JEE Advanced 2022 Paper 2 Question Paper

Question 1

Let α and β be real numbers such that $-\frac{\pi}{4} < \beta < 0 < \alpha < \frac{\pi}{4}$. If $\sin(\alpha + \beta) = \frac{1}{3}$ and $\cos\left(\alpha - \beta\right) = \frac{2}{3}$, then the greatest integer less than or equal to $\left(\frac{\sin\alpha}{\cos\beta} + \frac{\cos\beta}{\sin\alpha} + \frac{\cos\alpha}{\sin\beta} + \frac{\sin\beta}{\cos\alpha}\right)^{2}$ is ________.

Accepted Answer

1

Question 2

If y(x) is the solution of the differential equation $xdy - \left(y^{2} - 4y\right)dx = 0$ for x > 0, y(1) = 2, and the slope of the curve y = y(x) is never zero, then the value of $10y\left(\sqrt{2}\right)$ is ________.

Accepted Answer

8

Question 3

The greatest integer less than or equal to $\int_{1}^{2} \log_{2}\left(x^{3} + 1\right)dx + \int_{1}^{\log_{2}9} \left(2^{x} - 1\right)^{1/3} dx$ is ______.

Accepted Answer

5

Question 4

The product of all positive real values of x satisfying the equation $x^{\left(16\left(\log_{5}x\right)^{3} - 68\log_{5}x\right)} = 5^{-16}$ is ________.

Accepted Answer

1

Question 5

If $\beta = \lim_{x 	o 0} \frac{e^{x^{3}} - \left(1 - x^{3}ight)^{1/3} + \left(\left(1 - x^{2}ight)^{1/2} - 1ight)\sin x}{x\sin^{2}x}$, then the value of 6β is ________.

Accepted Answer

5

Question 6

Let β be real number. Consider the matrix A = $\begin{pmatrix} \beta & 0 & 1 \ 2 & 1 & -2 \ 3 & 1 & -2 \end{pmatrix}$. If $A^{7} - \left(\beta - 1ight)A^{6} - \beta A^{5}$ is a singular matrix, then the value of 9β is ________.

Accepted Answer

3

Question 7

Consider the hyperbola $\frac{x^{2}}{100} - \frac{y^{2}}{64} = 1$ with foci at S and S$_{1}$, where S lies on the positive x-axis. Let P be a point on the hyperbola, in the first quadrant. Let $\angle SPS_{1} = \alpha$, with $\alpha < \frac{\pi}{2}$. The straight line passing through the point S and having the same slope as that of the tangent at P to the hyperbola, intersects the straight line S$_{1}$P at P$_{1}$. Let δ be the distance of P from the straight line SP$_{1}$, and β = S$_{1}$P. Then the greatest integer less than or equal to $\frac{\beta\delta}{9}\sin\frac{\alpha}{2}$ is ________.

Accepted Answer

7

Question 8

Consider the function f, g : R → R defined by $f\left(xight) = x^{2} + \frac{5}{12}$ and $g(x) = \begin{cases} 2\left(1 - \frac{4|x|}{3}ight), & |x| \leq \frac{3}{4}, \ 0, & |x| > \frac{3}{4}. \end{cases}$ If α is the area of the region $\left\{\left(x, yight) \in R 	imes R : |x| \leq \frac{3}{4}, 0 \leq y \leq \min\left\{f\left(xight), g\left(xight)ight\}ight\}$, then the value of 9α is __________.

Accepted Answer

6

Question 9

Let PQRS be a quadrilateral in a plane, where $QR = 1$, $\angle PQR = \angle QRS = 70^\circ$, $\angle PQS = 15^\circ$ and $\angle PRS = 40^\circ$. If $\angle RPS = 	heta^\circ$, $PQ = \alpha$ and $PS = \beta$, then the interval(s) that contain(s) the value of $4\alpha\beta \sin	heta^\circ$ is/are

Accepted Answer

(A) $\left(0, \sqrt{2}\right)$

Accepted Answer

(B) $(1, 2)$

Answer

(C) $\left(\sqrt{2}, 3\right)$

Answer

(D) $\left(2\sqrt{2}, 3\sqrt{2}\right)$

Question 10

Let α = $\sum_{k=1}^{\infty} \sin^{2k}\left(\frac{\pi}{6}\right)$. Let g : [0, 1] → R be the function defined by g(x) = 2$^{αx}$ + 2$^{α(1−x)}$. Then, which of the following statements is/are TRUE?

