JEE Advanced 2022 Paper 1 Question Paper

Question 1

Let $\alpha$ be a positive real number. Let $f : R \rightarrow R$ and $g : (\alpha, \infty) \rightarrow R$ be the functions defined by
$f(x) = \sin\left(\frac{\pi x}{12}\right)$ and $g(x) = \frac{2\log_{e}\left(\sqrt{x} - \sqrt{\alpha}\right)}{\log_{e}\left(e^{\sqrt{x}} - e^{\sqrt{\alpha}}\right)}$.
Then the value of $\lim_{x \rightarrow \alpha^{+}} f\left(g(x)\right)$ is __________.

Accepted Answer

0.5

Question 2

In a study about a pandemic, data of 900 persons was collected. It was found that
190 persons had symptom of fever,
220 persons had symptom of cough,
220 persons had symptom of breathing problem,
330 persons had symptom of fever or cough or both,
350 persons had symptom of cough or breathing problem or both,
340 persons had symptom of fever or breathing problem or both,
30 persons had all three symptoms (fever, cough and breathing problem).
If a person is chosen randomly from these 900 persons, then the probability that the person has at most one symptom is __________.

Accepted Answer

0.80

Question 3

Let z be a complex number with non-zero imaginary part. If $\frac{2+3z+4z^{2}}{2-3z+4z^{2}}$ is a real number, then the value of $|z|^{2}$ is __________.

Accepted Answer

0.50

Question 4

Let $\bar{z}$ denote the complex conjugate of a complex number z and let $i = \sqrt{-1}$. In the set of complex numbers, the number of distinct roots of the equation $\bar{z} - z^{2} = i\left(\bar{z} + z^{2}\right)$ is __________.

Accepted Answer

4

Question 5

Let $l_{1}, l_{2}, ....., l_{100}$ be consecutive terms of an arithmetic with common difference $d_{1}$, and let $w_{1}, w_{2}, ....., w_{100}$ be consecutive terms of another arithmetic progression with common difference $d_{2}$, where $d_{1}d_{2} = 10$. For each $i$ = 1, 2, ....., 100, let $R_{i}$ be a rectangle with length $l_{i}$, width $w_{i}$ and area $A_{i}$. If $A_{51} - A_{50} = 1000$, then the value of $A_{100} - A_{90}$ is __________.

Accepted Answer

18900

Question 6

The number of 4-digit integers in the closed interval [2022, 4482] formed by using the digits 0, 2, 3, 4, 6, 7 is __________.

Accepted Answer

569

Question 7

Consider the equation $\int_{1}^{e} \frac{\left(\log_{e} x\right)^{\frac{1}{2}}}{x\left(a - \left(\log_{e} x\right)^{\frac{3}{2}}\right)^{2}} \, dx = 1$, $a \in \left(-\infty, 0\right) \cup \left(1, \infty\right)$.
Which of the following statements is/are TRUE?

Accepted Answer

(C) An irrational number $a$ satisfies the above equation

Accepted Answer

(D) More than one $a$ satisfy the above equation

Answer

(A) No $a$ satisfies the above equation

Answer

(B) An integer $a$ satisfies the above equation

Question 8

Let $a_{1}, a_{2}, a_{3}, .....$ be an arithmetic progression with $a_{1} = 7$ and common difference 8. Let $T_{1}, T_{2}, T_{3}, .....$ be such that $T_{1} = 3$ and $T_{n+1} - T_{n} = a_{n}$ for $n \geq 1$. Then, which of the following is/are TRUE?

Accepted Answer

(B) $\sum_{k=1}^{20} T_{k} = 10510$

Accepted Answer

(C) $T_{30} = 3454$

Answer

(A) $T_{20} = 1604$

Answer

(D) $\sum_{k=1}^{30} T_{k} = 35610$

Question 9

Let $P_{1}$ and $P_{2}$ be two planes given by $P_{1} : 10x + 15y + 12z - 60 = 0$, $P_{2} : -2x + 5y + 4z - 20 = 0$. Which of the following straight lines can be an edge of some tetrahedron whose two faces lie on $P_{1}$ and $P_{2}$?

Accepted Answer

(A) $\frac{x-1}{0} = \frac{y-1}{0} = \frac{z-1}{5}$

Accepted Answer

(B) $\frac{x-6}{-5} = \frac{y}{2} = \frac{z}{3}$

Accepted Answer

(D) $\frac{x}{1} = \frac{y-4}{-2} = \frac{z}{3}$

Answer

(C) $\frac{x}{-2} = \frac{y-4}{5} = \frac{z}{4}$

Question 10

Let $S$ be the reflection of a point $Q$ with respect to the plane given by $\vec{r} = -\left(t + p\right)\hat{i} + t\hat{j} + \left(1 + p\right)\hat{k}$ where $t$, $p$ are real parameters and $\hat{i}$, $\hat{j}$, $\hat{k}$ are the unit vectors along the three positive coordinate axes. If the position vectors of $Q$ and $S$ are $10\hat{i} + 15\hat{j} + 20\hat{k}$ and $\alpha\hat{i} + \beta\hat{j} + \gamma\hat{k}$ respectively, then which of the following is/are TRUE?

