JEE Main 2024 — 31 Jan Shift 2 (Previous Year Paper)

The temperature $T(t)$ of a body at time $t=0$ is 160°F and it decreases continuously as per the differential equation $\frac{dT}{dt}=-K(T-80)$, where K is a positive constant. If $T(15)=120$°F, then $T(45)$ is equal to:

1. A.85°F
2. B.90°F✓
3. C.95°F
4. D.80°F

Correct answer: B

If the function $f:(-\infty,-1]\to(a,b]$ defined by $f(x)=e^{x^3-3x+1}$ is one – one and onto, then the distance of the point $P(2b+4,a+2)$ from the line $x+e^{-3}y=4$ is:

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

Correct answer: C

If $a=\sin^{-1}(\sin5)$ and $b=\cos^{-1}(\cos5)$, then $a^2+b^2$ is equal to:

1. A.$8\pi^2-40\pi+50$✓
2. B.$4\pi^2+25$
3. C.$4\pi^2-20\pi+50$
4. D.25

Correct answer: A

Let P be a parabola with vertex (2, 3) and directrix $2x+y=6$. Let an ellipse $E:\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$, $a>b$, of eccentricity $\frac{1}{\sqrt2}$ pass through the focus of the parabola P. Then, the square of the length of the latus rectum of E, is:

1. A.$\frac{512}{25}$
2. B.$\frac{385}{8}$
3. C.$\frac{656}{25}$✓
4. D.$\frac{347}{8}$

Correct answer: C

The number of solutions, of the equation $e^{\sin x}-2e^{-\sin x}=2$, is:

1. A.More than 2
2. B.0✓
3. C.1
4. D.2

Correct answer: B

Let the mean and the variance of 6 observations a, b, 68, 44, 48, 60 be 55 and 194, respectively. If a > b, then a + 3b is:

1. A.210
2. B.180✓
3. C.200
4. D.190

Correct answer: B

A coin is biased so that a head is twice as likely to occur as a tail. If the coin is tossed 3 times, then the probability of getting two tails and one head is:

1. A.$\frac19$
2. B.$\frac29$✓
3. C.$\frac2{27}$
4. D.$\frac1{27}$

Correct answer: B

If for some $m,n$: ${}^6C_m+2\left({}^6C_{m+1}\right)+{}^6C_{m+2}>{}^8C_3$ and ${}^{n-1}P_3:{}^nP_4=1:8$ then ${}^nP_{m+1}+{}^{n+1}C_m$ is equal to:

1. A.380
2. B.372✓
3. C.376
4. D.384

Correct answer: B

Let $f:\mathbb{R}\to(0,\infty)$ be strictly increasing function such that $\lim_{x\to\infty}\frac{f(7x)}{f(x)}=1$. Then, the value of $\lim_{x\to\infty}\left[\frac{f(5x)}{f(x)}-1\right]$ is equal to:

1. A.0✓
2. B.1
3. C.$\frac75$
4. D.4

Correct answer: A

Let $A(a,b)$, $B(3,4)$ and $C(-6,-8)$ respectively denote the centroid, circumcentre and orthocentre of a triangle. Then, the distance of the point $P(2a+3,7b+5)$ from the line $2x+3y-4=0$ measured parallel to the line $x-2y-1=0$ is:

1. A.$\frac{\sqrt5}{17}$
2. B.$\frac{17\sqrt5}{7}$✓
3. C.$\frac{15\sqrt5}{7}$
4. D.$\frac{14\sqrt5}{6}$

Correct answer: B

Let $f,g:(0,\infty)\to\mathbb{R}$ be two functions defined by $f(x)=\int_{-x}^{x}(|t|-t^2)e^{-t^2}dt$ and $g(x)=\int_0^{x^2}t^{1/2}e^{-t}dt$. Then, the value of $9\left(f\left(\sqrt{\log_e9}\right)+g\left(\sqrt{\log_e9}\right)\right)$ is equal to:

1. A.6
2. B.10
3. C.9
4. D.8✓

Correct answer: D

The shortest distance, between lines $L_1$ and $L_2$, where $L_1:\frac{x-1}{2}=\frac{y+1}{-3}=\frac{z+4}{2}$ and $L_2$ is the line, passing through the points $A(-4,4,3)$, $B(-1,6,3)$ and perpendicular to the line $\frac{x-3}{-2}=\frac y3=\frac{z-1}{1}$, is:

1. A.$\frac{141}{\sqrt{221}}$✓
2. B.$\frac{42}{\sqrt{117}}$
3. C.$\frac{24}{\sqrt{117}}$
4. D.$\frac{121}{\sqrt{221}}$

Correct answer: A

The number of ways in which 21 identical apples can be distributed among three children such that each child gets at least 2 apples, is:

1. A.142
2. B.130
3. C.136✓
4. D.406

Correct answer: C

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

1. A.34
2. B.31
3. C.33✓
4. D.32

Correct answer: C

The area of the region enclosed by the parabolas $y=4x-x^2$ and $3y=(x-4)^2$ is equal to:

1. A.4
2. B.$\frac{32}{9}$
3. C.$\frac{14}{3}$
4. D.6✓

Correct answer: D

Let $2^{nd}$, $8^{th}$ and $44^{th}$ terms of a non-constant A.P. be respectively the $1^{st}$, $2^{nd}$ and $3^{rd}$ terms of a G.P. If the first term of the A.P. is 1, then the sum of its first 20 terms is equal to:

1. A.980
2. B.970✓
3. C.960
4. D.990

Correct answer: B

Let $z_1$ and $z_2$ be two complex numbers such that $z_1+z_2=5$ and $z_1^3+z_2^3=20+15i$. Then, $|z_1^4+z_2^4|$ equals:

1. A.$25\sqrt3$
2. B.75✓
3. C.$15\sqrt{15}$
4. D.$30\sqrt3$

Correct answer: B

Consider the function $f:(0,\infty)\to\mathbb{R}$ defined by $f(x)=e^{-|\log_ex|}$. If $m$ and $n$ be respectively the number of points at which $f$ is not continuous and $f$ is not differentiable, then $m+n$ is:

1. A.3
2. B.0
3. C.1✓
4. D.2

Correct answer: C

Let a variable line passing through the centre of the circle $x^2+y^2-16x-4y=0$, meet the positive co-ordinate axes at the points A and B. Then the minimum value of OA + OB, where O is the origin, is equal to:

1. A.18✓
2. B.12
3. C.20
4. D.24

Correct answer: A

Let A be a $3\times3$ real matrix such that $A\begin{pmatrix}1\\0\\1\end{pmatrix}=2\begin{pmatrix}1\\0\\1\end{pmatrix}$, $A\begin{pmatrix}-1\\0\\1\end{pmatrix}=4\begin{pmatrix}-1\\0\\1\end{pmatrix}$, $A\begin{pmatrix}0\\1\\0\end{pmatrix}=2\begin{pmatrix}0\\1\\0\end{pmatrix}$. Then, the system $(A-3I)\begin{pmatrix}x\\y\\z\end{pmatrix}=\begin{pmatrix}1\\2\\3\end{pmatrix}$ has.

1. A.Exactly two solutions
2. B.Unique solutions✓
3. C.Infinitely many solutions
4. D.No solution

Correct answer: B

Let $a,b,c$ be the lengths of three sides of a triangle satisfying the condition $(a^2+b^2)x^2-2b(a+c)x+(b^2+c^2)=0$. If the set of all possible values of $x$ is the interval $(\alpha,\beta)$ then $12(\alpha^2+\beta^2)$ is equal to ______.

Correct answer: 36

Let $A=\{1,2,3,\ldots,100\}$. Let R be a relation on A defined by $(x,y)\in R$ if and only if $2x=3y$. Let $R_1$ be a symmetric relation on A such that $R\subset R_1$ and the number of elements in $R_1$ is n. Then the minimum value of n is ______.

Correct answer: 66

Let $\vec a=3\hat i+2\hat j+\hat k$, $\vec b=2\hat i-\hat j+3\hat k$ and $\vec c$ be a vector such that $(\vec a+\vec b)\times\vec c=2(\vec a\times\vec b)+24\hat j-6\hat k$ and $(\vec a-\vec b+\hat i)\cdot\vec c=-3$. Then $|\vec c|^2$ is equal to ______.

Correct answer: 38

$\left|\frac{120}{\pi^3}\int_0^\pi\frac{x^2\sin x\cos x}{\sin^4x+\cos^4x}dx\right|$ is equal to ______.

