JEE Main 2026 — 24 Jan Shift 1 (9:00 AM - 12:00 PM) (Previous Year

Let R be a relation defined on the set $\{1, 2, 3, 4\}\times\{1, 2, 3, 4\}$ by $R=\{((a, b), (c, d)): 2a+3b=3c+4d\}$. Then the number of elements in R is

1. A.18
2. B.12✓
3. C.6
4. D.15

Correct answer: B

If the domain of the function $f(x)=\log_{(10x^2-17x+7)}(18x^2-11x+1)$ is $(-\infty, a)\cup(b, c)\cup(d, \infty)-\{e\}$, then $90(a+b+c+d+e)$ equals:

1. A.177
2. B.170
3. C.307
4. D.316✓

Correct answer: D

Let $S=\left\{z\in\mathbb{C}: \left|\frac{z-6i}{z-2i}\right|=1\text{ and }\left|\frac{z-8+2i}{z+2i}\right|=\frac{3}{5}\right\}$. Then $\sum_{z\in S}|z|^2$ is equal to

1. A.398
2. B.385✓
3. C.423
4. D.413

Correct answer: B

Let 729, 81, 9, 1, ... be a sequence and $P_n$ denote the product of the first n terms of this sequence. If $2\sum_{n=1}^{40}(P_n)^{\frac{1}{n}}=\frac{3^\alpha-1}{3^\beta}$ and $\gcd(\alpha, \beta)=1$, then $\alpha+\beta$ is equal to

1. A.73✓
2. B.75
3. C.76
4. D.74

Correct answer: A

The number of the real solutions of the equation: $x|x+3|+|x-1|-2=0$ is

1. A.5
2. B.4
3. C.2
4. D.3✓

Correct answer: D

Consider an A.P.: $a_1, a_2, \ldots, a_n$; $a_1>0$. If $a_2-a_1=-\frac{3}{4}$, $a_n=\frac{1}{4}a_1$, and $\sum_{i=1}^{n}a_i=\frac{525}{2}$, then $\sum_{i=1}^{17}a_i$ is equal to

1. A.136
2. B.476
3. C.238✓
4. D.952

Correct answer: C

Let $S=\frac{1}{25!}+\frac{1}{3!23!}+\frac{1}{5!21!}+\ldots$ up to 13 terms. If $13S=\frac{2^k}{n!}$, $k\in\mathbb{N}$, then $n+k$ is equal to

1. A.52
2. B.51
3. C.49✓
4. D.50

Correct answer: C

The mean and variance of a data of 10 observations are 10 and 2, respectively. If an observations $\alpha$ in this data is replaced by $\beta$, then the mean and variance become 10.1 and 1.99, respectively. Then $\alpha+\beta$ equals

1. A.10
2. B.15
3. C.20✓
4. D.5

Correct answer: C

From a lot containing 10 defective and 90 non-defective bulbs, 8 bulbs are selected one by one with replacement. Then the probability of getting at least 7 defective bulbs is

1. A.$\frac{67}{10^8}$
2. B.$\frac{73}{10^8}$✓
3. C.$\frac{7}{10^7}$
4. D.$\frac{81}{10^8}$

Correct answer: B

Let each of the two ellipses $E_1: \frac{x^2}{a^2}+\frac{y^2}{b^2}=1$, $(a>b)$ and $E_2: \frac{x^2}{A^2}+\frac{y^2}{B^2}=1$, $(A<B)$ have eccentricity $\frac{4}{5}$. Let the lengths of the latus recta of $E_1$ and $E_2$ be $l_1$ and $l_2$, respectively, such that $2l_1^2=9l_2$. If the distance between the foci of $E_1$ is 8, then the distance between the foci of $E_2$ is

1. A.$\frac{16}{5}$
2. B.$\frac{96}{5}$
3. C.$\frac{8}{5}$
4. D.$\frac{32}{5}$✓

Correct answer: D

Let a circle of radius 4 pass through the origin O, the points $A(-\sqrt{3}a, 0)$ and $B(0, -\sqrt{2}b)$, where a and b are real parameters and $ab\ne0$. Then the locus of the centroid of $\Delta OAB$ is a circle of radius