Accepted Answer

(A) $3\left(\alpha + \beta\right) = -101$

Accepted Answer

(B) $3\left(\beta + \gamma\right) = -71$

Accepted Answer

(C) $3\left(\gamma + \alpha\right) = -86$

Answer

(D) $3\left(\alpha + \beta + \gamma\right) = -121$

Question 11

Consider the parabola $y^{2} = 4x$. Let $S$ be the focus of the parabola. A pair of tangents drawn to the parabola from the point $P = \left(-2, 1\right)$ meet the parabola at $P_{1}$ and $P_{2}$. Let $Q_{1}$ and $Q_{2}$ be points on the lines $SP_{1}$ and $SP_{2}$ respectively such that $PQ_{1}$ is perpendicular to $SP_{1}$ and $PQ_{2}$ is perpendicular to $SP_{2}$. Then, which of the following is/are TRUE?

Accepted Answer

(B) $Q_{1}Q_{2} = \frac{3\sqrt{10}}{5}$

Accepted Answer

(C) $PQ_{1} = 3$

Accepted Answer

(D) $SQ_{2} = 1$

Answer

(A) $SQ_{1} = 2$

Question 12

Let $|M|$ denote the determinant of a square matrix $M$. Let $g : \left[0, \frac{\pi}{2}ight] ightarrow R$ be the function defined by
$g(	heta) = \sqrt{f(	heta) - 1} + \sqrt{f\left(\frac{\pi}{2} - 	hetaight) - 1}$
where $f(	heta) = \frac{1}{2}\begin{vmatrix} 1 & \sin	heta & 1 \ -\sin	heta & 1 & \sin	heta \ -1 & -\sin	heta & 1 \end{vmatrix} + \begin{vmatrix} \sin\pi & \cos\left(	heta + \frac{\pi}{4}ight) & 	an\left(	heta - \frac{\pi}{4}ight) \ \sin\left(	heta - \frac{\pi}{4}ight) & -\cos\frac{\pi}{2} & \log_{e}\left(\frac{4}{\pi}ight) \ \cot\left(	heta + \frac{\pi}{4}ight) & \log_{e}\left(\frac{\pi}{4}ight) & 	an\pi \end{vmatrix}$.
Let $p(x)$ be a quadratic polynomial whose roots are the maximum and minimum values of the function $g(	heta)$ and $p(2) = 2 - \sqrt{2}$. Then, which of the following is/are TRUE?

Accepted Answer

(A) $p\left(\frac{3 + \sqrt{2}}{4}\right) < 0$

Accepted Answer

(C) $p\left(\frac{5\sqrt{2} - 1}{4}\right) > 0$

Answer

(B) $p\left(\frac{1 + 3\sqrt{2}}{4}\right) > 0$

Answer

(D) $p\left(\frac{5 - \sqrt{2}}{4}\right) < 0$

Question 13

Consider the following lists:

The correct option is:

Accepted Answer

(B) (I) → (P); (II) → (P); (III) → (T); (IV) → (R)

Answer

(A) (I) → (P); (II) → (S); (III) → (P); (IV) → (S)

Answer

(C) (I) → (Q); (II) → (P); (III) → (T); (IV) → (S)

Answer

(D) (I) → (Q); (II) → (S); (III) → (P); (IV) → (R)

Question 14

Two players, $P_{1}$ and $P_{2}$, play a game against each other. In every round of the game, each player rolls a fair die once, where the six faces of the die have six distinct numbers. Let $x$ and $y$ denote the readings on the die rolled by $P_{1}$ and $P_{2}$, respectively. If x > y, then $P_{1}$ scores 5 points and $P_{2}$ scores 0 points. If $x = y$, then each player scores 2 points. If $x < y$, then $P_{1}$ scores 0 point and $P_{2}$ scores 5 points. Let $X_{i}$ and $Y_{i}$ be the total scores of $P_{1}$ and $P_{2}$, respectively, after playing the $i^{	ext{th}}$ round.

The correct option is:

Accepted Answer

(A) (I) → (Q; (II) → (R); (III) → (T); (IV) → (S)

Answer

(B) (I) → (Q; (II) → (R); (III) → (T); (IV) → (T)

Answer

(C) (I) → (P); (II) → (R); (III) → (Q); (IV) → (S)

Answer

(D) (I) → (P); (II) → (R); (III) → (Q); (IV) → (T)

Question 15

Let $p$, $q$, $r$ be nonzero real numbers that are, respectively, the $10^{	ext{th}}$, $100^{	ext{th}}$ and $1000^{	ext{th}}$ terms of a harmonic progression. Consider the system of linear equation
$x + y + z = 1$
$10x + 100y + 1000z = 0$
$qrx + pry + pqz = 0$

The correct option is:

Accepted Answer

(B) (I) → (Q); (II) → (S); (III) → (S); (IV) → (R)

Answer

(A) (I) → (T); (II) → (R); (III) → (S); (IV) → (T)

Answer

(C) (I) → (Q); (II) → (R); (III) → (P); (IV) → (R)

Answer

(D) (I) → (T); (II) → (S); (III) → (P); (IV) → (T)

Question 16

Consider the ellipse $\frac{x^{2}}{4} + \frac{y^{2}}{3} = 1$. Let $H\left(\alpha, 0\right)$, $0 < \alpha < 2$, be a point. A straight line drawn through $H$ parallel to $y$-axis crosses the ellipse and its auxiliary circle at points $E$ and $F$ respectively, in the first quadrant. The tangents to the ellipse at the point $E$ intersects the positive $x$-axis at a point $G$. Suppose the straight line joining $F$ and the origin makes an angle $\phi$ with the positive $x$-axis.

The correct option is:

Accepted Answer

(C) (I) → (Q); (II) → (T); (III) → (S); (IV) → (P)

Answer

(A) (I) → (R); (II) → (S); (III) → (Q); (IV) → (P)

Answer

(B) (I) → (R); (II) → (T); (III) → (S); (IV) → (P)

Answer

(D) (I) → (Q); (II) → (S); (III) → (Q); (IV) → (P)

Question 17

Two spherical stars A and B have densities $\rho_A$ and $\rho_B$, respectively. A and B have the same radius, and their masses $M_A$ and $M_B$ are related by $M_B = 2 M_A$. Due to an interaction process, star A loses some of its mass, so that its radius is halved, while its spherical shape is retained, and its density remains $\rho_A$. The entire mass lost by A is deposited as a thick spherical shell on B with the density of the shell being $\rho_A$. If $v_A$ and $v_B$ are the escape velocities from A and B after the interaction process, the ratio $\frac{v_B}{v_A} = \sqrt{\frac{10n}{15^{1/3}}}$ . The value of n is

Accepted Answer

2.30

Question 18

The minimum kinetic energy needed by an alpha particle to cause the nuclear reaction $^{16}_{7}N + ^{4}_{2}He \rightarrow ^{1}_{1}H + ^{19}_{8}O$ in a laboratory frame is n (in MeV). Assume that $^{16}_{7}N$ is at rest in the laboratory frame. The masses of $^{16}_{7}N$, $^{4}_{2}He$, $^{1}_{1}H$ and $^{19}_{8}O$ can be taken to be 16.006 u, 4.003 u, 1.008 u and 19.003 u, respectively, where 1 u = 930 MeVc$^{-2}$. The value of n is __________.

Accepted Answer

2.32

Question 19

In the following circuit $C_1 = 12\ \mu F$, $C_2 = C_3 = 4\ \mu F$ and $C_4 = C_5 = 2\ \mu F$. The charge stored in $C_3$ is ________ $\mu C$.

Accepted Answer

8.00

Question 20

A rod of length 2 cm makes an angle $\frac{2\pi}{3}$ rad with the principal axis of a thin convex lens. The lens has a focal length of 10 cm and is placed at a distance of $\frac{40}{3}$ cm from the object as shown in the figure, The height of the image is $\frac{30\sqrt{3}}{13}$ and the angle made by it with respect to the principal axis is $\alpha$ rad. The value of $\alpha$ is $\frac{\pi}{n}\ rad$ , where n is ___________

Accepted Answer

6.00

Question 21

At time t=0, a disk of radius 1 m starts to roll without slipping on a horizontal plane with an angular acceleration of $\alpha = \frac{2}{3}\ rad\ s^{-2}$ . A small stone is stuck to the disk. At t = 0, it is at the contact point of the disk and the plane. Later, at time $t = \sqrt{\pi}$ s, the stone detaches itself and flies off tangentially from the disk. The maximum height (in m) reached by the stone measured from the plane is $\frac{1}{2} + \frac{x}{10}$. The value of x is______ [Take g= 10ms$^{-2}$.]

Accepted Answer

0.52

Question 22

A solid sphere of mass 1 kg and radius 1 m rolls without slipping on a fixed inclined plane with an angle of inclination $	heta=30^\circ$ from the horizontal. Two forces of magnitude 1N each, parallel to the incline, act on the sphere, both at distance r = 0.5 m from the center of the sphere, as shown in the figure. The acceleration of the sphere down the plane is ________ ms$^{-2}$. (Take g = 10 ms$^{-2}$.)

Accepted Answer

2.85 or 2.86

Question 23

Consider an LC circuit, with inductance L=0.1 H and capacitance $C = 10^{-3}$ F, kept on a plane. The area of the circuit is 1 m$^2$. It is placed in a constant magnetic field of strength $B_0$ which is perpendicular to the plane of the circuit. At time t = 0, the magnetic field strength starts increasing linearly as $B = B_0 + \beta t$ with $\beta = 0.04 Ts^{-1}$. The maximum magnitude of the current in the circuit is__________ mA .

