JEE Main 2026 — 22 Jan Shift 1 (9:00 AM - 12:00 PM) (Previous Year

Let the relation R on the set $M=\{1, 2, 3, \ldots, 16\}$ be given by $R=\{(x, y): 4y=5x-3, x, y\in M\}$. Then the minimum number of elements required to be added in R, in order to make the relation symmetric, is equal to

1. A.3
2. B.4
3. C.2✓
4. D.1

Correct answer: C

If the domain of the function $f(x)=\sin^{-1}\left(\frac{5-x}{3+2x}\right)+\frac{1}{\log_e(10-x)}$ is $(-\infty, \alpha]\cup[\beta, \gamma)-\{\delta\}$, then $6(\alpha+\beta+\gamma+\delta)$ is equal to

1. A.68
2. B.66
3. C.70✓
4. D.67

Correct answer: C

The number of distinct real solutions of the equation $x|x+4|+3|x+2|+10=0$ is

1. A.2
2. B.0
3. C.3
4. D.1✓

Correct answer: D

If $A=\begin{bmatrix}2 & 3\\ 3 & 5\end{bmatrix}$, then the determinant of the matrix $(A^{2025}-3A^{2024}+A^{2023})$ is

1. A.28
2. B.16✓
3. C.24
4. D.12

Correct answer: B

If the sum of the first four terms of an A.P. is 6 and the sum of its first six terms is 4, then the sum of its first twelve terms is

1. A.-22✓
2. B.-20
3. C.-26
4. D.-24

Correct answer: A

The coefficient of $x^{48}$ in $(1+x)+2(1+x)^2+3(1+x)^3+\ldots+100(1+x)^{100}$ is equal to

1. A.$100\cdot{}^{101}C_{49}-{}^{101}C_{50}$✓
2. B.$100\cdot{}^{100}C_{49}-{}^{100}C_{48}$
3. C.$100\cdot{}^{100}C_{49}-{}^{100}C_{50}$
4. D.${}^{100}C_{50}+{}^{101}C_{49}$

Correct answer: A

Two distinct numbers $a$ and $b$ are selected at random from 1, 2, 3, ..., 50. The probability, that their product $ab$ is divisible by 3, is

1. A.$\frac{8}{25}$
2. B.$\frac{561}{1225}$
3. C.$\frac{664}{1225}$✓
4. D.$\frac{272}{1225}$

Correct answer: C

If a random variable $x$ has the probability distribution: $x$ = 0, 1, 2, 3, 4, 5, 6, 7 with P($x$) = 0, 2k, k, 3k, 2k$^2$, 2k, k$^2$+k, 7k$^2$ respectively, then $P(3<x\le6)$ is equal to

1. A.0.22
2. B.0.33✓
3. C.0.34
4. D.0.64

Correct answer: B

If the line $\alpha x+2y=1$, where $\alpha\in\mathbb{R}$, does not meet the hyperbola $x^2-9y^2=9$, then a possible value of $\alpha$ is:

1. A.0.5
2. B.0.6
3. C.0.8✓
4. D.0.7

Correct answer: C

If the chord joining the points $P_1(x_1, y_1)$ and $P_2(x_2, y_2)$ on the parabola $y^2=12x$ subtends a right angle at the vertex of the parabola, then $x_1x_2-y_1y_2$ is equal to

1. A.292
2. B.288✓
3. C.284
4. D.280

Correct answer: B

Let the set of all values of $r$, for which the circles $(x+1)^2+(y+4)^2=r^2$ and $x^2+y^2-4x-2y-4=0$ intersect at two distinct points be the interval $(\alpha, \beta)$. Then $\alpha\beta$ is equal to

1. A.25✓
2. B.21
3. C.24
4. D.20

Correct answer: A

The number of solutions of $\tan^{-1}4x+\tan^{-1}6x=\frac{\pi}{6}$, where $-\frac{1}{2\sqrt{6}}<x<\frac{1}{2\sqrt{6}}$, is equal to

1. A.1✓
2. B.2
3. C.0
4. D.3

Correct answer: A

Let $\overrightarrow{AB}=2\hat{i}+4\hat{j}-5\hat{k}$ and $\overrightarrow{AD}=\hat{i}+2\hat{j}+\lambda\hat{k}$, $\lambda\in\mathbb{R}$. Let the projection of the vector $\vec{v}=\hat{i}+\hat{j}+\hat{k}$ on the diagonal $\overrightarrow{AC}$ of the parallelogram ABCD be of length one unit. If $\alpha, \beta$, where $\alpha>\beta$, be the roots of the equation $\lambda^2x^2-6\lambda x+5=0$, then $2\alpha-\beta$ is equal to

