JEE Main 2024 — 29 Jan Shift 2 (Previous Year Paper)

If $R$ is the smallest equivalence relation on the set $\{1,2,3,4\}$ such that $\{(1,2),(1,3)\}\subset R$, then the number of elements in $R$ is ______.

1. A.10✓
2. B.8
3. C.12
4. D.15

Correct answer: A

If the mean and variance of five observations are $\frac{24}{5}$ and $\frac{194}{25}$ respectively and the mean of the first four observations is $\frac72$, then the variance of the first four observations in equal to:

1. A.$\frac{105}{4}$
2. B.$\frac54$✓
3. C.$\frac{77}{12}$
4. D.$\frac45$

Correct answer: B

Let $y=\log_e\left(\frac{1-x^2}{1+x^2}\right)$, $-1<x<1$. Then at $x=\frac12$, the value of $225(y'-y'')$ is equal to:

1. A.746
2. B.742
3. C.732
4. D.736✓

Correct answer: D

The function $f(x)=\frac{x}{x^2-6x-16}$, $x\in\mathbb{R}-\{-2,8\}$.

1. A.decreases in $(-\infty,-2)\cup(-2,8)\cup(8,\infty)$✓
2. B.increases in $(-\infty,-2)\cup(-2,8)\cup(8,\infty)$
3. C.decreases in $(-\infty,-2)$ and increases in $(8,\infty)$
4. D.decreases in $(-2,8)$ and increases in $(-\infty,-2)\cup(8,\infty)$

Correct answer: A

If $\int\frac{\sin^{\frac32}x+\cos^{\frac32}x}{\sqrt{\sin^3x\cos^3x\sin(x-\theta)}}dx=A\sqrt{\cos\theta\tan x-\sin\theta}+B\sqrt{\cos\theta-\sin\theta\cot x}+C$, where $C$ is the integration constant, then AB is equal to:

1. A.$2\sec\theta$
2. B.$4\sec\theta$
3. C.$8\operatorname{cosec}(2\theta)$✓
4. D.$4\operatorname{cosec}(2\theta)$

Correct answer: C

The function $f(x)=2x+3(x)^{\frac23}$, $x\in\mathbb{R}$ has:

1. A.exactly one point of local minima and no point of local maxima
2. B.exactly one point of local maxima and no point of local minima
3. C.exactly two points of local maxima and exactly one point of local minima
4. D.exactly one point of local maxima and exactly one point of local minima✓

Correct answer: D

If $\log_ea$, $\log_eb$, $\log_ec$ are in an A.P. and $\log_ea-\log_e2b$, $\log_e2b-\log_e3c$, $\log_e3c-\log_ea$ are also in an A.P., then $a:b:c$ is equal to:

1. A.25 : 10 : 4
2. B.6 : 3 : 2
3. C.16 : 4 : 1
4. D.9 : 6 : 4✓

Correct answer: D

Let $A=\begin{bmatrix}2&1&2\\6&2&11\\3&3&2\end{bmatrix}$ and $P=\begin{bmatrix}1&2&0\\5&0&2\\7&1&5\end{bmatrix}$. The sum of the prime factors of $|P^{-1}AP-2I|$ is equal to:

1. A.26✓
2. B.27
3. C.66
4. D.23

Correct answer: A

The distance of the point (2, 3) from the line $2x-3y+28=0$, measured parallel to the line $\sqrt3x-y+1=0$, is equal to:

1. A.$4\sqrt2$
2. B.$4+6\sqrt3$✓
3. C.$3+4\sqrt2$
4. D.$6\sqrt3$

Correct answer: B

If each term of a geometric progression $a_1,a_2,a_3,\ldots$ with $a_1=\frac18$ and $a_2\ne a_1$, is the arithmetic mean of the next two terms and $S_n=a_1+a_2+\ldots+a_n$, then $S_{20}-S_{18}$ is equal to:

1. A.$-2^{15}$✓
2. B.$2^{15}$
3. C.$2^{18}$
4. D.$-2^{18}$

Correct answer: A

An integer is chosen at random from the integers 1, 2, 3, ...., 50. The probability that the chosen integer is a multiple of atleast one of 4, 6 and 7 is:

1. A.$\frac{21}{50}$✓
2. B.$\frac{14}{25}$
3. C.$\frac8{25}$
4. D.$\frac9{50}$

Correct answer: A

Number of ways of arranging 8 identical books into 4 identical shelves where any number of shelves may remain empty is equal to:

1. A.16
2. B.12
3. C.18
4. D.15✓

Correct answer: D

Let $P(3,2,3)$, $Q(4,6,2)$ and $R(7,3,2)$ be the vertices of $\Delta PQR$. Then, the angle $\angle QPR$ is:

1. A.$\frac\pi3$✓
2. B.$\cos^{-1}\left(\frac1{18}\right)$
3. C.$\frac\pi6$
4. D.$\cos^{-1}\left(\frac7{18}\right)$

Correct answer: A

Let a unit vector $\hat u=x\hat i+y\hat j+z\hat k$ make angles $\frac\pi2,\frac\pi3$ and $\frac{2\pi}{3}$ with the vectors $\frac1{\sqrt2}\hat i+\frac1{\sqrt2}\hat k$, $\frac1{\sqrt2}\hat j+\frac1{\sqrt2}\hat k$ and $\frac1{\sqrt2}\hat i+\frac1{\sqrt2}\hat j$ respectively. If $\vec v=\frac1{\sqrt2}\hat i+\frac1{\sqrt2}\hat k+\frac1{\sqrt2}\hat j$, then $|\hat u-\vec v|^2$ is equal to:

1. A.$\frac{11}{2}$
2. B.9
3. C.$\frac52$✓
4. D.7

Correct answer: C

Let $\vec{OA}=\vec a$, $\vec{OB}=12\vec a+4\vec b$ and $\vec{OC}=\vec b$, where $O$ is the origin. If $S$ is the parallelogram with adjacent sides OA and OC, then $\frac{\text{area of the quadrilateral }OABC}{\text{area of }S}$ is equal to ______.

1. A.10
2. B.7
3. C.6
4. D.8✓

Correct answer: D

The sum of the solutions $x\in\mathbb{R}$ of the equation $\frac{3\cos2x+\cos^32x}{\cos^6x-\sin^6x}=x^3-x^2+6$ is:

1. A.1
2. B.0
3. C.−1✓
4. D.3

Correct answer: C

Let $x=\frac mn$ ($m,n$ are co-prime natural numbers) be a solution of the equation $\cos(2\sin^{-1}x)=\frac19$ and let $\alpha,\beta\,(\alpha>\beta)$ be the roots of the equation $mx^2-nx-m+n=0$. Then the point $(\alpha,\beta)$ lies on the line.

1. A.$5x+8y=9$✓
2. B.$5x-8y=-9$
3. C.$3x+2y=2$
4. D.$3x-2y=-2$

Correct answer: A

Let $A$ be the point of intersection of the lines $3x+2y=14$, $5x-y=6$ and $B$ be the point of intersection of the lines $4x+3y=8$, $6x+y=5$. The distance of the point $P(5,-2)$ from the line $AB$ is:

1. A.$\frac52$
2. B.6✓
3. C.8
4. D.$\frac{13}{2}$

Correct answer: B

Let $r$ and $\theta$ respectively be the modulus and amplitude of the complex number $z=2-i\left(2\tan\frac{5\pi}{8}\right)$, then $(r,\theta)$ is equal to:

1. A.$\left(2\sec\frac{3\pi}{8},\frac{5\pi}{8}\right)$
2. B.$\left(2\sec\frac{5\pi}{8},\frac{3\pi}{8}\right)$
3. C.$\left(2\sec\frac{3\pi}{8},\frac{3\pi}{8}\right)$✓
4. D.$\left(2\sec\frac{11\pi}{8},\frac{11\pi}{8}\right)$

Correct answer: C

If $\sin\left(\frac yx\right)=\log_e|x|+\frac\alpha2$ is the solution of the differential equation $x\cos\left(\frac yx\right)\frac{dy}{dx}=y\cos\left(\frac yx\right)+x$ and $y(1)=\frac\pi3$, then $\alpha^2$ is equal to:

1. A.4
2. B.12
3. C.9
4. D.3✓

Correct answer: D

Let the area of the region $\{(x,y):0\le x\le3,\ 0\le y\le\min\{x^2+2,2x+2\}\}$ be $A$. Then $12A$ is equal to ______.

Correct answer: 164

Remainder when $64^{32^{32}}$ is divided by 9 is equal to ______.