Accepted Answer

4.00

Question 24

A projectile is fired from horizontal ground with speed v and projection angle $	heta$. When the acceleration due to gravity is g, the range of the projectile is d. If at the highest point in its trajectory, the projectile enters a different region where the effective acceleration due to gravity is $g' = \frac{g}{0.81}$ , then the new range is d'=nd. The value of n is __________.

Accepted Answer

0.95

Question 25

A medium having dielectric constant $K > 1$ fills the space between the plates of a parallel plate capacitor. The plates have large area, and the distance between them is $d$. The capacitor is connected to a battery of voltage $V$, as shown in Figure (a). Now, both the plates are moved by a distance d/2 of from their original positions, as shown in Figure (b).
In the process of going from the configuration depicted in Figure (a) to that in Figure (b), which of the following statement(s) is(are) correct?

Accepted Answer

(B) The capacitance is decreased by a factor of $\frac{1}{K+1}$ .

Answer

(A) The electric field inside the dielectric material is reduced by a factor of 2K.

Answer

(C) The voltage between the capacitor plates is increased by a factor of (K+1).

Answer

(D) The work done in the process DOES NOT depend on the presence of the dielectric material.

Question 26

The figure shows a circuit having eight resistances of $1\Omega$ each, labelled $R_1$ to $R_8$, and two ideal batteries with voltages $\varepsilon_1 =12$ V and $\varepsilon_2 = 6$ V.
Which of the following statement(s) is(are) correct?

Accepted Answer

(A) The magnitude of current flowing through $R_1$ is 7.2 A.

Accepted Answer

(B) The magnitude of current flowing through $R_2$ is 1.2 A.

Accepted Answer

(C) The magnitude of current flowing through $R_3$ is 4.8 A.

Accepted Answer

(D) The magnitude of current flowing through $R_5$ is 2.4 A.

Question 27

An ideal gas of density $\rho = 0.2$ kg m$^{-3}$ enters a chimney of height h at the rate of $\alpha = 0.8$ kg s$^{-1}$ from its lower end, and escapes through the upper end as shown in the figure. The cross-sectional area of the lower end is $A_1 = 0.1$ m$^2$ and the upper end is $A_2 = 0.4$ m$^2$. The pressure and the temperature of the gas at the lower end are 600 Pa and 300 K, respectively, while its temperature at the upper end is 150 K. The chimney is heat insulated so that the gas undergoes adiabatic expansion. Take g = 10 ms$^{-2}$ and the ratio of specific heats of the gas $\gamma = 2$. Ignore atmospheric pressure.
Which of the following statement(s) is(are) correct?

Accepted Answer

(B) The velocity of the gas at the lower end of the chimney is 40 ms$^{-1}$ and at the upper end is 20 ms$^{-1}$.

Answer

(A) The pressure of the gas at the upper end of the chimney is 300 Pa.

Answer

(C) The height of the chimney is 590m.

Answer

(D) The density of the gas at the upper end is 0.05 kg m$^{-3}$

Question 28

Three plane mirrors form an equilateral triangle with each side of length L. There is a small hole at a distance $l > 0$ from one of the corners as shown in the figure. A ray of light is passed through the hole at an angle $	heta$ and can only come out through the same hole. The cross section of the mirror configuration and the ray of light lie on the same plane.
Which of the following statement(s) is(are) correct?

Accepted Answer

(A) The ray of light will come out for $	heta = 30^\circ$, for $0 < l < L$.

Accepted Answer

(B) There is an angle for $l = \frac{L}{2}$ at which the ray of light will come out after two reflections.

Answer

(C) The ray of light will NEVER come out for $	heta = 60^\circ$, and $l = \frac{L}{3}$

Answer

(D) The ray of light will come out for $	heta= 60^\circ$, and $0 < l < \frac{L}{2}$ after six reflections.

Question 29

Six charges are placed around a regular hexagon of side length a as shown in the figure. Five of them have charge q , and the remaining one has charge x . The perpendicular from each charge to the nearest hexagon side passes through the center O of the hexagon and is bisected by the side.
Which of the following statement(s) is(are) correct in SI units?

Accepted Answer

(A) When x = q , the magnitude of the electric field at O is zero.

Accepted Answer

(B) When x = $-$q , the magnitude of the electric field at O is $\frac{q}{6\pi \epsilon_0 a^2}$

Accepted Answer

(C) When x = 2q, the potential at O is $\frac{7q}{4\sqrt{3}\pi \epsilon_0 a}$ .

Answer

(D) When x = $-$ 3q , the potential at O is $-\frac{3q}{4\sqrt{3}\pi \epsilon_0 a}$

Question 30

The binding energy of nucleons in a nucleus can be affected by the pairwise Coulomb repulsion. Assume that all nucleons are uniformly distributed inside the nucleus. Let the binding energy of a proton be $E_b^p$ and the binding energy of a neutron be $E_b^n$ in the nucleus.
Which of the following statement(s) is(are) correct?

