JEE Main 2024 — 30 Jan Shift 1 (Previous Year Paper)

Let $\vec a=a_1\hat i+a_2\hat j+a_3\hat k$ and $\vec b=b_1\hat i+b_2\hat j+b_3\hat k$ be two vectors such that $|\vec a|=1$, $\vec a\cdot\vec b=2$ and $|\vec b|=4$. If $\vec c=2(\vec a\times\vec b)-3\vec b$, then the angle between $\vec b$ and $\vec c$ is equal to:

1. A.$\cos^{-1}\left(\frac{2}{\sqrt3}\right)$
2. B.$\cos^{-1}\left(\frac23\right)$
3. C.$\cos^{-1}\left(-\frac{1}{\sqrt3}\right)$
4. D.$\cos^{-1}\left(-\frac{\sqrt3}{2}\right)$✓

Correct answer: D

If $2\sin^3x+\sin2x\cos x+4\sin x-4=0$ has exactly 3 solutions in the interval $\left[0,\frac{n\pi}{2}\right]$, $n\in N$, then the roots of the equation $x^2+nx+(n-3)=0$ belong to:

1. A.$(0,\infty)$
2. B.$\left(-\frac{\sqrt{17}}{2},\frac{\sqrt{17}}{2}\right)$
3. C.$\mathbb{Z}$
4. D.$(-\infty,0)$✓

Correct answer: D

Consider the system of linear equations $x+y+z=4\mu$, $x+2y+2\lambda z=10\mu$, $x+3y+4\lambda^2z=\mu^2+15$, where, $\lambda,\mu\in\mathbb{R}$. Which one of the following statements is NOT correct?

1. A.The system has infinite number of solutions if $\lambda=\frac12$ and $\mu=15$
2. B.The system is inconsistent if $\lambda=\frac12$ and $\mu\ne1$✓
3. C.The system is consistent if $\lambda\ne\frac12$
4. D.The system has unique solution if $\lambda\ne\frac12$ and $\mu\ne1,15$

Correct answer: B

The area (in square units) of the region bounded by the parabola $y^2=4(x-2)$ and the line $y=2x-8$, is:

1. A.9✓
2. B.8
3. C.6
4. D.7

Correct answer: A

Let M denote the median of the following frequency distribution | Class | 0-4 | 4-8 | 8-12 | 12-16 | 16-20 | | Frequency | 3 | 9 | 10 | 8 | 6 | Then 20 M is equal to:

1. A.52
2. B.208✓
3. C.104
4. D.416

Correct answer: B

A line passing through the point A(9, 0) makes an angle of 30° with the positive direction of x-axis. If this line is rotated about A through an angle of 15° in the clockwise direction, then its equation in the new position is:

1. A.$\frac{y}{\sqrt3-2}+x=9$✓
2. B.$\frac{x}{\sqrt3-2}+y=9$
3. C.$\frac{x}{\sqrt3+2}+y=9$
4. D.$\frac{y}{\sqrt3+2}+x=9$

Correct answer: A

If the domain of the function $f(x)=\cos^{-1}\left(\frac{2-|x|}{4}\right)+\{\log_e(3-x)\}^{-1}$ is $[-\alpha,\beta)-\{\gamma\}$, then $\alpha+\beta+\gamma$ is equal to:

1. A.11✓
2. B.8
3. C.12
4. D.9

Correct answer: A

Let $S_n$ denote the sum of first $n$ terms of an arithmetic progression. If $S_{20}=790$ and $S_{10}=145$, then $S_{15}-S_5$ is:

1. A.390
2. B.410
3. C.405
4. D.395✓

Correct answer: D

Let $f:\left[-\frac\pi2,\frac\pi2\right]\to\mathbb{R}$ be a differentiable function such that $f(0)=\frac12$. If the $\lim_{x\to0}\frac{x\int_0^xf(t)dt}{e^{x^2}-1}=\alpha$, then $8\alpha^2$ is equal to:

1. A.2✓
2. B.16
3. C.4
4. D.1

Correct answer: A

Let $g:\mathbb{R}\to\mathbb{R}$ be a non constant twice differentiable function such that $g'\left(\frac12\right)=g'\left(\frac32\right)$. If a real valued function $f$ is defined as $f(x)=\frac12[g(x)+g(2-x)]$, then:

1. A.$f'\left(\frac32\right)+f'\left(\frac12\right)=1$
2. B.$f''(x)=0$ for at least two $x$ in (0, 2)✓
3. C.$f''(x)=0$ for exactly one $x$ in (0, 1)
4. D.$f''(x)=0$ for no $x$ in (0, 1)

Correct answer: B

Let $y=y(x)$ be the solution of the differential equation $\sec x\,dy+\{2(1-x)\tan x+x(2-x)\}dx=0$ such that $y(0)=2$. Then $y(2)$ is equal to:

1. A.1
2. B.$2\{\sin(2)+1\}$
3. C.2✓
4. D.$2\{1-\sin(2)\}$

Correct answer: C

If $f(x)=\begin{vmatrix}2\cos^4x&2\sin^4x&3+\sin^22x\\3+2\cos^4x&2\sin^4x&\sin^22x\\2\cos^4x&3+2\sin^4x&\sin^22x\end{vmatrix}$, then $\frac15f'(0)$ is equal to:

1. A.2
2. B.6
3. C.0✓
4. D.1

Correct answer: C

If the length of the minor axis of an ellipse is equal to half of the distance between the foci, then the eccentricity of the ellipse is:

1. A.$\frac{\sqrt5}{3}$
2. B.$\frac{\sqrt3}{2}$
3. C.$\frac{1}{\sqrt3}$
4. D.$\frac{2}{\sqrt5}$✓

Correct answer: D

Two integers $x$ and $y$ are chosen with replacement from the set {0, 1, 2, 3,..., 10}. Then the probability that $|x-y|>5$, is:

1. A.$\frac{62}{121}$
2. B.$\frac{31}{121}$
3. C.$\frac{30}{121}$✓
4. D.$\frac{60}{121}$

Correct answer: C

Let $A(2,3,5)$ and $C(-3,4,-2)$ be opposite vertices of a parallelogram $ABCD$. If the diagonal $\vec{BD}=\hat i+2\hat j+3\hat k$, then the area of the parallelogram is equal to:

1. A.$\frac12\sqrt{410}$
2. B.$\frac12\sqrt{306}$
3. C.$\frac12\sqrt{586}$
4. D.$\frac12\sqrt{474}$✓

Correct answer: D

If $z=x+iy$, $xy\ne0$, satisfies the equation $z^2+i\bar z=0$, then $|z^2|$ is equal to:

1. A.$\frac14$
2. B.1✓
3. C.9
4. D.4

Correct answer: B

Let $(\alpha,\beta,\gamma)$ be the foot of perpendicular from the point (1, 2, 3) on the line $\frac{x+3}{5}=\frac{y-1}{2}=\frac{z+4}{3}$. Then $19(\alpha+\beta+\gamma)$ is equal to:

1. A.102
2. B.101✓
3. C.100
4. D.99

Correct answer: B

If the circles $(x+1)^2+(y+2)^2=r^2$ and $x^2+y^2-4x-4y+4=0$ intersect at exactly two distinct points, then:

1. A.$5<r<9$
2. B.$0<r<7$
3. C.$\frac12<r<7$
4. D.$3<r<7$✓

Correct answer: D

The maximum area of a triangle whose one vertex is at (0, 0) and the other two vertices lie on the curve $y=-2x^2+54$ at points $(x,y)$ and $(-x,y)$, where $y>0$, is:

1. A.92
2. B.122
3. C.88
4. D.108✓

Correct answer: D

The value of $\lim_{n\to\infty}\sum_{k=1}^{n}\frac{n^3}{(n^2+k^2)(n^2+3k^2)}$ is:

1. A.$\frac{(2\sqrt3+3)\pi}{24}$
2. B.$\frac{13(2\sqrt3-3)\pi}{8}$
3. C.$\frac{\pi}{8(2\sqrt3+3)}$
4. D.$\frac{13\pi}{8(4\sqrt3+3)}$✓

Correct answer: D

Let the latus rectum of the hyperbola $\frac{x^2}{9}-\frac{y^2}{b^2}=1$ subtend an angle of $\frac\pi3$ at the centre of the hyperbola. If $b^2$ is equal to $\frac lm(1+\sqrt n)$, where $l$ and $m$ are co-prime numbers, then $l^2+m^2+n^2$ is equal to ______.

Correct answer: 182

If $d_1$ is the shortest distance between the lines $x+1=2y=-12z$, $x=y+2=6z-6$ and $d_2$ is the shortest distance between the lines $\frac{x-1}{2}=\frac{y+8}{-7}=\frac{z-4}{5}$, $\frac{x-1}{2}=\frac{y-2}{1}=\frac{z-6}{-3}$, then the value of $\frac{32\sqrt3d_1}{d_2}$ is:

Correct answer: 16

A group of 40 students appeared in an examination of 3 subjects – Mathematic, Physics and Chemistry. It was found that all students passed in at least one of the subjects, 20 students passed in Mathematics, 25 students passed in Physics, 16 students passed in Chemistry, at most 11 students passed in both Mathematics and Physics, at most 15 students passed in both Physics and Chemistry, at most 15 students passed in both Mathematics and Chemistry. The maximum number of students passed in all the three subjects is ______.

Correct answer: 10

If the function $f(x)=\begin{cases}\frac{1}{|x|}, & |x|\ge2\\ ax^2+2b, & |x|<2\end{cases}$ is differentiable on $\mathbb{R}$, then $48(a+b)$ is equal to ______.

Correct answer: 15

Let $y=y(x)$ be the solution of the differential equation $(1-x^2)dy=\left[xy+(x^3+2)\sqrt{3(1-x^2)}\right]dx$, $-1<x<1$, $y(0)=0$. If $y\left(\frac12\right)=\frac mn$, $m$ and $n$ are co-prime numbers, then $m+n$ is equal to ______.

Correct answer: 97

Let $\alpha,\beta\in N$ be roots of the equation $x^2-70x+\lambda=0$, where $\frac\lambda2,\frac\lambda3\notin N$. If $\lambda$ assumes the minimum possible value, then $\frac{(\sqrt{\alpha-1}+\sqrt{\beta-1})(\lambda+35)}{|\alpha-\beta|}$ is equal to:

Correct answer: 60

Let $\alpha=1^2+4^2+8^2+13^2+19^2+26^2+\ldots$ upto 10 terms and $\beta=\sum_{n=1}^{10}n^4$. If $4\alpha-\beta=55k+40$, then $k$ is equal to ______.

Correct answer: 353

Number of integral terms in the expansion of $\left\{7^{\left(\frac12\right)}+11^{\left(\frac16\right)}\right\}^{824}$ is equal to ______.

Correct answer: 138

The value of $9\int_0^9\left[\sqrt{\frac{10x}{x+1}}\right]dx$, where $[t]$ denotes the greatest integer less than or equal to $t$, is

Correct answer: 155

Let $A=\{1,2,3,\ldots,7\}$ and let $P(A)$ denote the power set of $A$. If the number of functions $f:A\to P(A)$ such that $a\in f(a),\ \forall a\in A$ is $m^n$, $m$ and $n\in N$ and $m$ is least, then $m+n$ is equal to ______.

