|p+q|$ is equal to ______.

Correct answer: 9

In an experiment, a set of reading are obtained as follows - 1.24 mm, 1.25 mm, 1.23 mm, 1.21 mm. The expected least count of the instrument used in recording these readings is ______ mm.

1. A.0.01✓
2. B.0.1
3. C.0.05
4. D.0.001

Correct answer: A

The time period of a simple harmonic oscillator is $T=2\pi\sqrt{\frac{k}{m}}$. Measured value of mass (m) of the object is 10 g with an accuracy of 10 mg and time for 50 oscillations of the spring is found to be 60 s using a watch of 2 s resolution. Percentage error in determination of spring constant (k) is ______ %.

1. A.7.60
2. B.6.76✓
3. C.3.43
4. D.3.35

Correct answer: B

As shown in the figure, a spring is kept in a stretched position with some extension by holding the masses 1 kg and 0.2 kg with a separation more than spring natural length and are released. Assuming the horizontal surface to be frictionless, the angular frequency (in SI unit) of the system is :

1. A.27
2. B.20
3. C.5
4. D.30✓

Correct answer: D

A small block of mass m slides down from the top of a frictionless inclined surface, while the inclined plane is moving towards left with constant acceleration $a_0$. The angle between the inclined plane and ground is $\theta$ and its base length is L. Assuming that initially the small block is at the top of the inclined plane, the time it takes to reach the lowest point of the inclined plane is ______.

1. A.$\sqrt{\frac{4L}{g\sin2\theta-a_0(1+\cos2\theta)}}$✓
2. B.$\sqrt{\frac{2L}{g\sin\theta-a_0\cos\theta}}$
3. C.$\sqrt{\frac{4L}{g\cos^2\theta-a_0\sin\theta\cos\theta}}$
4. D.$\sqrt{\frac{2L}{g\sin2\theta-a_0(1+\cos2\theta)}}$

Correct answer: A

A particle starts moving from time $t=0$ and its coordinate is given as $x(t)=4t^3-3t$. A. The particle returns to its original position (origin) 0.866 units later B. The particle is 1 unit away from origin at its turning point C. Acceleration of the particle is non-negative D. The particle is 0.5 units away from origin at its turning point E. Particle never turns back as acceleration is non-negative. Choose the correct answer from the options given below :

1. A.C, E Only
2. B.A, B, C Only✓
3. C.A, C, D Only
4. D.A, C Only

Correct answer: B

When the position vector $\vec{r}=x\hat{i}+y\hat{j}+z\hat{k}$ changes sign as $-\vec{r}$, which one of the following vector will not flip under sign change ?

1. A.Linear momentum
2. B.Angular momentum✓
3. C.Velocity
4. D.Acceleration

Correct answer: B

Match List - I with List - II. List - I: A. Coefficient of viscosity; B. Surface tension; C. Pressure; D. Surface energy. List - II: I. $[ML^{-1}T^{-2}]$; II. $[ML^2T^{-2}]$; III. $[ML^0T^{-2}]$; IV. $[ML^{-1}T^{-1}]$. Choose the correct answer from the options given below :

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

Correct answer: C

The speed of a longitudinal wave in a metallic bar is 400 m/s. If the density and Young's modulus of the bar material are increased by 0.5% and 1%, respectively then the speed of the wave is changed approximately to ______ m/s.

1. A.399
2. B.398
3. C.402
4. D.401✓

Correct answer: D

The mean free path of a molecule of diameter $5\times10^{-10}$ m at the temperature $41^\circ$C and pressure $1.38\times10^5$ Pa, is given as ______ m. (Given $k_B=1.38\times10^{-23}$ J/K).

1. A.$2\sqrt{2}\times10^{-8}$✓
2. B.$10\sqrt{2}\times10^{-8}$
3. C.$2\times10^{-8}$
4. D.$2\sqrt{2}\times10^{-10}$

Correct answer: A

Identify the correct statements : A. Electrostatic field lines form closed loops . B. The electric field lines point radially outward when charge is greater than zero. C. The Gauss - Law is valid only for inverse - square force. D. The workdone in moving a charged particle in a static electric field around a closed path is zero. E. The motion of a particle under Coulomb's force must take place in a plane. Choose the correct answer from the options given below :