1. A.4
2. B.6
3. C.3✓
4. D.1

Correct answer: C

Let $P(\alpha, \beta, \gamma)$ be the point on the line $\frac{x-1}{2}=\frac{y+1}{-3}=z$ at a distance $4\sqrt{14}$ from the point $(1, -1, 0)$ and nearer to the origin. Then the shortest distance, between the lines $\frac{x-\alpha}{1}=\frac{y-\beta}{2}=\frac{z-\gamma}{3}$ and $\frac{x+5}{2}=\frac{y-10}{1}=\frac{z-3}{1}$, is equal to

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

Correct answer: D

If the image of the point $P(1, 2, a)$ in the line $\frac{x-6}{3}=\frac{y-7}{2}=\frac{7-z}{2}$ is $Q(5, b, c)$, then $a^2+b^2+c^2$ is equal to

1. A.293
2. B.298✓
3. C.264
4. D.283

Correct answer: B

Let $f(x)=x^{2025}-x^{2000}$, $x\in[0, 1]$ and the minimum value of the function $f(x)$ in the interval $[0, 1]$ be $(80)^{80}(n)^{-81}$. Then $n$ is equal to

1. A.-40
2. B.-81✓
3. C.-80
4. D.-41

Correct answer: B

Let $f:[1, \infty)\to\mathbb{R}$ be a differentiable function. If $6\int_1^x f(t)\,dt=3xf(x)+x^3-4$ for all $x\ge1$, then the value of $f(2)-f(3)$ is

1. A.3✓
2. B.-4
3. C.-3
4. D.4

Correct answer: A

Let the line $x=-1$ divide the area of the region $\{(x, y): 1+x^2\le y\le3-x\}$ in the ratio $m:n$, $\gcd(m, n)=1$. Then $m+n$ is equal to

1. A.27✓
2. B.26
3. C.25
4. D.28

Correct answer: A

Let the solution curve of the differential equation $x\,dy-y\,dx=\sqrt{x^2+y^2}\,dx$, $x>0$, $y(1)=0$, be $y=y(x)$. Then $y(3)$ is equal to

1. A.4✓
2. B.2
3. C.1
4. D.6

Correct answer: A

The value of $\int_{-\pi/2}^{\pi/2}\left(\frac{1}{[x]+4}\right)dx$, where $[\cdot]$ denotes the greatest integer function, is

1. A.$\frac{1}{60}(\pi-7)$
2. B.$\frac{1}{60}(21\pi-1)$
3. C.$\frac{7}{60}(3\pi-1)$✓
4. D.$\frac{7}{60}(\pi-3)$

Correct answer: C

Let $\alpha=\frac{-1+i\sqrt{3}}{2}$ and $\beta=\frac{-1-i\sqrt{3}}{2}$, $i=\sqrt{-1}$. If $(7-7\alpha+9\beta)^{20}+(9+7\alpha-7\beta)^{20}+(-7+9\alpha+7\beta)^{20}+(14+7\alpha+7\beta)^{20}=m^{10}$, then $m$ is ______

Correct answer: 49

Let A be a $3\times3$ matrix such that $A+A^T=O$. If $A\begin{bmatrix}1\\-1\\0\end{bmatrix}=\begin{bmatrix}3\\3\\2\end{bmatrix}$, $A^2\begin{bmatrix}1\\-1\\0\end{bmatrix}=\begin{bmatrix}-3\\19\\-24\end{bmatrix}$ and $\det(\operatorname{adj}(2\operatorname{adj}(A+I)))=(2)^\alpha\cdot(3)^\beta\cdot(11)^\gamma$, $\alpha, \beta, \gamma$ are non-negative integers, then $\alpha+\beta+\gamma$ is equal to ______

Correct answer: 18

Let ABC be a triangle. Consider four points $p_1, p_2, p_3, p_4$ on the side AB, five points $p_5, p_6, p_7, p_8, p_9$ on the side BC, and four points $p_{10}, p_{11}, p_{12}, p_{13}$ on the side AC. None of these points is a vertex of the triangle ABC. Then the total number of pentagons, that can be formed by taking all the vertices from the points $p_1, p_2, \ldots, p_{13}$, is ______