Correct answer: 44

The diffraction pattern of a light of wavelength 400 nm diffracting from a slit of width 0.2 mm is focused on the focal plane of a convex lens of focal length 100 cm. The width of the 1st secondary maxima will be:

1. A.0.02 mm
2. B.2 mm✓
3. C.0.2 mm
4. D.2 cm

Correct answer: B

The electric field of an electromagnetic wave in free space is represented as $\vec E=E_0\cos(\omega t-kz)\hat i$. The corresponding magnetic induction vector will be:

1. A.$\vec B=E_0C\cos(\omega t-kz)\hat j$
2. B.$\vec B=\frac{E_0}{C}\cos(\omega t-kz)\hat j$✓
3. C.$\vec B=E_0C\cos(\omega t+kz)\hat j$
4. D.$\vec B=\frac{E_0}{C}\cos(\omega t+kz)\hat j$

Correct answer: B

A particle is placed at the point A of a frictionless track ABC as shown in figure. It is gently pushed towards right. The speed of the particle when it reaches the point B is: (Take $g=10$ m/s²).

1. A.$\sqrt{10}$ m/s✓
2. B.$2\sqrt{10}$ m/s
3. C.10 m/s
4. D.20 m/s

Correct answer: A

A series L.R circuit connected with an ac source $E=(25\sin1000t)$ V has a power factor of $\frac1{\sqrt2}$. If the source of emf is changed to $E=(20\sin2000t)$ V, the new power factor of the circuit will be:

1. A.$\frac1{\sqrt3}$
2. B.$\frac1{\sqrt2}$
3. C.$\frac1{\sqrt5}$✓
4. D.$\frac1{\sqrt7}$

Correct answer: C

A Zener diode of breakdown voltage 10 V is used as a voltage regulator as shown in the figure. The current through the Zener diode is:

1. A.30 mA✓
2. B.0
3. C.20 mA
4. D.50 mA

Correct answer: A

The electrostatic potential due to an electric dipole at a distance 'r' varies as:

1. A.$r$
2. B.$\frac1r$
3. C.$\frac1{r^3}$
4. D.$\frac1{r^2}$✓

Correct answer: D

Young's modules of material of a wire of length 'L' and cross-sectional area A is Y. If the length of the wire is doubled and cross-sectional area is halved then Young's modules will be:

1. A.$Y$✓
2. B.$2Y$
3. C.$\frac Y4$
4. D.$4Y$

Correct answer: A

All surfaces shown in figure are assumed to be frictionless and the pulleys and the string are light. The acceleration of the block of mass 2 kg is:

1. A.$\frac g3$✓
2. B.$\frac g2$
3. C.$\frac g4$
4. D.$g$

Correct answer: A

A particle of mass $m$ is projected with a velocity '$u$' making an angle of 30° with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when the particle is at its maximum height $h$ is:

1. A.$\frac{\sqrt3}{16}\frac{mu^3}{g}$✓
2. B.$\frac{mu^3}{\sqrt2g}$
3. C.$\frac{\sqrt3}{2}\frac{mu^2}{g}$
4. D.zero

Correct answer: A

At which temperature the r.m.s velocity of a hydrogen molecule equal to that of an oxygen molecule at 47°C?

1. A.−73 K
2. B.20 K✓
3. C.80 K
4. D.4 K

Correct answer: B

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

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

Correct answer: A

A potential divider circuit is shown in figure. The output voltage $V_0$ is:

1. A.12 mV
2. B.0.5 V✓
3. C.4 V
4. D.2 mV

Correct answer: B

Primary coil of a transformer is connected to 220 V ac. Primary and secondary turns of the transforms are 100 and 10 respectively. Secondary coil of transformer is connected to two series resistances shown in figure. The output voltage $(V_0)$ is:

1. A.15 V
2. B.44 V
3. C.22 V
4. D.7 V✓

Correct answer: D

Two insulated circular loop A and B of radius 'a' carrying a current of 'I' in the anti clockwise direction as shown in the figure. The magnitude of the magnetic induction at the centre will be:

1. A.$\frac{2\mu_0I}{a}$
2. B.$\frac{\mu_0I}{\sqrt2a}$✓
3. C.$\frac{\sqrt2\mu_0I}{a}$
4. D.$\frac{\mu_0I}{2a}$

Correct answer: B

The work function of a substance is 3.0 eV. The longest wavelength of light that can cause the emission of photoelectrons from this substance is approximately.