1. A.A, B, C, D Only
2. B.A, C, E Only
3. C.B, C, D, E Only✓
4. D.A, B, D, E Only

Correct answer: C

Identify the correct statements : A. Effective capacitance of a series combination of capacitors is always smaller than the smallest capacitance of the capacitor in the combination. B. When a dielectric medium is placed between the charged plates of a capacitor, displacement of charges cannot occur due to insulation property of dielectric. C. Increasing of area of capacitor plate or decreasing of thickness of dielectric is an alternate method to increase the capacitance. D. For a point charge, concentric spherical shells centered at the location of the charge are equipotential surfaces. Choose the correct answer from the options given below :

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

Correct answer: D

A Wheatstone bridge is initially at room temperature and all arms of the bridge have same value of resistances ($R_1=R_2=R_3=R_4$). When $R_3$ resistance is heated to some temperature, its resistance value has gone up by 10%. The potential difference $(V_a-V_b)$ (after $R_3$ is heated) is ______ V.

1. A.0
2. B.0.95✓
3. C.2
4. D.1.05

Correct answer: B

A long cylindrical conductor with large cross section carries an electric current distributed uniformly over its cross-section. Magnetic field due to this current is : A. maximum at either ends of the conductor and minimum at the midpoint B. maximum at the axis of the conductor C. minimum at the surface of the conductor D. minimum at the axis of the conductor E. same at all points in the cross-section of the conductor. Choose the correct answer from the options given below :

1. A.D Only✓
2. B.B, C Only
3. C.A, D Only
4. D.E Only

Correct answer: A

Which one of the following is **not** a measurable quantity ?

1. A.Voltage difference
2. B.Voltage✓
3. C.Resistance
4. D.Displacement current

Correct answer: B

A plane electromagnetic wave is moving in free space with velocity $c=3\times10^8$ m/s and its electric field is given as $\vec{E}=54\sin(kz-\omega t)\hat{j}$ V/m, where $\hat{j}$ is the unit vector along $y$-axis. The magnetic field vector $\vec{B}$ of the wave is :

1. A.$-1.8\times10^{-7}\sin(kz-\omega t)\hat{i}$ T✓
2. B.$1.4\times10^{-7}\sin(kz-\omega t)\hat{k}$ T
3. C.$1.4\times10^{-7}\sin(kz-\omega t)\hat{i}$ T
4. D.$+1.8\times10^{-7}\sin(kz-\omega t)\hat{i}$ T

Correct answer: A

For a transparent prism, if the angle of minimum deviation is equal to its refracting angle, the refractive index n of the prism satisfies.

1. A.$\sqrt{2}<n<2$✓
2. B.$\sqrt{2}<n<2\sqrt{2}$
3. C.$n\ge2$
4. D.$1<n<2$

Correct answer: A

A biconvex lens is formed by using two thin planoconvex lenses, as shown in the figure. The refractive index and radius of curved surfaces are also mentioned in figure. When an object is placed on the left side of lens at a distance of 30 cm from the biconvex lens, the magnification of the image will be :

1. A.-2.5
2. B.+2.5
3. C.+2
4. D.-2✓

Correct answer: D

Number of photons of equal energy emitted per second by a 6 mW laser source operating at 663 nm is ______. (Given : $h=6.63\times10^{-34}$ J.s and $c=3\times10^8$ m/s)

1. A.$10\times10^{15}$
2. B.$5\times10^{16}$
3. C.$5\times10^{15}$
4. D.$2\times10^{16}$✓

Correct answer: D

A nucleus has mass number $\alpha$ and radius $R_\alpha$. Another nucleus has mass number $\beta$ and radius $R_\beta$. If $\beta=8\alpha$ then $R_\alpha/R_\beta$ is :

1. A.1
2. B.8
3. C.0.5✓
4. D.2

Correct answer: C

Two p-n junction diodes $D_1$ and $D_2$ are connected as shown in figure. A and B are input signals and C is the output. The given circuit will function as a ______.

1. A.NOR Gate
2. B.NAND Gate
3. C.AND Gate✓
4. D.OR Gate

Correct answer: C

A fly wheel having mass 3 kg and radius 5 m is free to rotate about a horizontal axis. A string having negligible mass is wound around the wheel and the loose end of the string is connected to 3 kg mass. The mass is kept at rest initially and released. Kinetic energy of the wheel when the mass descends by 3 m is ______ J. ($g=10$ m/s$^2$)

Correct answer: 30

Two tuning forks A and B are sounded together giving rise to 8 beats in 2 s. When fork A is loaded with wax, the beat frequency is reduced to 4 beats in 2 s. If the original frequency of tuning fork B is 380 Hz then original frequency of tuning fork A is ______ Hz.