Correct answer: 15

If $\lim_{x\to0}\frac{ax^2e^x-b\log_e(1+x)+cxe^{-x}}{x^2\sin x}=1$, then $16(a^2+b^2+c^2)$ is equal to ______.

Correct answer: 81

Let $A(-2,-1)$, $B(1,0)$, $C(\alpha,\beta)$ and $D(\gamma,\delta)$ be the vertices of a parallelogram ABCD. If the point C lies on $2x-y=5$ and the point D lies on $3x-2y=6$, then the value of $|\alpha+\beta+\gamma+\delta|$ is equal to ______.

Correct answer: 32

A line passes through $A(4,-6,-2)$ and $B(16,-2,4)$. The point $P(a,b,c)$, where a, b, c are non-negative integers, on the line AB lies at a distance of 21 units, from the point A. The distance between the points $P(a,b,c)$ and $Q(4,-12,3)$ is equal to ______.

Correct answer: 22

Let the coefficient of $x^r$ in the expansion of $(x+3)^{n-1}+(x+3)^{n-2}(x+2)+(x+3)^{n-3}(x+2)^2+\ldots+(x+2)^{n-1}$ be $\alpha_r$. If $\sum_{r=0}^n\alpha_r=\beta^n-\gamma^n$, $\beta,\gamma\in\mathbb{N}$, then the value of $\beta^2+\gamma^2$ equals ______.

Correct answer: 25

Let A be $3\times3$ matrix and det$(A)=2$. If $n=\det(\underbrace{\text{adj}(\text{adj}(\ldots(\text{adj}A)))}_{2024\text{ times}})$, then the remainder when $n$ is divided by 9 is equal to ______.

Correct answer: 7

Let $y=y(x)$ be the solution of the differential equation $\sec^2x\,dx+\left(e^{2y}\tan^2x+\tan x\right)dy=0$, $0<x<\frac\pi2$, $y\left(\frac\pi4\right)=0$. If $y\left(\frac\pi6\right)=\alpha$, then $e^{8\alpha}$ is equal to ______.

Correct answer: 9

A gas mixture consists of 8 moles of argon and 6 moles of oxygen at temperature T. Neglecting all vibrational modes, the total internal energy of the system is:

1. A.27 RT✓
2. B.21 RT
3. C.20 RT
4. D.29 RT

Correct answer: A

Given below are two statements: Statement I : Electromagnetic waves carry energy as they travel through space and this energy is equally shared by the electric and magnetic fields. Statement II : When electromagnetic waves strike a surface, a pressure is exerted on the surface. In the light of the above statements, choose the most appropriate answer from the options given below:

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

Correct answer: A

In a photoelectric effect experiment a light of frequency 1.5 times the threshold frequency is made to fall on the surface of photosensitive material. Now if the frequency is halved and intensity is doubled, the number of photo electron emitted will be:

1. A.Zero✓
2. B.Quadrupled
3. C.Halved
4. D.Doubled

Correct answer: A

The resistance per centimeter of a meter bridge wire is r, with XΩ resistance in left gap. Balancing length from left end is at 40 cm with 25Ω resistance in right gap. Now the wire is replaced by another wire of 2r resistance per centimeter. The new balancing length for same setting will be at :

1. A.20 cm
2. B.40 cm✓
3. C.80 cm
4. D.10 cm

Correct answer: B

Force between two point charges $q_1$ and $q_2$ placed in vacuum at 'r' cm apart is F. Force between them when placed in a medium having dielectric constant K = 5 at 'r/5' cm apart will be:

1. A.25F
2. B.F/25
3. C.5F✓
4. D.F/5

Correct answer: C

The mass of the moon is $\frac1{144}$ times the mass of a planet and its diameter is $\frac1{16}$ times the diameter of a planet. If the escape velocity on the planet is v, the escape velocity on the moon will be:

1. A.$\frac v6$
2. B.$\frac v4$
3. C.$\frac v3$✓
4. D.$\frac v{12}$

Correct answer: C

A uniform magnetic field of $2\times10^{-3}$ T acts along positive Y-direction. A rectangular loop of sides 20 cm and 10 cm with current of 5A is in Y – Z plane. The current is in anticlockwise sense with reference to negative X axis. Magnitude and direction of the torque is:

1. A.$2\times10^{-4}$ N-m along positive X-direction
2. B.$2\times10^{-4}$ N-m along positive Y-direction
3. C.$2\times10^{-4}$ N-m along positive Z-direction
4. D.$2\times10^{-4}$ N-m along negative Z-direction✓

Correct answer: D

Consider two physical quantities A and B related to each other as $E=\frac{B-x^2}{At}$ where E, x and t have dimensions of energy, length and time respectively. The dimension of AB is:

1. A.$L^0M^{-1}T^1$
2. B.$L^{-2}M^{-1}T^1$
3. C.$L^{-2}M^1T^0$
4. D.$L^2M^{-1}T^1$✓

Correct answer: D

The output of the given circuit diagram is:

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

Correct answer: D

The speed of sound in oxygen at S.T.P. will be approximately : (given, R = 8.3 J K$^{-1}$, γ = 1.4)

1. A.333 m/s
2. B.341 m/s
3. C.310 m/s✓
4. D.325 m/s

Correct answer: C

If two vectors $\vec A$ and $\vec B$ having equal magnitude R are inclined at an angle θ, then :

1. A.$|\vec A+\vec B|=2R\cos\left(\frac\theta2\right)$✓
2. B.$|\vec A-\vec B|=2R\cos\left(\frac\theta2\right)$
3. C.$|\vec A+\vec B|=2R\sin\left(\frac\theta2\right)$
4. D.$|\vec A-\vec B|=\sqrt2R\sin\left(\frac\theta2\right)$

Correct answer: A

The mass number of nucleus having radius equal to half of the radius of nucleus with mass number 192 is:

1. A.20
2. B.32
3. C.40
4. D.24✓

Correct answer: D

When unpolarized light is incident at an angle of 60° on a transparent medium from air, the reflected ray is completely polarized. The angle of refraction in the medium is :

1. A.30°✓
2. B.45°
3. C.60°
4. D.90°

Correct answer: A

A light string passing over a smooth light fixed pulley connects two blocks of masses $m_1$ and $m_2$. If the acceleration of the system is g/8, then the ratio masses is:

1. A.$\frac97$✓
2. B.$\frac53$
3. C.$\frac81$
4. D.$\frac43$

Correct answer: A

AN AC voltage $V=20\sin200\pi t$ is applied to a series LCR circuit which drives a current $I=10\sin\left(200\pi t+\frac\pi3\right)$. The average power dissipated is:

1. A.21.6 W
2. B.50 W✓
3. C.200 W
4. D.173.2 W

Correct answer: B

A body of mass 2 kg begins to move under the action of a time dependent force given by $\vec F=(6t\hat i+6t^2\hat j)$ N. The power developed by the force at the time t is given by:

1. A.$(6t^4+9t^5)$ W
2. B.$(3t^3+6t^5)$ W
3. C.$(9t^5+6t^3)$ W
4. D.$(9t^3+6t^5)$ W✓

Correct answer: D

By what percentage will the illumination of the lamp decrease if the current drops by 20%?

1. A.36 %✓
2. B.56%
3. C.46%
4. D.26%

Correct answer: A

A small spherical ball of radius r, falling through a viscous medium of negligible density has terminal velocity 'v'. Another ball of the same mass but of radius 2r, falling through the same viscous medium will have terminal velocity:

1. A.$\frac v4$
2. B.$4v$
3. C.$2v$
4. D.$\frac v2$✓

Correct answer: D

The measured value of the length of a simple pendulum is 20 cm with 2mm accuracy. The time for 50 oscillations was measured to be 40 seconds with 1 second resolution. From these measurements, the accuracy in the measurement of acceleration due to gravity is N%. The value of N is:

1. A.6✓
2. B.8
3. C.5
4. D.4

Correct answer: A

A nucleus has mass number $A_1$ and volume $V_1$. Another nucleus has mass number $A_2$ and Volume $V_2$. If relation between mass number is $A_2=4A_1$ then $\frac{V_2}{V_1}=$ ______.

Correct answer: 4

Two circular coils P and Q of 100 turns each have same radius of π cm. The currents in P and R are 1A and 2A respectively. P and Q are placed with their planes mutually perpendicular with their centres coincide. The resultant magnetic field induction at the centre of the coils is $\sqrt x$ mT, where $x$ ______. [Use $\mu_0=4\pi\times10^{-7}$ T m A$^{-1}$]

Correct answer: 20

The time period of simple harmonic motion of mass M in the given figure is $\pi\sqrt{\frac{\alpha M}{5k}}$, where the value of α is ______.