1. A.400 nm
2. B.200 nm
3. C.414 nm✓
4. D.215 nm

Correct answer: C

The gravitational potential at a point above the surface of earth is $-5.12\times10^7$ J/kg and the acceleration due to gravity at that point is 6.4 m/s². Assume that the mean radius of earth to be 6400 km. The height of this point above the earth's surface is:

1. A.1200 km
2. B.1600 km✓
3. C.1000 km
4. D.540 km

Correct answer: B

An electric toaster has resistance of 60 Ω at room temperature (27 °C). The toaster is connected to a 220 V supply. If the current flowing through it reaches 2.75 A, the temperature attained by toaster is around: (if $\alpha=2\times10^{-4}$/°C)

1. A.1694°C✓
2. B.1667°C
3. C.694°C
4. D.1235°C

Correct answer: A

A spherical body of mass 100 g is dropped from a height of 10 m from the ground. After hitting the ground, the body rebounds to a height of 5 m. The impulse of force impaired by the ground to the body is given by : (given, $g=9.8$ m/s²)

1. A.43.2 kg m s$^{-1}$
2. B.2.39 kg m s$^{-1}$✓
3. C.23.9 kg m s$^{-1}$
4. D.4.32 kg m s$^{-1}$

Correct answer: B

The ratio of the magnitude of the kinetic energy to the potential energy of an electron in the 5th excited state of a hydrogen atom is:

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

Correct answer: C

A capacitor of capacitance C and potential V has energy E. It is connected to another capacitor of capacitance 2C and potential 2V. Then the loss of energy is $\frac x3E$, where $x$ is ______.

Correct answer: 2

The displacement and the increase in the velocity of a moving particle in the time interval of $t$ to $(t+1)$ s are 125 m and 50 m/s, respectively. The distance travelled by the particle in $(t+2)^{th}$ s is ______ m.

Correct answer: 175

A electron of hydrogen atom on an excited state is having energy $E_n=-0.85$ eV. The maximum number of allowed transitions to lower energy level is ______.

Correct answer: 6

Consider a Disc of mass 5 kg, radius 2 m, rotating with angular velocity of 10 rad/s about an axis perpendicular to the plane of rotation. An identical disc is kept gently over the rotating disc along the same axis. The energy dissipated so that both the discs continue to rotate together without slipping is ______ J.

Correct answer: 250

In a closed organ pipe, the frequence of fundamental note is 30 Hz. A certain amount of water is now poured in the organ pipe so that the fundamental frequency is increased to 110 Hz. If the organ pipe has a cross-sectional area of 2 cm², the amount of water poured in the organ tube is ______ g. (Take speed of sound in air is 330 m/s)

Correct answer: 400

A ceiling fan having 3 blades of length 80 cm each is rotating with an angular velocity of 1200 rpm. The magnetic field of earth in that region is 0.5 G and angle of dip is 30°. The emf induced across the blades is $N\pi\times10^{-5}$ V. The value of N is ______.

Correct answer: 32

Two cells are connected in opposition as shown. Cell $E_1$ is of 8 V emf and 2 Ω internal resistance; the cell $E_2$ is of 2 V emf and 4 Ω internal resistance. The terminal potential difference of cell $E_2$ is ______ V.

Correct answer: 6

The distance between object and its two times magnified real image as produced by a convex lens is 45 cm. The focal length of the lens used is ______ cm.