Correct answer: 660

If $\frac{\cos^2 48^\circ-\sin^2 12^\circ}{\sin^2 24^\circ-\sin^2 6^\circ}=\frac{\alpha+\beta\sqrt{5}}{2}$, where $\alpha, \beta\in\mathbb{N}$, then $\alpha+\beta$ is equal to ______

Correct answer: 4

If $\int(\sin x)^{-\frac{11}{2}}(\cos x)^{-\frac{5}{2}}dx=-\frac{p_1}{q_1}(\cot x)^{\frac{9}{2}}-\frac{p_2}{q_2}(\cot x)^{\frac{5}{2}}-\frac{p_3}{q_3}(\cot x)^{\frac{1}{2}}+\frac{p_4}{q_4}(\cot x)^{-\frac{3}{2}}+C$, where $p_i$ and $q_i$ are positive integers with $\gcd(p_i, q_i)=1$ for $i=1, 2, 3, 4$ and C is the constant of integration, then $\frac{15p_1p_2p_3p_4}{q_1q_2q_3q_4}$ is equal to ______

Correct answer: 16

Match the LIST-I with LIST-II. List-I: A. Spring constant; B. Thermal conductivity; C. Boltzmann constant; D. Inductive reactance. List-II: I. $ML^2T^{-2}K^{-1}$; II. $ML^0T^{-2}$; III. $ML^2T^{-3}A^{-2}$; IV. $MLT^{-3}K^{-1}$. Choose the correct answer from the options given below:

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

Correct answer: A

A meter bridge with two resistances $R_1$ and $R_2$ as shown in figure was balanced (null point) at 40 cm from the point P. The null point changed to 50 cm from the point P, when 16 $\Omega$ resistance is connected in parallel to $R_2$. The values of resistances $R_1$ and $R_2$ are ______.

1. A.$R_2=4\ \Omega$, $R_1=\frac{4}{3}\ \Omega$
2. B.$R_2=16\ \Omega$, $R_1=\frac{16}{3}\ \Omega$
3. C.$R_2=8\ \Omega$, $R_1=\frac{16}{3}\ \Omega$✓
4. D.$R_2=12\ \Omega$, $R_1=\frac{12}{3}\ \Omega$

Correct answer: C

The escape velocity from a spherical planet A is 10 km/s. The escape velocity from another planet B whose density and radius are 10% of those of planet A, is ______ m/s.

1. A.$1000\sqrt{2}$
2. B.1000
3. C.$200\sqrt{5}$
4. D.$100\sqrt{10}$✓

Correct answer: D

A projectile is thrown upward at an angle $60^\circ$ with the horizontal. The speed of the projectile is 20 m/s when its direction of motion is $45^\circ$ with the horizontal. The initial speed of the projectile is ______ m/s.

1. A.$20\sqrt{2}$✓
2. B.40
3. C.$20\sqrt{3}$
4. D.$40\sqrt{2}$

Correct answer: A

Net gravitational force at the center of a square is found to be $F_1$ when four particles having mass M, 2M, 3M and 4M are placed at the four corners of the square as shown in figure and it is $F_2$ when the positions of 3M and 4M are interchanged. The ratio $\frac{F_1}{F_2}$ is $\frac{\alpha}{\sqrt{5}}$. The value of $\alpha$ is ______.

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

Correct answer: D

A solid sphere of mass 5 kg and radius 10 cm is kept in contact with another solid sphere of mass 10 kg and radius 20 cm. The moment of inertia of this pair of spheres about the tangent passing through the point of contact is ______ kg.m$^2$.

1. A.0.18
2. B.0.63✓
3. C.0.72
4. D.0.36

Correct answer: B

Rods $x$ and $y$ of equal dimensions but of different materials are joined as shown in figure. Temperatures of end points A and F are maintained at $100^\circ$C and $40^\circ$C respectively. Given the thermal conductivity of rod $x$ is three times of that of rod $y$, the temperature at junction points B and E are (close to):

1. A.$60^\circ$C and $45^\circ$C respectively
2. B.$89^\circ$C and $73^\circ$C respectively✓
3. C.$80^\circ$C and $70^\circ$C respectively
4. D.$80^\circ$C and $60^\circ$C respectively

Correct answer: B

Given below are two statements: Statement I: Pressure of a fluid is exerted only on a solid surface in contact as the fluid-pressure does not exist everywhere in a still fluid. Statement II: Excess potential energy of the molecules on the surface of a liquid, when compared to interior, results in surface tension. In the light of the above statements, choose the correct answer from the options given below