Accepted Answer

(A) $E_b^p - E_b^n$ is proportional to $Z(Z-1)$ where Z is the atomic number of the nucleus.

Accepted Answer

(B) $E_b^p - E_b^n$ is proportional to $A^{-\frac{1}{3}}$ where A is the mass number of the nucleus.

Accepted Answer

(D) $E_b^p$ increases if the nucleus undergoes a beta decay emitting a positron.

Answer

(C) $E_b^p - E_b^n$ is positive.

Question 31

List I describes four systems, each with two particles A and B in relative motion as shown in figures. List II gives possible magnitudes of their relative velocities (in m s$^{-1}$) at time $t = \frac{\pi}{3}$s.
Which one of the following options is correct ?

Accepted Answer

(C) I $\rightarrow$ S, II $\rightarrow$ T, III $\rightarrow$ P, IV $\rightarrow$ R

Answer

(A) I $\rightarrow$ R, II $\rightarrow$ T, III $\rightarrow$ P, IV $\rightarrow$ S

Answer

(B) I $\rightarrow$ S, II $\rightarrow$ P, III $\rightarrow$ Q, IV $\rightarrow$ R

Answer

(D) I $\rightarrow$ T, II $\rightarrow$ P, III $\rightarrow$ R, IV $\rightarrow$ S

Question 32

List I describes thermodynamic processes in four different systems. List II gives the magnitudes (either exactly or as a close approximation) of possible changes in the internal energy of the system due to the process.
Which one of the following options is correct ?

Accepted Answer

(C) I $\rightarrow$ P, II $\rightarrow$ R, III $\rightarrow$ T, IV $\rightarrow$ Q

Answer

(A) I $\rightarrow$ T, II $\rightarrow$ R, III $\rightarrow$ S, IV $\rightarrow$ Q

Answer

(B) I $\rightarrow$ S, II $\rightarrow$ P, III $\rightarrow$ T, IV $\rightarrow$ P

Answer

(D) I $\rightarrow$ Q, II $\rightarrow$ R, III $\rightarrow$ S, IV $\rightarrow$ T

Question 33

2 mol of Hg(g) is combusted in a fixed volume bomb calorimeter with excess of $\mathrm{O_2}$ at 298 K and 1 atm into HgO(s). During the reaction, temperature increases from 298.0 K to 312.8 K. If heat capacity of the bomb calorimeter and enthalpy of formation of Hg(g) are 20.00 kJ $\mathrm{K^{-1}}$ and 61.32 kJ $\mathrm{mol^{-1}}$ at 298 K, respectively, the calculated standard molar enthalpy of formation of HgO(s) at 298 K is X kJ $\mathrm{mol^{-1}}$. The value of $|X|$ is ________.
[Given: Gas constant R = 8.3 J $\mathrm{K^{-1}}$ $\mathrm{mol^{-1}}$]

Accepted Answer

90.39

Question 34

The reduction potential $\left(\mathrm{E}^{0}	ext{, in V}ight)$ of $\mathrm{MnO_4^-(aq)\,/\,Mn(s)}$ is
$\left[	ext{Given}: \mathrm{E}^{0}_{\left(\mathrm{MnO_4^-(aq)/MnO_2((s))}ight)} = 1.68\,\mathrm{V};\ \mathrm{E}^{0}_{\left(\mathrm{MnO_2(s)/Mn^{2+}(aq)}ight)} = 1.21\,\mathrm{V};\ \mathrm{E}^{0}_{\left(\mathrm{Mn^{2+}(aq)/Mn((s))}ight)} = -1.03\,\mathrm{V}ight]$

Accepted Answer

0.77

Question 35

A solution is prepared by mixing 0.01 mol each of $\mathrm{H_2CO_3}$, $\mathrm{NaHCO_3}$, $\mathrm{Na_2CO_3}$, and NaOH in 100 mL of water. pH of the resulting solution is ________.
[Given: $p\mathrm{Ka_1}$ and $p\mathrm{Ka_2}$ of $\mathrm{H_2CO_3}$ are 6.37 and 10.32, respectively; $\log 2 = 0.30$]

Accepted Answer

10.02

Question 36

The treatment of an aqueous solution of 3.74 g of $\mathrm{Cu(NO_3)_2}$ with excess KI results in a brown solution along with the formation of a precipitate. Passing $\mathrm{H_2S}$ through this brown solution gives another precipitate $\mathbf{X}$. The amount of $\mathbf{X}$ (in g) is ________.
[Given: Atomic mass of H = 1, N = 14, O = 16, S = 32, K = 39, Cu = 63, I = 127]

Accepted Answer

0.32

Question 37

Dissolving 1.24 g of white phosphorous in boiling NaOH solution in an inert atmosphere gives a gas $\mathbf{Q}$. The amount of $\mathrm{CuSO_4}$ (in g) required to completely consume the gas $\mathbf{Q}$ is ________.
[Given: Atomic mass of H = 1, O = 16, Na = 23, P = 31, S = 32, Cu = 63]

Accepted Answer

2.38

Question 38

Consider the following reaction.
On estimation of bromine in 1.00 g of $\mathbf{R}$ using Carius method, the amount of AgBr formed (in g) is ________.
[Given: Atomic mass of H = 1, C = 12, O = 16, P = 31, Br = 80, Ag = 108].