Correct answer: 1

Let $\alpha,\beta$ be the roots of the equation $x^2-\sqrt6x+3=0$ such that $\text{Im}(\alpha)>\text{Im}(\beta)$. Let $a,b$ be integers not divisible by 3 and $n$ be a natural number such that $\frac{\alpha^{99}}{\beta}+\alpha^{98}=3^n(a+ib)$, $i=\sqrt{-1}$. Then $n+a+b$ is equal to ______.

Correct answer: 49

Let the set $C=\{(x,y)\mid x^2-2^y=2023,\ x,y\in\mathbb{N}\}$. Then $\sum_{(x,y)\in C}(x+y)$ is equal to ______.

Correct answer: 46

If $\int_{\pi/6}^{\pi/3}\sqrt{1-\sin2x}\,dx=\alpha+\beta\sqrt2+\gamma\sqrt3$, where $\alpha,\beta$ and $\gamma$ are rational numbers, then $3\alpha+4\beta-\gamma$ is equal to ______.

Correct answer: 6

Let $f(x)=\sqrt{\lim_{r\to x}\left\{\frac{2r^2\left[(f(r))^2-f(x)f(r)\right]}{r^2-x^2}-r^3e^{\frac{f(r)}{r}}\right\}}$ be differentiable in $(-\infty,0)\cup(0,\infty)$ and $f(1)=1$. Then the value of $ea$, such that $f(a)=0$, is equal to ______.

Correct answer: 2

Let for any three distinct consecutive terms $a,b,c$ of an A.P. the lines $ax+by+c=0$ be concurrent at the point $P$ and $Q(\alpha,\beta)$ be a point such that the system of equations $x+y+z=6$ $2x+5y+\alpha z=\beta$ and $x+2y+3z=4$, has infinitely many solutions. The $(PQ)^2$ is equal to ______.

Correct answer: 113

Let the slope of the line $45x+5y+3=0$ be $27r_1+\frac{9r_2}{2}$ for some $r_1,r_2\in\mathbb{R}$. Then $\lim_{x\to3}\left(\int_3^x\frac{8t^2}{\frac{3r_2x}{2}-r_2x^2-r_1x^3-3x}dt\right)$ is equal to ______.

Correct answer: 12

Let $O$ be the origin, and $M$ and $N$ be the points on the lines $\frac{x-5}{4}=\frac{y-4}{1}=\frac{z-5}{3}$ and $\frac{x+8}{12}=\frac{y+2}{5}=\frac{z-11}{9}$ respectively such that $MN$ is the shortest distance between the given lines. Then $\vec{OM}\cdot\vec{ON}$ is equal to ______.

Correct answer: 9

Let $P(\alpha,\beta)$ be a point on the parabola $y^2=4x$. If $P$ also lies on the chord of the parabola $x^2=8y$ whose mid-point is $\left(1,\frac54\right)$, then $(\alpha-28)(\beta-8)$ is equal to ______.

Correct answer: 192

N moles of a polyatomic gas ($f=6$) must be mixed with two moles of a monoatomic gas so that the mixture behaves as a diatomic gas. The value of N is:

1. A.4✓
2. B.2
3. C.3
4. D.6

Correct answer: A

The truth table for this given circuit is:

1. A.A B Y: 0 0 0; 0 1 0; 1 0 0; 1 1 1
2. B.A B Y: 0 0 1; 0 1 0; 1 0 1; 1 1 0
3. C.A B Y: 0 0 1; 0 1 1; 1 0 1; 1 1 0
4. D.A B Y: 0 0 0; 0 1 1; 1 0 0; 1 1 1✓

Correct answer: D

Two particles X and Y having equal charges are being accelerated through the same potential difference. Thereafter they enter normally in a region of uniform magnetic field and describes circular paths of radii $R_1$ and $R_2$ respectively. The mass ratio of X and Y is:

1. A.$\left(\frac{R_1}{R_2}\right)$
2. B.$\left(\frac{R_1}{R_2}\right)^2$✓
3. C.$\left(\frac{R_2}{R_1}\right)^2$
4. D.$\left(\frac{R_2}{R_1}\right)$

Correct answer: B

In the given circuit, the current in resistance $R_3$ is:

1. A.1.5 A
2. B.2.5 A
3. C.2 A
4. D.1 A✓

Correct answer: D

In Young's double slit experiment, light from two identical sources are superimposing on a screen. The path difference between the two lights reaching at a point on the screen is $\frac{7\lambda}{4}$. The ratio of intensity of fringe at this point with respect to the maximum intensity of the fringe is:

1. A.$\frac12$✓
2. B.$\frac34$
3. C.$\frac13$
4. D.$\frac14$

Correct answer: A

An electric field is given by $(6\hat i+5\hat j+3\hat k)$ N/C. The electric flux through a surface area $30\hat i$ m² lying in YZ-plane (in SI unit) is:

1. A.180✓
2. B.150
3. C.90
4. D.60

Correct answer: A

A plane electromagnetic wave of frequency 35 MHz travels in free space along the X-direction. At a particular point (in space and time) $\vec E=9.6\hat j$ V/m. The value of magnetic field at this point is:

1. A.$9.6\hat j$ T
2. B.$3.2\times10^{-8}\hat i$ T
3. C.$9.6\times10^{-8}\hat k$ T
4. D.$3.2\times10^{-8}\hat k$ T✓

Correct answer: D

A bob of mass 'm' is suspended by a light string of length 'L'. It is imparted a minimum horizontal velocity at the lowest point A such that it just completes half circle reaching the top most position B. The ratio of kinetic energies $\frac{(K.E.)_A}{(K.E.)_B}$ is:

1. A.5 : 1✓
2. B.3 : 2
3. C.1 : 5
4. D.2 : 5

Correct answer: A

A wire of length L and radius r is clamped at one end. If its other end is pulled by a force F, its length increases by l. If the radius of the wire and the applied force both are reduced to half of their original values keeping original length constant, the increase in length will become:

1. A.2 times✓
2. B.$\frac32$ times
3. C.4 times
4. D.3 times

Correct answer: A

If the distance between object and its two times magnified virtual image produced by a curved mirror is 15 cm. the focal length of the mirror must be:

1. A.−12 cm
2. B.15 cm
3. C.10/3 cm
4. D.−10 cm✓

Correct answer: D

The bob of a pendulum was released from a horizontal position. The length of the pendulum is 10 m. If it dissipates 10% of its initial energy against air resistance, the speed with which the bob arrives at the lowest point is: [Use, g : 10 m s$^{-2}$]

1. A.$6\sqrt5$ m s$^{-1}$✓
2. B.$2\sqrt5$ m s$^{-1}$
3. C.$5\sqrt6$ m s$^{-1}$
4. D.$5\sqrt5$ m s$^{-1}$

Correct answer: A

A physical quantity $Q$ is found to depend on quantities a, b, c by the relation $Q=\frac{a^4b^3}{c^2}$. The percentage error in a, b and c are 3%, 4% and 5% respectively. Then, the percentage error in Q is:

1. A.43%
2. B.66%
3. C.34%✓
4. D.14%

Correct answer: C

Given below are two statements: Statement I : Most of the mass of the atom and all its positive charge are concentrated in a tiny nucleus and the electrons revolve around it, is Rutherford's model. Statement II : An atom is a spherical cloud of positive charges with electrons embedded in it, is a special case of Rutherford's model. In the light of the above statements, choose the most appropriate 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 true
4. D.Both statement I and statement II are false

Correct answer: B

A stone of mass 900 g is tied to a string and moved in a vertical circle of radius 1 m making 10 rpm. The tension in the string, when the stone is at the lowest point is (if $\pi^2=9.8$ and $g=9.8$ m/s²):

1. A.9.8 N✓
2. B.8.82 N
3. C.97 N
4. D.17.8 N

Correct answer: A

A small liquid drop of radius R is divided into 27 identical liquid drops. If the surface tension is T, then the work done in the process will be:

1. A.$\frac18\pi R^2T$
2. B.$4\pi R^2T$
3. C.$8\pi R^2T$✓
4. D.$3\pi R^2T$

Correct answer: C

Two sources of light emit with a power of 200 W. The ratio of number of photons of visible light emitted by each source having wavelengths 300 nm and 500 nm respectively, will be:

1. A.1 : 3
2. B.1 : 5
3. C.5 : 3
4. D.3 : 5✓

Correct answer: D

The temperature of a gas having $2.0\times10^{25}$ molecules per cubic meter at 1.38 atm (Given, $k=1.38\times10^{-23}$ J K$^{-1}$)

1. A.100 K
2. B.300 K
3. C.200 K
4. D.500 K✓

Correct answer: D

A planet takes 200 days to complete one revolution around the Sun. If the distance of the planet from Sun is reduced to one fourth of the original distance, how many days will it take to complete one revolution:

1. A.25✓
2. B.50
3. C.20
4. D.100

Correct answer: A

A particle is moving in a straight line. The variation of position 'x' as a function of time 't' is given as $x=(t^3-6t^2+20t+15)$ m. The velocity of the body when its acceleration becomes zero is:

1. A.4 m/s
2. B.6 m/s
3. C.8 m/s✓
4. D.10 m/s

Correct answer: C

In an a.c. circuit, voltage and current are given by: $V=100\sin(100t)$ V and $I=100\sin\left(100t+\frac\pi3\right)$ mA respectively. The average power dissipated in one cycle is:

1. A.2.5 W✓
2. B.10 W
3. C.5 W
4. D.25 W

Correct answer: A

In the given figure, the charge stored in 6 μF capacitor. when points A and B are joined by a connecting wire is ______ μC.

Correct answer: 36

Two metallic wires P and Q have same volume and are made up of same material. If their area of cross sections are in the ratio 4: 1 and force $F_1$ is applied to P, an extension of $\Delta l$ is produced. The force which is required to produce same extension in Q is $F_2$. The value of $\frac{F_1}{F_2}$ is ______.

Correct answer: 16

In the given circuit, the current flowing through the resistance 20 Ω is 0.3 A, while the ammeter reads 0.9 A. The value of $R_1$ is ______ Ω.

Correct answer: 30

A simple harmonic oscillator has an amplitude A and time period $6\pi$ second. Assuming the oscillation starts from its mean position. the time required by it to travel from $x=A$ to $x=\frac{\sqrt3}{2}A$ will be $\frac\pi x$ s, where $x=$ ______.

Correct answer: 2

In a single slit diffraction pattern, a light of wavelength 6000 Å is used. The distance between the first and third minima in the diffraction pattern is found to be 3 mm when the screen in placed 50 cm away from slits. The width of the slit is ______ $\times10^{-4}$ m.

Correct answer: 2

A particle is moving in a circle of radius 50 cm in such a way that at any instant the normal and tangential components of it's acceleration are equal. If its speed at $t=0$ is 4 m/s, the time taken to complete the first revolution will be $\frac1\alpha[1-e^{-2\pi}]$ s, where $\alpha=$ ______.

Correct answer: 8

A charge of 4.0 μC is moving with a velocity of $4.0\times10^6$ m s$^{-1}$ along the positive y-axis under a magnetic field $\vec B$ of strength $(2\hat k)$ T. The force acting on the charge is $x\hat i$ N. The value of $x$ is ______.

Correct answer: 32

A horizontal straight wire 5 m long extending from east to west falling freely at right angle to horizontal component of earths magnetic field $0.60\times10^{-4}$ Wb m$^{-2}$. The instantaneous value of emf induced in the wire when its velocity is 10 m s$^{-1}$ is ______ $\times10^{-3}$ V.

Correct answer: 3

A body of mass 5 kg moving with a uniform speed $3\sqrt2$ m s$^{-1}$ in X-Y plane along the line $y=x+4$. The angular momentum of the particle about the origin will be ______ kg m² s$^{-1}$.

Correct answer: 60

Hydrogen atom is bombarded with electrons accelerated through a potential difference of V, which causes excitation of hydrogen atoms. If the experiment is being performed at T = 0 K, the minimum potential difference needed to observe any Balmer series lines in the emission spectra will be $\frac\alpha{10}$ V, where $\alpha=$ ______.

Correct answer: 121

According to IUPAC system, the compound (cyclohexene ring bearing OH on the carbon adjacent to the C=C, as shown) is named as:

1. A.Cyclohex-1-en-2-ol
2. B.Cyclohex-1-en-3-ol
3. C.Cyclohex-2-en-1-ol✓
4. D.1-Hydroxyhex-2-ene

Correct answer: C

Match List I with List II. List I (Spectral Series for Hydrogen): A. Lyman; B. Balmer; C. Paschen; D. Pfund List II (Spectral Region/Higher Energy State): I. Infrared region; II. UV region; III. Infrared region; IV. Visible region Choose the correct answer from the options given below:

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

Correct answer: C

Alkyl halide is converted into alkyl isocyanide by reaction with:

1. A.$\text{NH}_4\text{CN}$
2. B.AgCN✓
3. C.KCN
4. D.NaCN

Correct answer: B

Match List I with List II. List I (Compound): A. Ethanol; B. Phenol; C. m-Nitrophenol; D. p-Nitrophenol List II ($pK_a$ Value): I. 10.0; II. 15.9; III. 7.1; IV. 8.3 Choose the correct answer from the options given below:

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

Correct answer: A

A reagent which gives brilliant red precipitate with Nickel ions in basic medium is:

1. A.dimethyl glyoxime✓
2. B.sodium nitroprusside
3. C.meta-dinitrobenzene
4. D.neutral $\text{FeCl}_3$

Correct answer: A

Given below are two statements: Statement I : Fluorine has most negative electron gain enthalpy in its group. Statement II : Oxygen has least negative electron gain enthalpy in its group. In the light of the above statements, choose the most appropriate 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 true
4. D.Both Statement I and Statement II are false

Correct answer: A

Which of the following acts as a strong reducing agent? (Atomic number: Ce = 58, Eu = 63, Gd = 64, Lu = 71)

1. A.$\text{Lu}^{3+}$
2. B.$\text{Ce}^{4+}$
3. C.$\text{Gd}^{3+}$
4. D.$\text{Eu}^{2+}$✓

Correct answer: D

Which of the following reaction is correct?

1. A.$\text{C}_2\text{H}_5\text{CONH}_2+\text{Br}_2+\text{NaOH}\to\text{C}_2\text{H}_5\text{CH}_2\text{NH}_2+\text{Na}_2\text{CO}_3+\text{NaBr}+\text{H}_2\text{O}$
2. B.Cyclohexene $+\ \text{Br}_2\xrightarrow{\Delta,\ \text{UV light}}$ 1,2-dibromocyclohexane
3. C.$\text{CH}_3\text{CH}_2\text{CH}_2\text{NH}_2\xrightarrow{\text{HNO}_2,\ 0^\circ\text{C},\ \text{H}_2\text{O}}\text{CH}_3\text{CH}_2\text{OH}+\text{N}_2+\text{HCl}$
4. D.1-Methylcyclohexene $+$ HI $\to$ 1-iodo-1-methylcyclohexane✓

Correct answer: D

On passing a gas, 'X', through Nessler's reagent, a brown precipitate is obtained. The gas 'X' is:

1. A.$\text{Cl}_2$
2. B.$\text{CO}_2$
3. C.$\text{NH}_3$✓
4. D.$\text{H}_2\text{S}$

Correct answer: C

Match List I with List II. List I (Bio polymer): A. Starch; B. Cellulose; C. Nucleic acid; D. Protein List II (Monomer): I. nucleotide; II. α-glucose; III. β-glucose; IV. α-amino acid Choose the correct answer from the options given below:

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

Correct answer: D

Which one of the following will show geometrical isomerism?

1. A.4-Bromo-1-methylidenecyclohexane (=CH$_2$ exocyclic, Br para)
2. B.3-Bromo-1-(bromomethylidene)cyclohexane (=CHBr exocyclic, Br meta)✓
3. C.4-Bromo-1-(bromomethylidene)cyclohexane (=CHBr exocyclic, Br para)
4. D.3-Bromo-1-methylidenecyclohexane (=CH$_2$ exocyclic, Br meta)

Correct answer: B

The correct IUPAC name of $\text{K}_2\text{MnO}_4$ is:

1. A.Potassium tetraoxidomanganate (VI)✓
2. B.Dipotassium tetraoxidomanganate (VII)
3. C.Potassium tetraoxopermanganate (VI)
4. D.Potassium tetraoxidomanganese (VI)

Correct answer: A

Phenol treated with chloroform in presence of sodium hydroxide, which further hydrolyzed in presence of an acid results.

1. A.Benzene-1,2-diol
2. B.2-Hydroxybenzaldehyde✓
3. C.Benzene-1,3-diol
4. D.Salicylic acid

Correct answer: B

Chromatographic technique/s based on the principle of differential adsorption is/are: A. Column chromatography B. Thin layer chromatography C. Paper chromatography Choose the most appropriate answer from the options given below:

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

Correct answer: B

The product A formed in the following reaction is: Aniline $\xrightarrow{\text{NaNO}_2\text{, HCl, }0^\circ\text{C; then Cu}_2\text{Cl}_2}$ A

1. A.Chlorobenzene✓
2. B.Anilinium chloride ($\text{C}_6\text{H}_5\overset{+}{\text{N}}\text{H}_3\text{Cl}^-$)
3. C.1,2-Dichlorobenzene
4. D.2-Chloroaniline