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

Correct answer: D

A cylindrical tube AB of length $l$, closed at both ends contains an ideal gas of 1 mol having molecular weight M. The tube is rotated in a horizontal plane with constant angular velocity $\omega$ about an axis perpendicular to AB and passing through the edge at end A, as shown in the figure. If $P_A$ and $P_B$ are the pressures at A and B respectively, then (Consider the temperature is same at all points in the tube)

1. A.$P_B=P_A\exp(M\omega^2l^2/RT)$
2. B.$P_B=P_A$
3. C.$P_B=P_A\exp(M\omega^2l^2/3RT)$
4. D.$P_B=P_A\exp(M\omega^2l^2/2RT)$✓

Correct answer: D

The volume of an ideal gas increases 8 times and temperature becomes $(1/4)^{th}$ of initial temperature during a reversible change. If there is no exchange of heat in this process $(\Delta Q=0)$ then identify the gas from the following options (Assuming the gases given in the options are ideal gases):

1. A.He✓
2. B.O$_2$
3. C.CO$_2$
4. D.NH$_3$

Correct answer: A

XPQY is a vertical smooth long loop having a total resistance R where PX is parallel to QY and separation between them is $l$. A constant magnetic field B perpendicular to the plane of the loop exists in the entire space. A rod CD of length L $(L>l)$ and mass m is made to slide down from rest under the gravity as shown in figure. The terminal speed acquired by the rod is ______ m/s. ($g$ = acceleration due to gravity)

1. A.$\frac{mgR}{B^2l^2}$✓
2. B.$\frac{2mgR}{B^2L^2}$
3. C.$\frac{8mgR}{B^2l^2}$
4. D.$\frac{2mgR}{B^2l^2}$

Correct answer: A

Six point charges are kept $60^\circ$ apart from each other on the circumference of a circle of radius R as shown in figure. The net electric field at the center of the circle is ______. ($\epsilon_0$ is permittivity of free space)

1. A.$\frac{Q}{4\pi\epsilon_0R^2}(\sqrt{3}\hat{i}-\hat{j})$
2. B.$-\frac{Q}{4\pi\epsilon_0R^2}(\sqrt{3}\hat{i}-\hat{j})$✓
3. C.$-\left(\frac{5Q}{8\pi\epsilon_0R^2}\right)(\hat{i}-3\hat{j})$
4. D.$-\frac{5Q}{8\pi\epsilon_0R^2}(\hat{i}+\sqrt{3}\hat{j})$

Correct answer: B

A simple pendulum has a bob with mass m and charge q. The pendulum string has negligible mass. When a uniform and horizontal electric field $\vec{E}$ is applied, the tension in the string changes. The final tension in the string, when pendulum attains an equilibrium position is ______. ($g$: acceleration due to gravity)

1. A.$\sqrt{m^2g^2-q^2E^2}$
2. B.$\sqrt{m^2g^2+q^2E^2}$✓
3. C.$mg+qE$
4. D.$mg-qE$

Correct answer: B

Electric field in a region is given by $\vec{E}=Ax\hat{i}+By\hat{j}$, where $A=10$ V/m$^2$ and $B=5$ V/m$^2$. If the electric potential at a point (10, 20) is 500 V, then the electric potential at origin is ______ V.

1. A.1000
2. B.500
3. C.2000✓
4. D.0

Correct answer: C

Three identical coils $C_1$, $C_2$ and $C_3$ are closely placed such that they share a common axis. $C_2$ is exactly midway. $C_1$ carries current I in anti-clockwise direction while $C_3$ carries current I in clockwise direction. An induced current flows through $C_2$ will be in clockwise direction when

1. A.$C_1$ and $C_3$ move with equal speeds away from $C_2$
2. B.$C_1$ moves away from $C_2$ and $C_3$ moves towards $C_2$
3. C.$C_1$ moves towards $C_2$ and $C_3$ moves away from $C_2$✓
4. D.$C_1$ and $C_3$ move with equal speeds towards $C_2$

Correct answer: C

Consider an equilateral prism (refractive index $\sqrt{2}$). A ray of light is incident on its one surface at a certain angle $i$. If the emergent ray is found to graze along the other surface then the angle of refraction at the incident surface is close to ______.