Accepted Answer

1.50

Question 39

The weight percentage of hydrogen in $\mathbf{Q}$, formed in the following reaction sequence, is ________.
[Given: Atomic mass of H = 1, C = 12, N = 14, O = 16, S = 32, Cl = 35]

Accepted Answer

1.31

Question 40

If the reaction sequence given below is carried out with 15 moles of acetylene, the amount of the product $\mathbf{D}$ formed (in g) is ________.
The yields of $\mathbf{A}$, $\mathbf{B}$, $\mathbf{C}$ and $\mathbf{D}$ are given in parentheses.
[Given: Atomic mass of H = 1, C = 12, O = 16, Cl = 35]

Accepted Answer

136.00

Question 41

For diatomic molecules, the correct statement(s) about the molecular orbitals formed by the overlap of two $\mathrm{2p_z}$ orbitals is(are)

Accepted Answer

(A) $\sigma$ orbital has a total of two nodal planes

Accepted Answer

(D) $\pi^*$ orbital has one node in the xy-plane containing the molecular axis.

Answer

(B) $\sigma^*$ orbital has one node in the xz-plane containing the molecular axis.

Answer

(C) $\pi$ orbital has one node in the plane which is perpendicular to the molecular axis and goes through the center of the molecule.

Question 42

The correct opion(s) related to adsorption process is (are)

Accepted Answer

(A) Chemisorption results in unimolecular layer.

Accepted Answer

(D) Lowering the temperature favours physisorption process

Answer

(B) The enthalpy change during physisorption is in the range of 100 to 140 kJ $\mathrm{mol^{-1}}$

Answer

(C) Chemisorption is an endothermic process

Question 43

The electrochemical extraction of aluminum from bauxite ore involves

Accepted Answer

(B) the neutralization of aluminate solution by passing $\mathrm{CO_2}$ gas to precipitate hydrated alumina ($\mathrm{Al_2O_3 \cdot 3H_2O}$).

Accepted Answer

(C) the dissolution of $\mathrm{Al_2O_3}$ in hot aqueous NaOH.

Accepted Answer

(D) the electrolysis of $\mathrm{Al_2O_3}$ mixed with $\mathrm{Na_3AlF_6}$ to give Al and $\mathrm{CO_2}$.

Answer

(A) the reaction of $\mathrm{Al_2O_3}$ with coke (C) at a temperature $> 2500\ ^\circ\mathrm{C}$.

Question 44

The treatment of galena with $\mathrm{HNO_3}$ produces a gas that is

Accepted Answer

(A) paramagnetic

Accepted Answer

(D) colorless

Answer

(B) bent in geometry

Answer

(C) an acidic oxide

Question 45

Considering the reaction sequence given below, the correct statement(s) is(are)

Accepted Answer

(B) Treating $\mathbf{P}$ with conc. $\mathrm{NH_4OH}$ solution followed by acidification gives $\mathbf{Q}$.

Accepted Answer

(C) Treating $\mathbf{Q}$ with a solution of $\mathrm{NaNO_2}$ in aq. HCl liberates $\mathrm{N_2}$.

Accepted Answer

(D) $\mathbf{P}$ is more acidic than $\mathrm{CH_3CH_2COOH}$.

Answer

(A) $\mathbf{P}$ can be reduced to a primary alcohol using $\mathrm{NaBH_4}$.

Question 46

Considering the following reaction sequence,
the correct option(s) is(are)

Accepted Answer

(A) (A)

Accepted Answer

(B) (B)

Accepted Answer

(C) (C)

Answer

(D) (D)

Question 47

Match the rate expressions in LIST-I for the decomposition of X with the corresponding profiles provided in LIST-II. $\mathrm{X_s}$ and k are constants having appropriate units.
LIST-I
(I) rate $= \frac{k[X]}{X_s + [X]}$ under all possible initial concentrations of X
(II) rate $= \frac{k[X]}{X_s + [X]}$ where initial concentrations of X are much less than $\mathrm{X_s}$
(III) rate $= \frac{k[X]}{X_s + [X]}$ where initial concentrations of X are much higher than $\mathrm{X_s}$
(IV) rate $= \frac{k[X]^{2}}{X_s + [X]}$ where initial concentration of X is much higher than $\mathrm{X_s}$

Accepted Answer

(A) I $\rightarrow$ P; II $\rightarrow$ Q; III $\rightarrow$ S; IV $\rightarrow$ T

Answer

(B) I $\rightarrow$ R; II $\rightarrow$ S; III $\rightarrow$ S; IV $\rightarrow$ T