Correct answer: 10

Each of three blocks P, Q and R shown in figure has a mass of 3 kg. Each of the wires A and B has cross-sectional area 0.005 cm² and Young's modulus $2\times10^{11}$ N m$^{-2}$. Neglecting friction, the longitudinal strain on wire B is ______ $\times10^{-4}$. (Take $g=10$ m/s²)

Correct answer: 2

The horizontal component of earth's magnetic field at a place is $3.5\times10^{-5}$ T. A very long straight conductor carrying current of $\sqrt2$ A in the direction from South-East to North-West is placed. The force per unit length experienced by the conductor is ______ $\times10^{-6}$ N/m.

Correct answer: 35

Example of vinylic halide is:

1. A.(Halomethylidene)cyclohexane — X on an exocyclic =CH– carbon✓
2. B.1-(Halomethyl)cyclohexene — CH$_2$X on a ring C=C carbon
3. C.Halobenzene-type: X on a benzene ring
4. D.3-Halocyclohexene — X on the sp$^3$ carbon next to C=C

Correct answer: A

$\text{C}_6\text{H}_5\text{COCl}\xrightarrow{\text{H}_2,\ \text{Pd-BaSO}_4}\text{C}_6\text{H}_5\text{CHO}$ This reduction reaction is known as:

1. A.Rosenmund reduction✓
2. B.Etard reduction
3. C.Wolff-Kishner reduction
4. D.Stephen reduction

Correct answer: A

Choose the correct statements from the following: (A) Ethane-1, 2-diamine is a chelating ligand. (B) Metallic aluminium is produced by electrolysis of aluminium oxide in presence of cryolite. (C) Cyanide ion is used as ligand for leaching of silver. (D) Phosphine act as a ligand in Wilkinson catalyst. (E) The stability constants of $\text{Ca}^{2+}$ and $\text{Mg}^{2+}$ are similar with EDTA complexes. Choose the correct answer from the options given below:

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

Correct answer: B

The final product A, formed in the following multistep reaction sequence is: Bromobenzene $\xrightarrow{\text{(i) Mg, ether then CO}_2\text{, H}^+\ \text{(ii) NH}_3,\ \Delta\ \text{(iii) Br}_2\text{, NaOH}}$ A

1. A.Benzamide
2. B.Benzoyl bromide
3. C.Aniline✓
4. D.Benzoic acid

Correct answer: C

Given below are two statements: Statement (I): The gas liberated on warming a salt with dil $\text{H}_2\text{SO}_4$, turns a piece of paper dipped in lead acetate into black, it is a confirmatory test for sulphide ion. Statement (II): In statement-I the colour of paper turns black because of formation of lead sulphite. In the light of the above statements, choose the most appropriate 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 true
4. D.Both Statement I and Statement II are false

Correct answer: B

Match List-I with List-II. List-I (Species): (A) $\text{Cr}^{+2}$; (B) $\text{Mn}^+$; (C) $\text{Ni}^{+2}$; (D) $\text{V}^+$ List-II (Electronic distribution): (I) $3d^8$; (II) $3d^34s^1$; (III) $3d^4$; (IV) $3d^54s^1$ Choose the correct answer from the options given below:

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

Correct answer: C

Match List-I with List-II. List-I (Molecule): (A) $\text{BrF}_5$; (B) $\text{H}_2\text{O}$; (C) $\text{ClF}_3$; (D) $\text{SF}_4$ List-II (Shape): (I) T-shape; (II) See saw; (III) Bent; (IV) Square pyramidal Choose the correct answer from the options given below:

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

Correct answer: B

Structure of 4-Methylpent-2-enal is:

1. A.$\text{CH}_3\text{-CH}_2\text{-C(CH}_3\text{)=CH-CHO}$
2. B.$\text{CH}_3\text{-CH(CH}_3\text{)-CH=CH-CHO}$✓
3. C.$\text{H}_2\text{C=CH-CH(CH}_3\text{)-CH}_2\text{-CHO}$
4. D.$\text{CH}_3\text{-CH}_2\text{-CH=C(CH}_3\text{)-CHO}$