1. A.$15^\circ$✓
2. B.$40^\circ$
3. C.$20^\circ$
4. D.$30^\circ$

Correct answer: A

7.9 MeV $\alpha$-particle scatters from a target material of atomic number 79. From the given data the estimated diameter of nuclei of the target material is (approximately) ______ m. [$\frac{1}{4\pi\epsilon_0}=9\times10^9$ Nm$^2$/C$^2$ and electron charge $=1.6\times10^{-19}$ C]

1. A.$1.69\times10^{-12}$
2. B.$1.44\times10^{-13}$
3. C.$2.88\times10^{-14}$
4. D.$5.76\times10^{-14}$✓

Correct answer: D

The minimum frequency of photon required to break a particle of mass 15.348 amu into 4 $\alpha$ particles is ______ kHz. [mass of He nucleus = 4.002 amu, 1 amu $=1.66\times10^{-27}$ kg, h $=6.6\times10^{-34}$ J.s and c $=3\times10^8$ m/s]

1. A.$9\times10^{19}$
2. B.$9\times10^{20}$
3. C.$14.94\times10^{20}$
4. D.$14.94\times10^{19}$✓

Correct answer: D

Find the correct combination of A, B, C and D inputs which can cause the LED to glow.

1. A.0100
2. B.1000
3. C.0011
4. D.1101✓

Correct answer: D

A circular disc has radius $R_1$ and thickness $T_1$. Another circular disc made of the same material has radius $R_2$ and thickness $T_2$. If the moment of inertia of both discs are same and $\frac{R_1}{R_2}=2$ then $\frac{T_1}{T_2}=\frac{1}{\alpha}$. The value of $\alpha$ is ______.

Correct answer: 16

Two loudspeakers ($L_1$ and $L_2$) are placed with a separation of 10 m, as shown in figure. Both speakers are fed with an audio input signal of same frequency with constant volume. A voice recorder, initially at point A, at equidistance to both loud speakers, is moved by 25 m along the line AB while monitoring the audio signal. The measured signal was found to undergo 10 cycles of minima and maxima during the movement. The frequency of the input signal is ______ Hz (Speed of sound in air is 324 m/s and $\sqrt{5}=2.23$)

Correct answer: 600

Inductance of a coil with $10^4$ turns is 10 mH and it is connected to a dc source of 10 V with internal resistance of 10 $\Omega$. The energy density in the inductor when the current reaches $\left(\frac{1}{e}\right)$ of its maximum value is $\alpha\pi\times\frac{1}{e^2}$ J/m$^3$. The value of $\alpha$ is ______. ($\mu_0=4\pi\times10^{-7}$ Tm/A).

Correct answer: 20

The electric field of a plane electromagnetic wave, travelling in an unknown non-magnetic medium is given by, $E_y=20\sin(3\times10^6x-4.5\times10^{14}t)$ V/m (where $x$, $t$ and other values have S.I. units). The dielectric constant of the medium is ______ (speed of light in free space is $3\times10^8$ m/s)

Correct answer: 4

A parallel beam of light travelling in air (refractive index 1.0) is incident on a convex spherical glass surface of radius of curvature 50 cm. Refractive index of glass is 1.5. The rays converge to a point at a distance $x$ cm from the centre of the curvature of the spherical surface. The value of $x$ is ______ cm.

Correct answer: 100

In the reaction, 2Al(s) + 6HCl(aq) $\to$ 2Al$^{3+}$(aq) + 6Cl$^-$(aq) + 3H$_2$(g)

1. A.11.2 L H$_2$(g) at STP is produced for every mole of HCl consumed.✓
2. B.12 L HCl(aq) is consumed for every 6L H$_2$(g) produced.
3. C.33.6 L H$_2$(g) is produced regardless of temperature and pressure for every mole of Al that reacts.
4. D.67.2 L H$_2$(g) at STP is produced for every mole of Al that reacts.

Correct answer: A

The energy required by electrons, present in the first Bohr orbit of hydrogen atom to be excited to second Bohr orbit is ______ J mol$^{-1}$. Given: $R_H=2.18\times10^{-11}$ ergs.

1. A.$9.835\times10^{12}$
2. B.$9.835\times10^{5}$✓
3. C.$1.635\times10^{-11}$
4. D.$1.635\times10^{-18}$

Correct answer: B

The formal charges on the atoms marked as (1) to (4) in the Lewis representation of HNO$_3$ molecule respectively are: H$-$O$^{(1)}-$N$^{(2)}$(=O$^{(3)}$)$-$O$^{(4)}$ [O(1) bonded to H and N with two lone pairs; O(3) double-bonded to N with two lone pairs; O(4) single-bonded to N with three lone pairs]