1. A.$\frac{8}{3}$✓
2. B.$\frac{5}{3}$
3. C.$\frac{11}{3}$
4. D.$\frac{7}{3}$

Correct answer: A

If $\cot x=\frac{5}{12}$ for some $x\in\left(\pi, \frac{3\pi}{2}\right)$, then $\sin7x\left(\cos\frac{13x}{2}+\sin\frac{13x}{2}\right)+\cos7x\left(\cos\frac{13x}{2}-\sin\frac{13x}{2}\right)$ is equal to

1. A.$\frac{1}{\sqrt{13}}$✓
2. B.$\frac{4}{\sqrt{26}}$
3. C.$\frac{5}{\sqrt{13}}$
4. D.$\frac{6}{\sqrt{26}}$

Correct answer: A

Let A(1, 0), B(2, $-$1) and C$\left(\frac{7}{3}, \frac{4}{3}\right)$ be three points. If the equation of the bisector of the angle ABC is $\alpha x+\beta y=5$, then the value of $\alpha^2+\beta^2$ is

1. A.10✓
2. B.8
3. C.13
4. D.5

Correct answer: A

The value of $\frac{\sqrt{3}\operatorname{cosec}20^\circ-\sec20^\circ}{\cos20^\circ\cos40^\circ\cos60^\circ\cos80^\circ}$ is equal to

1. A.32
2. B.64✓
3. C.12
4. D.16

Correct answer: B

Let $\vec{a}=2\hat{i}+\hat{j}-2\hat{k}$, $\vec{b}=\hat{i}+\hat{j}$ and $\vec{c}=\vec{a}\times\vec{b}$. Let $\vec{d}$ be a vector such that $|\vec{d}-\vec{a}|=\sqrt{11}$, $|\vec{c}\times\vec{d}|=3$ and the angle between $\vec{c}$ and $\vec{d}$ is $\frac{\pi}{4}$. Then $\vec{a}\cdot\vec{d}$ is equal to

1. A.1
2. B.3
3. C.11
4. D.0✓

Correct answer: D

Let the lines $L_1: \vec{r}=\hat{i}+2\hat{j}+3\hat{k}+\lambda(2\hat{i}+3\hat{j}+4\hat{k})$, $\lambda\in\mathbb{R}$ and $L_2: \vec{r}=(4\hat{i}+\hat{j})+\mu(5\hat{i}+2\hat{j}+\hat{k})$, $\mu\in\mathbb{R}$, intersect at the point R. Let P and Q be the points lying on lines $L_1$ and $L_2$, respectively, such that $|\overrightarrow{PR}|=\sqrt{29}$ and $|\overrightarrow{PQ}|=\sqrt{\frac{47}{3}}$. If the point P lies in the first octant, then $27(QR)^2$ is equal to

1. A.340
2. B.348
3. C.360✓
4. D.320

Correct answer: C

If the function $f(x)=\frac{e^x(e^{\tan x-x}-1)+\log_e(\sec x+\tan x)-x}{\tan x-x}$ is continuous at $x=0$, then the value of $f(0)$ is equal to

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

Correct answer: B

Let $\alpha, \beta\in\mathbb{R}$ be such that the function $f(x)=\begin{cases}2\alpha(x^2-2)+2\beta x, & x<1\\ (\alpha+3)x+(\alpha-\beta), & x\ge1\end{cases}$ be differentiable at all $x\in\mathbb{R}$. Then $34(\alpha+\beta)$ is equal to

1. A.48✓
2. B.84
3. C.24
4. D.36

Correct answer: A

Let $f(t)=\int\left(\frac{1-\sin(\log_et)}{1-\cos(\log_et)}\right)dt$, $t>1$. If $f(e^{\pi/2})=-e^{\pi/2}$ and $f(e^{\pi/4})=\alpha e^{\pi/4}$, then $\alpha$ equals

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

Correct answer: C

Let $A_1$ be the bounded area enclosed by the curves $y=x^2+2$, $x+y=8$ and $y$-axis that lies in the first quadrant. Let $A_2$ be the bounded area enclosed by the curves $y=x^2+2$, $y^2=x$, $x=2$, and $y$-axis that lies in the first quadrant. Then $A_1-A_2$ is equal to

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

Correct answer: C

The number of $3\times2$ matrices A, which can be formed using the elements of the set $\{-2, -1, 0, 1, 2\}$ such that the sum of all the diagonal elements of $A^TA$ is 5, is ______