Answer

(C) I $\rightarrow$ P; II $\rightarrow$ Q; III $\rightarrow$ Q; IV $\rightarrow$ R

Answer

(D) I $\rightarrow$ R; II $\rightarrow$ S; III $\rightarrow$ Q; IV $\rightarrow$ R

Question 48

LIST-I contains compounds and LIST-II contains reactions.
Match each compound in LIST-I with its formation reaction(s) in LIST-II, and choose the correct option

Accepted Answer

(D) I $\rightarrow$ Q; II $\rightarrow$ R; III $\rightarrow$ S; IV $\rightarrow$ P

Answer

(A) I $\rightarrow$ Q; II $\rightarrow$ P; III $\rightarrow$ S; IV $\rightarrow$ R

Answer

(B) I $\rightarrow$ T; II $\rightarrow$ P; III $\rightarrow$ Q; IV $\rightarrow$ R

Answer

(C) I $\rightarrow$ T; II $\rightarrow$ R; III $\rightarrow$ Q; IV $\rightarrow$ P

Question 49

LIST-I contains metal species and LIST-II contains their properties.
[Given: Atomic number of Cr = 24, Ru = 44, Fe = 26]
Match each metal species in LIST-I with their properties in LIST-II, and choose the correct option

Accepted Answer

(A) I $\rightarrow$ R, T; II $\rightarrow$ P, S; III $\rightarrow$ Q, T; IV $\rightarrow$ P, Q

Answer

(B) I $\rightarrow$ R, S; II $\rightarrow$ P, T; III $\rightarrow$ P, Q; IV $\rightarrow$ Q, T

Answer

(C) I $\rightarrow$ P, R; II $\rightarrow$ R, S; III $\rightarrow$ R, T; IV $\rightarrow$ P, T

Answer

(D) I $\rightarrow$ Q, T; II $\rightarrow$ S, T; III $\rightarrow$ P, T; IV $\rightarrow$ Q, R

Question 50

Match the compounds in LIST-I with the observations in LIST-II, and choose the correct option.

Accepted Answer

(D) I $\rightarrow$ P, S; II $\rightarrow$ T; III $\rightarrow$ Q, R; IV $\rightarrow$ P

Answer

(A) I $\rightarrow$ P, Q; II $\rightarrow$ S; III $\rightarrow$ Q, R; IV $\rightarrow$ P

Answer

(B) I $\rightarrow$ P; II $\rightarrow$ R, S; III $\rightarrow$ R; IV $\rightarrow$ Q, S

Answer

(C) I $\rightarrow$ Q, S; II $\rightarrow$ P, T; III $\rightarrow$ P; IV $\rightarrow$ S

List-I	List-II
I.A and B are moving on a horizontal circle of radius 1 m with uniform angular speed $\omega = 1$ rad s $^{-1}$ . The initial angular positions of A and B at time t = 0 are $\theta = 0$ and $\theta = \frac{\pi}{2}$ , respectively.	P. $\frac{\sqrt{3}+1}{2}$
II.Projectiles A and B are fired (in the same vertical plane) at t = 0 and t = 0.1 s respectively, with the same speed $v = \frac{5\pi}{\sqrt{2}}$ m s $^{-1}$ and at 45 $^\circ$ from the horizontal plane. The initial separation between A and B is large enough so that they do not collide. (g = 10 m s $^{-2}$ ).	Q. $\frac{\left(\sqrt{3}-1\right)}{\sqrt{2}}$
III.Two harmonic oscillators A and B moving in the x direction according to $x_A = x_0 \sin \frac{t}{t_0}$ and $x_B = x_0 \sin\left(\frac{t}{t_0} + \frac{\pi}{2}\right)$ respectively, starting from t = 0. Take $x_0 = 1$ m, $t_0 = 1$ s.	R. $\sqrt{10}$
IV.Particle A is rotating in a horizontal circular path of radius 1 m on the xy plane, with constant angular speed $\omega = 1$ rad s $^{-1}$ . Particle B is moving up at a constant speed 3 m s $^{-1}$ in the vertical direction as shown in the figure. (Ignore gravity.)	S. $\sqrt{2}$
	T. $\sqrt{25\pi^2+1}$

List-I	List-II
I. $10^{-3}$ kg of water at 100 $^\circ$ C is converted to steam at the same temperature, at a pressure of $10^{5}$ Pa. The volume of the system changes from $10^{-6}$ m $^3$ to $10^{-3}$ m $^3$ in the process. Latent heat of water = 2250 kJ/kg.	P.2 kJ
II.0.2 moles of a rigid diatomic ideal gas with volume V at temperature 500 K undergoes an isobaric expansion to volume 3 V. Assume R = 8.0 J mol $^{-1}$ K $^{-1}$ .	Q.7 kJ
III.One mole of a monatomic ideal gas is compressed adiabatically from volume $V = \frac{1}{3}m^3$ and pressure 2 kPa to volume $\frac{V}{8}$ .	R.4 kJ
IV.Three moles of a diatomic ideal gas whose molecules can vibrate, is given 9 $kJ$ of heat and undergoes isobaric expansion.	S.5 kJ
	T.3 kJ