1. A.+1, 0, 0, -1
2. B.0, -1, 0, +1
3. C.0, +1, 0, -1✓
4. D.0, 0, -1, +1

Correct answer: C

Match the LIST-I with LIST-II. List-I (Thermodynamic Process): A. Work done in reversible, isothermal expansion of 2 mol of ideal gas from 2 dm$^3$ to 20 dm$^3$ at 300 K. B. Work done in irreversible isothermal expansion of 1 mol ideal gas from 1 m$^3$ to 3 m$^3$ at 300 K against a constant pressure of 3kPa. C. Change in internal energy for adiabatic expansion of a 1 mol ideal gas with change of temperature = 320 K and $\bar{C}_V=\frac{3}{2}R$. D. Change in enthalpy at constant pressure of 1 mol ideal gas with change of temperature = 337 K and $\bar{C}_p=\frac{5}{2}R$. List-II (Magnitude in kJ): I. 4; II. 11.5; III. 6; IV. 7. Choose the correct answer from the options given below:

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

Correct answer: D

Given below are two statements: Statement I: The Henry's law constant $K_H$ is constant with respect to variations in solution's concentration over the range for which the solution is ideally dilute. Statement II: $K_H$ does not differ for the same solute in different solvents. In the light of the above statements, choose the correct answer from the options given below

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

Correct answer: D

Consider a solution of CO$_2$(g) dissolved in water in a closed container. Which one of the following plots correctly represents variation of log (partial pressure of CO$_2$ in vapour phase above water) [$y$-axis] with log (mole fraction of CO$_2$ in water) [$x$-axis] at $25^\circ$C?

1. A.Straight line with positive slope and positive y-intercept✓
2. B.Horizontal line
3. C.Straight line with negative slope
4. D.Straight line with positive slope passing through the origin

Correct answer: A

A 'p'-block element (E) and hydrogen form a binary cation (EH$_x$)$^+$, while EH$_3$ on treatment with K$_2$HgI$_4$ in alkaline medium gives a precipitate of basic mercury(II)amido-iodine. Given below are first ionisation enthalpy values (kJ mol$^{-1}$) for first element each from group 13, 14, 15 and 16. Identify the correct first ionisation enthalpy value for element E.

1. A.1402✓
2. B.801
3. C.1312
4. D.1086

Correct answer: A

A $\to$ product (First order reaction). Three sets of experiment were performed for a reaction under similar experimental conditions: Run 1 $\Rightarrow$ 100 mL of 10 M solution of reactant A; Run 2 $\Rightarrow$ 200 mL of 10 M solution of reactant A; Run 3 $\Rightarrow$ 100 mL of 10 M solution of reactant A + 100 mL of H$_2$O added. The correct variation of rate of reaction is

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

Correct answer: A

Two p-block elements X and Y form fluorides of the type EF$_3$. The fluoride compound XF$_3$ is a Lewis acid and YF$_3$ is a Lewis base. The hybridizations of the central atoms of XF$_3$ and YF$_3$ respectively are

1. A.Both sp$^2$
2. B.Both sp$^3$
3. C.sp$^2$ and sp$^3$✓
4. D.sp$^3$ and sp$^2$

Correct answer: C

Given below are two statements: Statement I: The halogen that makes longest bond with hydrogen in HX, has the smallest covalent radius in its group. Statement II: A group 15 element's hydride EH$_3$ has the lowest boiling point among corresponding hydrides of other group 15 elements. The maximum covalency of that element E is 4. In the light of the above statements, choose the correct answer from the options given below

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

Correct answer: A

A first row transition metal (M) does not liberate H$_2$ gas from dilute HCl. 1 mol of aqueous solution of MSO$_4$ is treated with excess of aqueous KCN and then H$_2$S(g) is passed through the solution. The amount of MS (metal sulphide) formed from the above reaction is ______ mol.

1. A.1
2. B.0✓
3. C.2
4. D.3

Correct answer: B

Consider the transition metal ions Mn$^{3+}$, Cr$^{3+}$, Fe$^{3+}$ and Co$^{3+}$ and all form low spin octahedral complexes. The correct decreasing order of unpaired electrons in their respective d-orbitals of the complexes is

1. A.Cr$^{3+}$ > Mn$^{3+}$ > Fe$^{3+}$ > Co$^{3+}$✓
2. B.Fe$^{3+}$ > Co$^{3+}$ > Mn$^{3+}$ > Cr$^{3+}$
3. C.Mn$^{3+}$ > Fe$^{3+}$ > Co$^{3+}$ > Cr$^{3+}$
4. D.Cr$^{3+}$ > Fe$^{3+}$ > Co$^{3+}$ > Mn$^{3+}$