Correct answer: 312

The number of numbers greater than 5000, less than 9000 and divisible by 3, that can be formed using the digits 0, 1, 2, 5, 9, if the repetition of the digits is allowed, is ______

Correct answer: 42

Let a line L passing through the point P(1,1,1) be perpendicular to the lines $\frac{x-4}{4}=\frac{y-1}{1}=\frac{z-1}{1}$ and $\frac{x-17}{1}=\frac{y-71}{1}=\frac{z}{0}$. Let the line L intersect the $yz$-plane at the point Q. Another line parallel to L and passing through the point S(1, 0, $-$1) intersects the $yz$-plane at the point R. Then the square of the area of the parallelogram PQRS is equal to ______.

Correct answer: 6

Let $(2\alpha, \alpha)$ be the largest interval in which the function $f(t)=\frac{|t+1|}{t^2}$, $t<0$, is strictly decreasing. Then the local maximum value of the function $g(x)=2\log_e(x-2)+\alpha x^2+4x-\alpha$, $x>2$, is ______

Correct answer: 4

Let a differentiable function $f$ satisfy the equation $\int_0^{36}f\left(\frac{tx}{36}\right)dt=4\alpha f(x)$. If $y=f(x)$ is a standard parabola passing through the points (2, 1) and ($-$4, $\beta$), then $\beta^\alpha$ is equal to ______.

Correct answer: 64

Match the LIST-I with LIST-II. List-I: A. Magnetic induction; B. Magnetic flux; C. Magnetic permeability; D. Self inductance. List-II: I. $MLT^{-2}A^{-2}$; II. $ML^2T^{-2}A^{-2}$; III. $ML^0T^{-2}A^{-1}$; IV. $ML^2T^{-2}A^{-1}$. Choose the correct answer from the options given below:

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

Correct answer: D

A spring of force constant 15 N/m is cut into two pieces. If the ratio of their length is 1:3, then the force constant of smaller piece is ______ N/m.

1. A.60✓
2. B.45
3. C.20
4. D.15

Correct answer: A

Two resistors 2 $\Omega$ and 3 $\Omega$ are connected in the gaps of bridge as shown in figure. The null point is obtained with the contact of jockey at some point on wire XY. When an unknown resistor is connected in parallel with 3 $\Omega$ resistor, the null point is shifted by 22.5 cm toward Y. The resistance of unknown resistor is ______ $\Omega$.

1. A.2✓
2. B.3
3. C.4
4. D.1

Correct answer: A

Three masses 200 kg, 300 kg and 400 kg are placed at the vertices of an equilateral triangle with sides 20 m. They are rearranged on the vertices of a bigger triangle of side 25 m and with the same centre. The work done in this process ______ J. (Gravitational constant $G=6.7\times10^{-11}$ N m$^2$/kg$^2$)

1. A.$9.86\times10^{-6}$
2. B.$2.85\times10^{-7}$
3. C.$4.77\times10^{-7}$
4. D.$1.74\times10^{-7}$✓

Correct answer: D

A boy throws a ball into air at $45^\circ$ from the horizontal to land it on a roof of a building of height H. If the ball attains maximum height in 2 s and lands on the building in 3 s after launch, then value of H is ______ m. ($g=10$ m/s$^2$)

1. A.25
2. B.10
3. C.15✓
4. D.20

Correct answer: C

Two masses 400 g and 350 g are suspended from the ends of a light string passing over a heavy pulley of radius 2 cm. When released from rest the heavier mass is observed to fall 81 cm in 9 s. The rotational inertia of the pulley is ______ kg.m$^2$. ($g=9.8$ m/s$^2$)

1. A.$9.5\times10^{-3}$✓
2. B.$1.86\times10^{-2}$
3. C.$8.3\times10^{-3}$
4. D.$4.75\times10^{-3}$

Correct answer: A

Density of water at $4^\circ$C and $20^\circ$C are 1000 kg/m$^3$ and 998 kg/m$^3$ respectively. The increase in internal energy of 4 kg of water when it is heated from $4^\circ$C to $20^\circ$C is ______ J. (specific heat capacity of water = 4.2 J/kg. and 1 atmospheric pressure $=10^5$ Pa)

1. A.315826.2
2. B.258700.8
3. C.234699.2
4. D.268799.2✓

Correct answer: D

A brass wire of length 2 m and radius 1 mm at $27^\circ$C is held taut between two rigid supports. Initially it was cooled to a temperature of $-43^\circ$C creating a tension T in the wire. The temperature to which the wire has to be cooled in order to increase the tension in it to 1.4T, is ______ $^\circ$C.