Correct answer: 384

An inductor stores 16 J of magnetic field energy and dissipates 32 W of thermal energy due to its resistance when an a.c. current of 2 A (rms) and frequency 50 Hz flows through it. The ratio of inductive reactance to its resistance is ______. ($\pi=3.14$)

Correct answer: 314

A thermodynamic system is taken through the cyclic process ABC as shown in the figure. The total work done by the system during the cycle ABC is ______ J.

Correct answer: 300

A beam of light consisting of wavelengths 650 nm and 550 nm illuminates the Young's double slits with separation of 2 mm such that the interference fringes are formed on a screen, placed at a distance of 1.2 m from the slits. The least distance of a point from the central maximum, where the bright fringes due to both the wavelengths coincide, is ______ $\times10^{-5}$ m.

Correct answer: 429

For the given reaction; CaCO$_3$ + 2HCl $\to$ CaCl$_2$ + H$_2$O + CO$_2$. If 90 g CaCO$_3$ is added to 300 mL of HCl which contains 38.55% HCl by mass and has density 1.13 g mL$^{-1}$, then which of the following option is **correct** ? Given molar mass of H, Cl, Ca and O are 1, 35.5, 40 and 16 g mol$^{-1}$ respectively.

1. A.60.32 g of HCl remains unreacted
2. B.32.85 g of CaCO$_3$ remains unreacted
3. C.97.30 g of HCl reacted
4. D.64.97 g of HCl remains unreacted✓

Correct answer: D

The wavelength of photon 'A' is 400 nm. The frequency of photon 'B' is $10^{16}$ s$^{-1}$. The wave number of photon 'C' is $10^4$ cm$^{-1}$. The correct order of energy of these photons is :

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

Correct answer: B

The plot of $\log_{10}K$ vs $\frac{1}{T}$ gives a straight line. The intercept and slope respectively are (where K is equilibrium constant).

1. A.$\frac{2.303R}{\Delta H^\circ}$, $\frac{2.303R}{\Delta S^\circ}$
2. B.$-\frac{\Delta S^\circ R}{2.303}$, $\frac{\Delta H^\circ R}{2.303}$
3. C.$\frac{\Delta S^\circ}{2.303R}$, $-\frac{\Delta H^\circ}{2.303R}$✓
4. D.$-\frac{\Delta H^\circ}{2.303R}$, $\frac{\Delta S^\circ}{2.303R}$

Correct answer: C

Consider the following aqueous solutions. I. 2.2 g Glucose in 125 mL of solution. II. 1.9 g Calcium chloride in 250 mL of solution. III. 9.0 g Urea in 500 mL of solution. IV. 20.5 g Aluminium sulphate in 750 mL of solution. The **correct** increasing order of boiling point of these solutions will be : [Given : Molar mass in g mol$^{-1}$ : H=1, C=12, N=14, O=16, Cl=35.5, Ca=40, Al=27 and S=32]

1. A.II < III < IV < I
2. B.III < I < II < IV
3. C.I < II < III < IV✓
4. D.II < III < I < IV

Correct answer: C

Observe the following equilibrium in a 1 L flask. A(g) $\rightleftharpoons$ B(g). At T(K), the equilibrium concentrations of A and B are 0.5 M and 0.375 M respectively. 0.1 moles of A is added into the flask and heated to T(K) to establish the equilibrium again. The new equilibrium concentrations (in M) of A and B are respectively

1. A.0.742, 0.557.
2. B.0.367, 0.275.
3. C.0.53, 0.4.
4. D.0.557, 0.418.✓

Correct answer: D

Match List - I with List - II according to shape. List - I: A. XeO$_3$; B. XeF$_2$; C. XeO$_2$F$_2$; D. XeOF$_4$. List - II: I. BrF$_5$; II. NH$_3$; III. [I$_3$]$^-$; IV. SF$_4$. Choose the **correct** answer from the options given below :

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

Correct answer: C

Consider the elements N, P, O, S, Cl and F. The number of valence electrons present in the elements with most and least metallic character from the above list is respectively.