Accepted Answer

(A) The minimum value of g(x) is $2^{\frac{7}{6}}$

Accepted Answer

(B) The maximum value of g(x) is 1 + $2^{\frac{1}{3}}$

Accepted Answer

(C) The function g(x) attains its maximum at more than one point

Answer

(D) The function g(x) attains its minimum at more than one point

Question 11

Let z̄ denote the complex conjugate of a complex number z. If z is a non-zero complex number for which both real and imaginary parts of $\left(\bar{z}\right)^{2}$ + $\frac{1}{z^{2}}$ are integers, than which of the following is/are possible value(s) of |z|?

Accepted Answer

(A) $\left(\frac{43+3\sqrt{205}}{2}\right)^{\frac{1}{4}}$

Answer

(B) $\left(\frac{7+\sqrt{33}}{4}\right)^{\frac{1}{4}}$

Answer

(C) $\left(\frac{9+\sqrt{65}}{4}\right)^{\frac{1}{4}}$

Answer

(D) $\left(\frac{7+\sqrt{13}}{6}\right)^{\frac{1}{4}}$

Question 12

Let G be a circle of radius R > 0. Let G$_{1}$, G$_{2}$, …, G$_{n}$ be n circles of equal radius r > 0. Suppose each of the n circles G$_{1}$, G$_{2}$, …, G$_{n}$ touches the circle G externally. Also, for i = 1, 2, …, n − 1, the circle G$_{i}$ touches G$_{i+1}$ externally, and G$_{n}$ touches G$_{1}$ externally. Then, which of the following statements is/are TRUE?

Accepted Answer

(C) If n = 8, then $\left(\sqrt{2}-1\right)$r < R

Accepted Answer

(D) If n = 12, then $\sqrt{2}\left(\sqrt{3}+1\right)$r > R .

Answer

(A) If n = 4, then $\left(\sqrt{2}-1\right)$r < R

Answer

(B) If n = 5, then r < R

Question 13

Let $\hat{i}$, $\hat{j}$ and $\hat{k}$ be the unit vectors along the three positive coordinate axes. Let
$\vec{a} = 3\hat{i} + \hat{j} - \hat{k}$,
$\vec{b} = \hat{i} + b_{2}\hat{j} + b_{3}\hat{k}$,   b$_{2}$, b$_{3}$ ∈ R
$\vec{c} = c_{1}\hat{i} + c_{2}\hat{j} + c_{3}\hat{k}$,   c$_{1}$, c$_{2}$, c$_{3}$ ∈ R
be the vectors such that b$_{2}$ b$_{3}$ > 0, $\vec{a} \cdot \vec{b} = 0$ and
$\begin{pmatrix} 0 & -c_{3} & c_{2} \ c_{3} & 0 & -c_{1} \ -c_{2} & c_{1} & 0 \end{pmatrix}\begin{pmatrix} 1 \ b_{2} \ b_{3} \end{pmatrix} = \begin{pmatrix} 3-c_{1} \ 1-c_{2} \ -1-c_{3} \end{pmatrix}$
Then, which of the following is/are TRUE?

Accepted Answer

(B) $\vec{b} \cdot \vec{c} = 0$

Accepted Answer

(C) $\left|\vec{b}\right| > \sqrt{10}$

Accepted Answer

(D) $\left|\vec{c}\right| \leq \sqrt{11}$ .

Answer

(A) $\vec{a} \cdot \vec{c} = 0$

Question 14

For x ∈ R, let the function y(x) be the solution of the differential equation
$\frac{dy}{dx} + 12y = \cos\left(\frac{\pi}{12}x\right)$, y(0) = 0 .
Then, which of the following statements is/are TRUE?

Accepted Answer

(C) There exists a real number β such that the line y = β intersects the curve y = y(x) at infinitely many points

Answer

(A) y(x) is an increasing function

Answer

(B) y(x) is a decreasing function

Answer

(D) y(x) is a periodic function

Question 15

Consider 4 boxes, where each box contains 3 red balls and 2 blue balls. Assume that all 20 balls are distinct. In how many different ways can 10 balls be chosen from these 4 boxes so that from each box at least one red ball and one blue ball are chosen?