1. A.-71✓
2. B.-65
3. C.-80
4. D.-86

Correct answer: A

A cylindrical block of mass M and area of cross section A is floating in a liquid of density $\rho$ and with its axis vertical. When depressed a little and released the block starts oscillating. The period of oscillation is ______.

1. A.$2\pi\sqrt{\frac{\rho A}{Mg}}$
2. B.$\pi\sqrt{\frac{\rho A}{Mg}}$
3. C.$2\pi\sqrt{\frac{M}{\rho Ag}}$✓
4. D.$\pi\sqrt{\frac{2M}{\rho Ag}}$

Correct answer: C

The electrostatic potential in a charged spherical region of radius r varies as $V=ar^3+b$, where a and b are constants. The total charge in the sphere of unit radius is $\alpha\times\pi a\epsilon_0$. The value of $\alpha$ is ______. (permittivity of vacuum is $\epsilon_0$)

1. A.-8
2. B.-12✓
3. C.-9
4. D.-6

Correct answer: B

Two resistors of 100 $\Omega$ each are connected in series with a 9 V battery. A voltmeter of 400 $\Omega$ resistance is connected to measure the voltage drop across one of the resistors. The voltmeter reading is ______ V.

1. A.2
2. B.3
3. C.4✓
4. D.4.5

Correct answer: C

For the series LCR circuit connected with 220 V, 50 Hz a.c source as shown in the figure, the power factor is $\frac{\alpha}{10}$. The value of $\alpha$ is ______.

1. A.4
2. B.8
3. C.10
4. D.6✓

Correct answer: D

There are three co-centric conducting spherical shells A, B and C of radii a, b and c respectively $(c>b>a)$ and they are charged with charge $q_1$, $q_2$ and $q_3$ respectively. The potentials of the spheres A, B and C respectively, are :

1. A.$\frac{1}{4\pi\epsilon_0}\left(\frac{q_1+q_2+q_3}{a}\right), \frac{1}{4\pi\epsilon_0}\left(\frac{q_1+q_2+q_3}{b}\right), \frac{1}{4\pi\epsilon_0}\left(\frac{q_1+q_2+q_3}{c}\right)$
2. B.$\frac{1}{4\pi\epsilon_0}\left(\frac{q_1}{a}+\frac{q_2}{b}+\frac{q_3}{c}\right), \frac{1}{4\pi\epsilon_0}\left(\frac{q_1+q_2+q_3}{b}\right), \frac{1}{4\pi\epsilon_0}\left(\frac{q_1+q_2+q_3}{c}\right)$
3. C.$\frac{1}{4\pi\epsilon_0}\left(\frac{q_1}{a}+\frac{q_2}{b}+\frac{q_3}{c}\right), \frac{1}{4\pi\epsilon_0}\left(\frac{q_1+q_2}{b}+\frac{q_3}{c}\right), \frac{1}{4\pi\epsilon_0}\left(\frac{q_1+q_2+q_3}{c}\right)$✓
4. D.$\frac{1}{4\pi\epsilon_0}\left(\frac{q_1+q_2+q_3}{a}\right), \frac{1}{4\pi\epsilon_0}\left(\frac{q_1+q_2}{b}+\frac{q_3}{c}\right), \frac{1}{4\pi\epsilon_0}\left(\frac{q_1}{a}+\frac{q_2}{b}+\frac{q_3}{c}\right)$

Correct answer: C

Three charges $+2q$, $+3q$ and $-4q$ are situated at $(0, -3a)$, $(2a, 0)$ and $(-2a, 0)$ respectively in the $xy$ plane. The resultant dipole moment about origin is ______.