1. A.7 and 5
2. B.6 and 7
3. C.5 and 6
4. D.5 and 7✓

Correct answer: D

Given below are two statements : Statement I : The increasing order of boiling point of hydrogen halides is HCl < HBr < HI < HF. Statement II : The increasing order of melting point of hydrogen halides is HCl < HBr < HF < HI. 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 false
3. C.Both Statement I and Statement II are true✓
4. D.Statement I is false but Statement II is true

Correct answer: C

Consider the following statements about manganate and permanganate ions. Identify the **correct** statements. A. The geometry of both manganate and permanganate ions is tetrahedral. B. The oxidation states of Mn in manganate and permanganate are +7 and +6, respectively. C. Oxidation of Mn(II) salt by peroxodisulphate gives manganate ion as the final product. D. Manganate ion is paramagnetic and permanganate ions is diamagnetic. E. Acidified permanganate ion reduces oxalate, nitrite and iodide ions. Choose the **correct** answer from the options given below :

1. A.A, D and E Only
2. B.A and D Only✓
3. C.A, C and D Only
4. D.A, B and C Only

Correct answer: B

The correct increasing order of spin-only magnetic moment values of the complex ions [MnBr$_4$]$^{2-}$ (A), [Cu(H$_2$O)$_6$]$^{2+}$ (B), [Ni(CN)$_4$]$^{2-}$ (C) and [Ni(H$_2$O)$_6$]$^{2+}$ (D) is :

1. A.A = B < C < D
2. B.A = B < D < C
3. C.C = D < B < A
4. D.C < B < D < A✓

Correct answer: D

Consider the following reactions: Na$_2$B$_4$O$_7$ $\xrightarrow{\Delta}$ 2X + Y; CuSO$_4$ + Y $\xrightarrow{\text{Non-Luminous flame}}$ Z + SO$_3$; 2Z + 2X + Carbon $\xrightarrow{\text{Luminous flame}}$ 2Q + Na$_2$B$_4$O$_7$ + CO. The oxidation states of Cu in Z and Q, respectively are :

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

Correct answer: A

The cyclic cations having the same number of hyperconjugation are : [four substituted cyclohexyl carbocations A, B, C, D shown in the figure]. Choose the **correct** answer from the options given below :

1. A.A, C and D only
2. B.A and B Only
3. C.A and C Only✓
4. D.B and C Only

Correct answer: C

Identify the **correct** statements : The presence of $-$NO$_2$ group in benzene ring A. activates the ring towards electrophilic substitutions. B. deactivates the ring towards electrophilic substitutions. C. activates the ring towards nucleophilic substitutions. D. deactivates the ring towards nucleophilic substitutions. Choose the **correct** answer from the options given below :

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

Correct answer: B

The reactions which produce alcohol as the product are : A. CH$_4$ + O$_2$ $\xrightarrow{Mo_2O_3, \Delta}$; B. 2CH$_3$CH$_3$ + 3O$_2$ $\xrightarrow{(CH_3COO)_2Mn, \Delta}$; C. (CH$_3$)$_3$CH $\xrightarrow{KMnO_4}$; D. 2CH$_4$ + O$_2$ $\xrightarrow{Cu/523\ K/100\ atm}$; E. CH$_3-$CH=CH$-$CH$_3$ $\xrightarrow{KMnO_4/H^+}$. Choose the **correct** answer from the options given below :

1. A.A and D Only
2. B.C and D Only✓
3. C.A, C and E Only
4. D.B, D and E Only

Correct answer: B

Which of the following reaction is NOT correctly represented ?

1. A.Toluene $\xrightarrow{Br_2, h\nu}$ benzyl bromide
2. B.Benzenediazonium chloride $\xrightarrow{Cu_2Br_2/HBr}$ bromobenzene
3. C.Toluene $\xrightarrow{Br_2, Fe, dark}$ ortho and para bromotoluenes
4. D.1-Methylcyclohexene $\xrightarrow{Br_2, h\nu}$ 1-(bromomethyl)cyclohexene✓

Correct answer: D

The correct order of acidic strength of the major products formed in the given reactions, is : A. PhNH$_2$ $\xrightarrow{\text{(1) NaNO}_2\text{ + HCl (<5}^\circ\text{C) (2) CuCN (3) H}_3\text{O}^+/\Delta}$ [A]; B. CH$_3$CH$_2$CHO $\xrightarrow{[Ag(NH_3)_2]^+, OH^-, \Delta}$ [B]; C. CH$_4$ + O$_2$ $\xrightarrow{\text{(i) Mo}_2\text{O}_3\text{ (ii) Na}_2\text{Cr}_2\text{O}_7/\text{H}^+}$ [C]; D. PhCH$_2$MgBr + CO$_2$ $\xrightarrow{\text{Dry ether, H}_3\text{O}^+}$ [D]. Choose the **correct** answer from the options given below :