Correct answer: 12

Light from a point source in air falls on a convex curved surface of radius 20 cm and refractive index 1.5. If the source is located at 100 cm from the convex surface, the image will be formed at ______ cm from the object.

Correct answer: 200

In the following circuit, the battery has an emf 2V and an internal resistance of $\frac23$Ω. The power consumption in the entire circuit is ______ W.

Correct answer: 3

Two blocks of mass 2kg and 4 kg are connected by a metal wire going over a smooth pulley as show in figure. The radius of wire is $4.0\times10^{-5}$ m and Young's modulus of the metal is $2.0\times10^{11}$ N/m². The longitudinal strain developed in the wire is $\frac{1}{\alpha\pi}$. The value of α is ______. [Use g = 10 m/s²]

Correct answer: 12

The distance between charges +q and – q is 2l and between +2q and – 2q is 4l. The electrostatic potential at point P at a distance r from centre O is $-\alpha\left[\frac{ql}{r^2}\right]\times10^9$ V, where the value of α is ______. [Use $\frac1{4\pi\epsilon_0}=9\times10^9$ N m² C$^{-2}$]

Correct answer: 27

A body of mass 'm' is projected with a speed 'u' making an angle of 45° with the ground. The angular momentum of the body about the point of projection, at the highest point is expressed as $\frac{\sqrt2mu^3}{Xg}$. The value of 'X' is ______.

Correct answer: 8

Two identical spheres each of mass 2kg and radius 50 cm are fixed at the ends of a light rod so that the separation between the centres is 150 cm. then, moment of inertia of the system about an axis perpendicular to the rod and passing through its middle point is $\frac{x}{20}$ kg m², where the value of x is ______.

Correct answer: 53

The magnetic flux φ (in weber) linked with a closed circuit of resistance 8Ω varies with time (in seconds) as $\phi=5t^2-36t+1$. The induced current in the circuit at t = 2s is ______ A.

Correct answer: 2

Given below are two statements : Statements I : $\text{S}_8$ solid undergoes disproportionation reaction under alkaline conditions to from $\text{S}^{2-}$ and $\text{S}_2\text{O}_3^{2-}$. Statement II : $\text{ClO}_4^-$ can undergo disproportionation reaction under acidic condition. In the light of the above statements, choose the most appropriate answer from the options given below:

1. A.Both statement I and statement II are incorrect
2. B.Statement I is incorrect but statement II is correct
3. C.Both statement I and statement II are correct
4. D.Statement I is correct but statement II is incorrect✓

Correct answer: D

Which of the following is least ionic ?

1. A.KCl
2. B.$\text{CoCl}_2$
3. C.AgCl✓
4. D.$\text{BaCl}_2$

Correct answer: C

The four quantum numbers for the electron in the outer most orbital of potassium (atomic no. 19) are:

1. A.n = 3, l = 0, m = 1, s = +1/2
2. B.n = 2, l = 0, m = 0, s = +1/2
3. C.n = 4, l = 0, m = 0, s = +1/2✓
4. D.n = 4, l = 2, m = −1, s = +1/2

Correct answer: C

Identify major product 'P' formed in the following reaction. Benzene + Benzoyl chloride $\xrightarrow{\text{Anhydrous AlCl}_3}$ 'P' (Major Product)

1. A.Benzaldehyde
2. B.Benzophenone✓
3. C.Acetophenone
4. D.3-Phenoxybenzoyl chloride

Correct answer: B

The azo-dye (Y) formed in the following reaction is. Sulphanilic acid + $\text{NaNO}_2$ + $\text{CH}_3\text{COOH}\to$ X. X + 1-naphthylamine → Y

1. A.$\text{HO}_3\text{S-C}_6\text{H}_4\text{-N=N-}$ naphthyl with $\text{NH}_2$ on the other ring
2. B.bis-azo compound (two $p$-sulphophenylazo groups on naphthalene)
3. C.structure with two sulphonic-acid-bearing rings and two azo links
4. D.$\text{HO}_3\text{S-C}_6\text{H}_4\text{-N=N-}$ at C-4 of 1-naphthylamine (4-amino-1-naphthyl azo, para to $\text{NH}_2$)✓