1. A.$2qa(7\hat{i}-3\hat{j})$✓
2. B.$2qa(3\hat{j}-7\hat{i})$
3. C.$2qa(3\hat{j}-\hat{i})$
4. D.$2qa(3\hat{i}-7\hat{j})$

Correct answer: A

Match the LIST-I with LIST-II. List-I: A. Radio-wave; B. Micro-wave; C. Infrared-wave; D. X-ray. List-II: I. is produced by Magnetron valve; II. due to change in the vibrational modes of atoms; III. due to inner shell electrons moving from higher energy level to lower energy level; IV. due to rapid acceleration of electrons. Choose the correct answer from the options given below:

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

Correct answer: C

An unpolarised light is incident at an interface of two dielectric media having refractive indices of 2 (incident medium) and $2\sqrt{3}$ (medium) respectively. To satisfy the condition that reflected and refracted rays are perpendicular to each other, the angle of incidence is ______.

1. A.$45^\circ$
2. B.$30^\circ$
3. C.$10^\circ$
4. D.$60^\circ$✓

Correct answer: D

In a microscope of tube length 10 cm two convex lenses are arranged with focal length of 2 cm and 5 cm. Total magnification obtained with this system for normal adjustment is $(5)^k$. The value of k is ______.

1. A.4
2. B.5
3. C.3.5
4. D.2✓

Correct answer: D

The exit surface of a prism with refractive index n is coated with a material having refractive index $\frac{n}{2}$. When this prism is set for minimum angle of deviation, it exactly meets the condition of critical angle. The prism angle is ______.

1. A.$30^\circ$
2. B.$60^\circ$✓
3. C.$15^\circ$
4. D.$45^\circ$

Correct answer: B

Given below are two statements: Statement I: For all elements, greater the mass of the nucleus, greater is the binding energy per nucleon. Statement II: For all elements, nuclei with less binding energy per nucleon transforms to nuclei with greater binding energy per nucleon. 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.Statement I is false but Statement II is true✓
4. D.Both Statement I and Statement II are true

Correct answer: C

Two electrons are moving in orbits of two hydrogen like atoms with speeds $3\times10^5$ m/s and $2.5\times10^5$ m/s respectively. If the radii of these orbits are nearly same then the possible order of energy states are ______ respectively.

1. A.10 and 12
2. B.8 and 10
3. C.6 and 5✓
4. D.9 and 8

Correct answer: C

A voltage regulating circuit consisting of Zener diode, having break-down voltage of 10 V and maximum power dissipation of 0.4 W, is operated at 15 V. The approximate value of protective resistance in this circuit is ______ $\Omega$.

Correct answer: 125

In the given figure the blocks A, B and C weigh 4 kg, 6 kg and 8 kg respectively. The co-efficient of sliding friction between any two surfaces is 0.5. The force $\vec{F}$ required to slide the block C with constant speed is ______ N. (Use $g=10$ m/s$^2$)

Correct answer: 210

Sixty four rain drops of radius 1 mm each falling down with a terminal velocity of 10 cm/s coalesce to form a bigger drop. The terminal velocity of bigger drop is ______ cm/s.

Correct answer: 160

A gas of certain mass filled in a closed cylinder at a pressure of 3.23 kPa has temperature $50^\circ$C. The gas is now heated to double its temperature. The modified pressure is ______ Pa.

Correct answer: 3730

A short bar magnet placed with its axis at $30^\circ$ with an external field of 800 Gauss, experiences a torque of 0.016 N.m. The work done in moving it from most stable to most unstable position is $\alpha\times10^{-3}$ J. The value of $\alpha$ is ______.

Correct answer: 64

Consider a mixture 'X' which is made by dissolving 0.4 mol of [Co(NH$_3$)$_5$SO$_4$]Br and 0.4 mol of [Co(NH$_3$)$_5$Br]SO$_4$ in water to make 4 L of solution. When 2 L of mixture 'X' is allowed to react with excess of AgNO$_3$, it forms precipitate 'Y'. The rest 2 L of mixture 'X' reacts with excess BaCl$_2$ to form precipitate 'Z'. Which of the following statements is CORRECT?

1. A.'Y' is BaSO$_4$ and 'Z' is AgBr.
2. B.0.1 mol of 'Y' is formed.
3. C.0.2 mol of 'Z' is formed.✓
4. D.0.4 mol of 'Z' is formed.