Accepted Answer

(A) 21816

Answer

(B) 85536

Answer

(C) 12096

Answer

(D) 156816

Question 16

If M = $\begin{pmatrix} \frac{5}{2} & \frac{3}{2} \ -\frac{3}{2} & -\frac{1}{2} \end{pmatrix}$ , then which of the following matrices is equal to M$^{2022}$?

Accepted Answer

(A) $\begin{pmatrix} 3034 & 3033 \ -3033 & -3032 \end{pmatrix}$

Answer

(B) $\begin{pmatrix} 3034 & -3033 \ 3033 & -3032 \end{pmatrix}$

Answer

(C) $\begin{pmatrix} 3033 & 3032 \ -3032 & -3031 \end{pmatrix}$

Answer

(D) $\begin{pmatrix} 3032 & 3031 \ -3031 & -3030 \end{pmatrix}$

Question 17

Suppose that
Box-I contains 8 red, 3 blue and 5 green balls,
Box-II contains 24 red, 9 blue and 15 green balls,
Box-III contains 1 blue, 12 green and 3 yellow balls,
Box-IV contains 10 green, 16 orange and 6 white balls,
A ball is chosen randomly for Box-I; call that ball b. If b is red then a ball is chosen randomly from Box-II, if b is blue then a ball is chosen randomly from Box-III, and if b is green then a ball is chosen randomly from Box-IV. The conditional probability of the event 'one of the chosen balls is white' given that the event 'at least one of the chosen ball is green' has happened, is equal to

Accepted Answer

(C) $\frac{5}{52}$

Answer

(A) $\frac{15}{256}$

Answer

(B) $\frac{3}{16}$

Answer

(D) $\frac{1}{8}$ .

Question 18

For positive integer n, define
f(n) = n + $\frac{16+5n-3n^{2}}{4n+3n^{2}}$ + $\frac{32+n-3n^{2}}{8n+3n^{2}}$ + $\frac{48-3n-3n^{2}}{12n+3n^{2}}$ + … + $\frac{25n-7n^{2}}{7n^{2}}$ .
Then, the value of $\lim_{n 	o \infty}$ f(n) is equal to

Accepted Answer

(B) 4 − $\frac{3}{4}$log$_{e}$$\left(\frac{7}{3}\right)$

Answer

(A) 3 + $\frac{4}{3}$log$_{e}$7

Answer

(C) 4 − $\frac{4}{3}$log$_{e}$$\left(\frac{7}{3}\right)$

Answer

(D) 3 + $\frac{3}{4}$log$_{e}$7 .

Question 19

A particle of mass 1 kg is subjected to a force which depends on the position as $\vec{F} = -k(x\hat{i} + y\hat{j})$ kg ms$^{-2}$ with k = 1 kg s$^{-2}$. At time t = 0, the particle's position $\vec{r} = \left(\frac{1}{\sqrt{2}}\hat{i} + \sqrt{2}\hat{j}\right)$ m and its velocity $\vec{v} = \left(-\sqrt{2}\hat{i} + \sqrt{2}\hat{j} + \frac{2}{\pi}\hat{k}\right)$ ms$^{-1}$, Let v$_x$ and v$_y$ denote the x and the y components of the particle's velocity, respectively. Ignore gravity. When z = 0.5 m, the value of (x v$_y$ − y v$_x$) is ______ m$^{2}$ s$^{-1}$.

Accepted Answer

3

Question 20

In a radioactive decay chain reaction, $^{230}_{90}Th$ nucleus decays into $^{214}_{84}Po$ nucleus. The ratio of the number of α to number of β$^{-}$ particles emitted in this process is__________

Accepted Answer

2

Question 21

Two resistances R$_1$=X Ω and R$_2$=1 Ω are connected to a wire AB of uniform resistivity, as shown in the figure. The radius of the wire varies linearly along its axis from 0.2mm at A to  1mm at B. A galvanometer (G) connected to the center of the wire, 50cm from each end along its axis, shows zero deflection when A and B  are connected to a battery. The value of X  is _________

Accepted Answer

5

Question 22

In a particular system of units, a physical quantity can be expressed in terms of the electric charge  e , electron mass  m$_e$ , Planck's constant  h , and Coulomb's constant $k = \frac{1}{4\pi\epsilon_0}$ , where ε$_0$ is the permittivity of vacuum. In terms of these physical constants, the dimension of the magnetic field is [B] = [e]$^{\alpha}$[m$_e$]$^{\beta}$[h]$^{\gamma}$[k]$^{\delta}$. The value of α + β + γ + δ is ______________.