Correct answer: B

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): There is a considerable increase in covalent radius from N to P. However from As to Bi only a small increase in covalent radius is observed. Reason (R): Covalent and ionic radii in a particular oxidation state increases down the group. In the light of the above statements, choose the most appropriate 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 false but (R) is true
3. C.Both (A) and (R) are true and (R) is the correct explanation of (A)
4. D.(A) is true but (R) is false

Correct answer: A

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): $\text{CH}_2=\text{CH-CH}_2\text{-Cl}$ is an example of allyl halide. Reason (R): Allyl halides are the compounds in which the halogen atom is attached to $sp^2$ hybridized carbon atom. In the light of the above statements, choose the most appropriate 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 false but (R) is true
3. C.Both (A) and (R) are true and (R) is the correct explanation of (A)
4. D.(A) is true but (R) is false✓

Correct answer: D

Diamagnetic Lanthanoid ions are:

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

Correct answer: A

Following is a confirmatory test for aromatic primary amines. Identify reagent (A) and (B). Aniline $\xrightarrow{(A)}$ benzenediazonium chloride $\xrightarrow[\text{NaOH}]{(B)}$ Scarlet red dye

1. A.A = $\text{NaNO}_2$ + HCl, 0–5°C; B = 1-naphthol (α-naphthol)
2. B.A = $\text{NaNO}_2$ + HCl, 0–5°C; B = aniline
3. C.A = $\text{NaNO}_2$ + HCl, 0–5°C; B = 2-naphthol (β-naphthol)✓
4. D.A = $\text{HNO}_3/\text{H}_2\text{SO}_4$; B = phenol

Correct answer: C

Which of the following molecule/species is most stable?

1. A.Cyclopropenyl carbene/anion species (lone pair on the sp$^3$ carbon of cyclopropene)
2. B.1,3-Cyclohexadiene
3. C.Cyclopropenyl cation✓
4. D.Cyclopentadienyl cation

Correct answer: C

Compound A formed in the following reaction reacts with B gives the product C. Find out A and B. $\text{CH}_3\text{-C}\equiv\text{CH}+\text{Na}\to A\xrightarrow{B}\text{CH}_3\text{-C}\equiv\text{C-CH}_2\text{-CH}_2\text{-CH}_3\ (C)+\text{NaBr}$

1. A.A = $\text{CH}_3\text{-C}\equiv\overset{-}{\text{C}}\overset{+}{\text{Na}}$, B = $\text{CH}_3\text{-CH}_2\text{-CH}_3$
2. B.A = $\text{CH}_3\text{-CH=CH}_2$, B = $\text{CH}_3\text{-CH}_2\text{-CH}_2\text{-Br}$
3. C.A = $\text{CH}_3\text{-C}\equiv\overset{-}{\text{C}}\overset{+}{\text{Na}}$, B = $\text{CH}_3\text{-CH}_2\text{-CH}_2\text{-Br}$✓
4. D.A = $\text{CH}_3\text{-CH}_2\text{-CH}_3$, B = $\text{CH}_3\text{-C}\equiv\text{CH}$

Correct answer: C

Given below are two statements: Statement (I): The orbitals having same energy are called as degenerate orbitals. Statement (II): In hydrogen atom, 3p and 3d orbitals are not degenerate orbitals. In the light of the above statements, choose the most appropriate 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

What happens to freezing point of benzene when small quantity of naphthalene is added to benzene?

1. A.First decreases and then increases
2. B.Decreases✓
3. C.Remains unchanged
4. D.Increases

Correct answer: B

Aluminium chloride in acidified aqueous solution forms an ion having geometry.

1. A.Trigonal bipyramidal
2. B.Tetrahedral
3. C.Square planar
4. D.Octahedral✓

Correct answer: D