Correct answer: C

Match the LIST-I with LIST-II. List-I (Isothermal process for ideal gas system): A. Reversible expansion; B. Free expansion; C. Irreversible expansion; D. Irreversible compression. List-II (Work done, $V_f>V_i$): I. $w=0$; II. $w=-nRT\ln\frac{V_f}{V_i}$; III. $w=-p_{ex}(V_f-V_i)$; IV. $w=-p_{ex}(V_i-V_f)$. Choose the correct answer from the options given below:

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

Correct answer: A

Given below are statements about some molecules/ions. Identify the CORRECT statements. A. The dipole moment value of NF$_3$ is higher than that of NH$_3$. B. The dipole moment value of BeH$_2$ is zero. C. The bond order of O$_2^{2-}$ and F$_2$ is same. D. The formal charge on the central oxygen atom of ozone is $-1$. E. In NO$_2$, all the three atoms satisfy the octet rule, hence it is very stable. Choose the correct answer from the options given below:

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

Correct answer: B

A solution is prepared by dissolving 0.3 g of a non-volatile non-electrolyte solute 'A' of molar mass 60 g mol$^{-1}$ and 0.9 g of a non-volatile non-electrolyte solute 'B' of molar mass 180 g mol$^{-1}$ in 100 mL H$_2$O at 27$^\circ$C. Osmotic pressure of the solution will be [Given: R = 0.082 L atm K$^{-1}$ mol$^{-1}$]

1. A.1.23 atm
2. B.0.82 atm
3. C.2.46 atm✓
4. D.1.47 atm

Correct answer: C

'W' g of a non-volatile electrolyte solid solute of molar mass 'M' g mol$^{-1}$ when dissolved in 100 mL water, decreases vapour pressure of water from 640 mm Hg to 600 mm Hg. If aqueous solution of the electrolyte boils at 375 K and $K_b$ for water is 0.52 K kg mol$^{-1}$, then the mole fraction of the electrolyte solute ($x_2$) in the solution can be expressed as (Given : density of water = 1 g/mL and boiling point of water = 373 K)

1. A.$\frac{1.3}{8}\times\frac{M}{W}$
2. B.$\frac{2.6}{16}\times\frac{M}{W}$
3. C.$\frac{1.3}{8}\times\frac{W}{M}$✓
4. D.$\frac{16}{2.6}\times\frac{W}{M}$

Correct answer: C

At 27$^\circ$C in presence of a catalyst, activation energy of a reaction is lowered by 10 kJ mol$^{-1}$. The logarithm of ratio of $\frac{k(\text{catalysed})}{k(\text{uncatalysed})}$ is.... (Consider that the frequency factor for both the reactions is same)

1. A.0.1741
2. B.1.741✓
3. C.3.482
4. D.17.41

Correct answer: B

A $\to$ D is an endothermic reaction occurring in three steps (elementary). (i) A $\to$ B $\Delta H_i$ = +ve (ii) B $\to$ C $\Delta H_{ii}$ = $-$ve (iii) C $\to$ D $\Delta H_{iii}$ = $-$ve. Which of the following graphs between potential energy (y-axis) vs reaction coordinate (x-axis) correctly represents the reaction profile of A $\to$ D?

1. A.Profile (1) as described
2. B.Profile (2): each step as stated, D ends above A✓
3. C.Profile (3) as described
4. D.Profile (4) as described

Correct answer: B

Given below are two statements: Statement I: K > Mg > Al > B is the correct order in terms of metallic character. Statement II: Atomic radius is always greater than the ionic radius for any element. 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: B

Among the following, the CORRECT combinations are A. IF$_3$ $\to$ T$-$shaped (sp$^3$d) B. IF$_5$ $\to$ Square pyramidal (sp$^3$d$^2$) C. IF$_7$ $\to$ Pentagonal bipyramidal (sp$^3$d$^3$) D. ClO$_4^-$ $\to$ Square planar (sp$^2$d). Choose the correct answer from the options given below:

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

Correct answer: D

Given below are two statements: Statement I: The number of paramagnetic species among [CoF$_6$]$^{3-}$, [TiF$_6$]$^{3-}$, V$_2$O$_5$ and [Fe(CN)$_6$]$^{3-}$ is 3. Statement II: K$_4$[Fe(CN)$_6$] < K$_3$[Fe(CN)$_6$] < [Fe(H$_2$O)$_6$]SO$_4$.H$_2$O < [Fe(H$_2$O)$_6$]Cl$_3$ is the correct order in terms of number of unpaired electron(s) present in the complexes. In the light of the above statements, choose the correct answer from the options given below