Correct answer: D

The fragrance of flowers is due to the presence of some steam volatile organic compounds called essential oils. These are generally insoluble in water at room temperature but are miscible with water vapour in vapour phase. A suitable method for the extraction of these oils from the flower is:

1. A.Crystallisation
2. B.Steam distillation✓
3. C.Distillation under reduced pressure
4. D.Distillation

Correct answer: B

Identify the name reaction. Benzene $\xrightarrow{\text{CO, HCl, Anhyd. AlCl}_3/\text{CuCl}}$ Benzaldehyde

1. A.Gatterman – Koch Reaction✓
2. B.Etard Reaction
3. C.Stephen Reaction
4. D.Rosenmund Reduction

Correct answer: A

Major product of the following reaction is: 1-Methylcyclopentene $\xrightarrow{\text{D-Cl}}$ ?

1. A.C1 carries H and Cl, C2 carries D and $\text{CH}_3$
2. B.C1 carries D and H... (D, $\text{CH}_3$ up on adjacent carbons; H, Cl down): D on C-2 with H, $\text{CH}_3$ and Cl on C-1✓
3. C.Cl and D up, H and $\text{CH}_3$ down on adjacent carbons
4. D.D and Cl up, H and $\text{CH}_3$ down on adjacent carbons

Correct answer: B

The correct order of reactivity in electrophilic substitution reaction of the following compounds is: A = benzene, B = toluene, C = chlorobenzene, D = nitrobenzene

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

Correct answer: C

Select the option with correct property:

1. A.$[\text{Ni(CO)}_4]$ and $[\text{NiCl}_4]^{2-}$ both Paramagnetic
2. B.$[\text{NiCl}_4]^{2-}$ Diamagnetic, $[\text{Ni(CO)}_4]$ Paramagnetic
3. C.$[\text{Ni(CO)}_4]$ and $[\text{NiCl}_4]^{2-}$ both Diamagnetic
4. D.$[\text{Ni(CO)}_4]$ Diamagnetic, $[\text{NiCl}_4]^{2-}$ Paramagnetic✓

Correct answer: D

Given below are two statements: Statement I : Aniline reacts with con. $\text{H}_2\text{SO}_4$, followed by heating at 453-473K gives p-aminobenzene sulphonic acid, which gives blood red colour in the 'Lassaigne's test' Statement II : In Friedel – Craft's alkylation and acylation reactions, aniline forms salt with the $\text{AlCl}_3$ catalyst. Due to this, nitrogen of aniline aquires a positive charge and acts as deactivating group. 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.Both statement I and statement II are true✓
3. C.Statement I is true but statement II is false
4. D.Both statement I and statement II are false

Correct answer: B

$\text{A}_{(g)}\rightleftharpoons\text{B}_{(g)}+\frac{\text{C}}{2}(g)$. The correct relationship between $K_P$, α and equilibrium pressure P is:

1. A.$K_P=\frac{\alpha^{1/2}P^{3/2}}{(2+\alpha)^{3/2}}$
2. B.$K_P=\frac{\alpha^{1/2}P^{1/2}}{(2+\alpha)^{3/2}}$
3. C.$K_P=\frac{\alpha^{1/2}P^{1/2}}{(2+\alpha)^{1/2}}$
4. D.$K_P=\frac{\alpha^{3/2}P^{1/2}}{(2+\alpha)^{1/2}(1-\alpha)}$✓

Correct answer: D

Consider the following elements. A' and B' are in the same period (B' to the right of A'); C' and D' are below A' and B' respectively in the next period (Group ↓, Period →). Which of the following is/are true about A', B', C' and D'? A. Order of atomic radii : B' < A' < D' < C' B. Order of metallic character : B' < A' < D' < C' C. Size of the element : D' < C' < B' < A' D. Order of ionic radii : B'$^+$ < A'$^+$ < D'$^+$ < C'$^+$ Choose the correct answer from the options given below:

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

Correct answer: C

Identify A and B in the following reaction sequence. Bromobenzene $\xrightarrow{\text{Conc HNO}_3}$ A $\xrightarrow{\text{(i) NaOH (ii) HCl}}$ B