LIST-I	LIST-II
I. $\mathrm{H_2O_2}$	P. $\mathrm{Mg(HCO_3)_2 + Ca(OH)_2 \rightarrow}$
II. $\mathrm{Mg(OH)_2}$	Q. $\mathrm{BaO_2 + H_2SO_4 \rightarrow}$
III. $\mathrm{BaCl_2}$	R. $\mathrm{Ca(OH)_2 + MgCl_2 \rightarrow}$
IV. $\mathrm{CaCO_3}$	S. $\mathrm{BaO_2 + HCl \rightarrow}$
	T. $\mathrm{Ca(HCO_3)_2 + Ca(OH)_2 \rightarrow}$

LIST-I	LIST-II
I. $\left[\mathrm{Cr(CN)_6}\right]^{4-}$	P. $\mathrm{t_{2g}}$ orbitals contain 4 electrons
II. $\left[\mathrm{RuCl_6}\right]^{2-}$	Q. $\mu(\mathrm{spin-only}) = 4.9\,\mathrm{BM}$
III. $\left[\mathrm{Cr(H_2O_6)}\right]^{2+}$	R.Low spin complex ion
IV. $\left[\mathrm{Fe(H_2O)_6}\right]^{2+}$	S.Metal ion in 4+ oxidation state
	T. $\mathrm{d^4}$ species

LIST-I	LIST-II
I.Aniline	P.Sodium fusion extract of the compound on boiling with $\mathrm{FeSO_4}$ , followed by acidification with conc. $\mathrm{H_2SO_4}$ , gives Prussian blue color.
II. $o$ -Cresol	Q.Sodium fusion extract of the compound on treatment with sodium nitroprusside gives blood red color.
III.Cysteine	R.Addition of the compound to a saturated solution of $\mathrm{NaHCO_3}$ results in effervescence.
IV.Caprolactam	S.The compound reacts with bromine water to give a white precipitate.
	T.Treating the compound with neutral $\mathrm{FeCl_3}$ solution produces violet color.

JEE Advanced 2022 Paper 1 Question Paper with Answers

Physics — JEE Advanced 2022 Paper 1

Chemistry — JEE Advanced 2022 Paper 1

Mathematics — JEE Advanced 2022 Paper 1

Chapters tested in this paper

Attempt JEE Advanced 2022 Paper 1 under exam timing.

List-I	List-II
I. $\left\{x \in \left[-\frac{2\pi}{3}, \frac{2\pi}{3}\right] : \cos x + \sin x = 1\right\}$	P.has two elements
II. $\left\{x \in \left[-\frac{5\pi}{18}, \frac{5\pi}{18}\right] : \sqrt{3}\tan 3x = 1\right\}$	Q.has three elements
III. $\left\{x \in \left[-\frac{6\pi}{5}, \frac{6\pi}{5}\right] : 2\cos\left(2x\right) = \sqrt{3}\right\}$	R.has four elements
IV. $\left\{x \in \left[-\frac{7\pi}{4}, \frac{7\pi}{4}\right] : \sin x - \cos x = 1\right\}$	S.has five elements
	T.has six elements

List-I	List-II
I.Probability of $\left(X_{2} \geq Y_{2}\right)$ is	P. $\frac{3}{8}$
II.Probability of $\left(X_{2} > Y_{2}\right)$ is	Q. $\frac{11}{16}$
III.Probability of $\left(X_{3} = Y_{3}\right)$ is	R. $\frac{5}{16}$
IV.Probability of $\left(X_{3} > Y_{3}\right)$ is	S. $\frac{355}{864}$
	T. $\frac{77}{432}$

List-I	List-II
I.If $\frac{q}{r} = 10$ , then the system of linear equations has	P. $x = 0$ , $y = \frac{10}{9}$ , $z = -\frac{1}{9}$
II.If $\frac{p}{r} \neq 100$ , then the system of linear equations has	Q. $x = \frac{10}{9}$ , $y = -\frac{1}{9}$ , $z = 0$ as a solution
III.If $\frac{p}{q} \neq 10$ , then the system of linear equation has	R.infinitely many solutions
IV.If $\frac{p}{q} = 10$ , then the system of linear equations has	S.no solution
	T.at least one solution

List-I	List-II
I.If $\phi = \frac{\pi}{4}$ , then the area of the triangle $FGH$ is	P. $\frac{\left(\sqrt{3} - 1\right)^{4}}{8}$
II.If $\phi = \frac{\pi}{3}$ , then the area of the triangle $FGH$ is	Q. $1$
III.If $\phi = \frac{\pi}{6}$ , then the area of the triangle $FGH$ is	R. $\frac{3}{4}$
IV.If $\phi = \frac{\pi}{12}$ , then the area of the triangle $FGH$ is	S. $\frac{1}{2\sqrt{3}}$
	T. $\frac{3\sqrt{3}}{2}$