Accepted Answer

4

Question 23

Consider a configuration of  n  identical units, each consisting of three layers. The first layer is a column of air of height $h = \frac{1}{3}$ cm, and the second and third layers are of equal thickness $d = \frac{\sqrt{3}-1}{2}$ cm , and refractive indices $\mu_1 = \sqrt{\frac{3}{2}}$ and μ$_2$ = $\sqrt{3}$, respectively. A light source O is placed on the top of the first unit, as shown in the figure. A ray of light from O is incident on the second layer of the first unit at an angle of θ=60° to the normal. For a specific value of n , the ray of light emerges from the bottom of the configuration at a distance $l = \frac{8}{\sqrt{3}}$ cm, as shown in the figure. The value of n is___________.

Accepted Answer

4

Question 24

A charge q is surrounded by a closed surface consisting of an inverted cone of height  h  and base radius R , and a hemisphere of radius  R  as shown in the figure. The electric flux through the conical surface is $\frac{nq}{6\epsilon_0}$  (in SI units). The value of n  is_________

Accepted Answer

3

Question 25

On a frictionless horizontal plane, a bob of mass m  =  0.1 kg is attached to a spring with natural length l$_0$=0.1  m.  The  spring  constant  is  k$_1$  =  0.009Nm$^{-1}$ when  the  length  of  the  spring  l>l$_0$ and  is k$_2$ = 0.016Nm$^{-1}$ when l < l$_0$. Initially the bob is released from l=0.15m . Assume that Hooke's law remains valid throughout the motion. If the time period of the full oscillation is T=(n π) s, then the integer closest to  n is _______

Accepted Answer

6

Question 26

An object and a concave mirror of focal length f=10cm both move along the principal axis of the mirror with constant speeds. The object moves with speed V$_0$=15 cm s$^{-1}$ towards the mirror with respect to a laboratory frame. The distance between the object and the mirror at a given moment is denoted by u . When u=30 cm , the speed of the mirror V$_m$  is such that the image is instantaneously at rest with respect to the laboratory frame, and the object forms a real image. The magnitude of V$_m$  is _________ cms$^{-1}$

Accepted Answer

3

Question 27

In the figure, the inner (shaded) region $A$ represents a sphere of radius $r_A = 1$, within which the electrostatic charge density varies with the radial distance $r$ from the center as $\rho_A = kr$, where $k$ is positive. In the spherical shell $B$ of outer radius $r_B$, the electrostatic charge density varies as $\rho_B = \frac{2k}{r}$. Assume that dimensions are taken care of. All physical quantities are in their SI units.
Which of the following statement(s) is(are) correct?

Accepted Answer

(B) If $r_B = \frac{3}{2}$, then the electric potential just outside $B$ is $\frac{k}{\epsilon_0}$.

Answer

(A) If $r_B = \sqrt{\frac{3}{2}}$, then the electric field is zero everywhere outside $B$.

Answer

(C) If $r_B = 2$, then the total charge of the configuration is $15\pi k$.

Answer

(D) If $r_B = \frac{5}{2}$, then the magnitude of the electric field just outside $B$ is $\frac{13\pi k}{\epsilon_0}$.

Question 28

In Circuit-1 and Circuit-2 shown in the figures, $R_1 = 1\,\Omega$, $R_2 = 2\,\Omega$ and $R_3 = 3\,\Omega$. $P_1$ and $P_2$ are the power dissipations in Circuit-1 and Circuit-2 when the switches $S_1$ and $S_2$ are in open conditions, respectively.
$Q_1$ and $Q_2$ are the power dissipations in Circuit-1 and Circuit-2 when the switches $S_1$ and $S_2$ are in closed conditions, respectively.
Which of the following statement(s) is(are) correct?

Accepted Answer

(A) When a voltage source of 6 V is connected across A and B in both circuits, $P_1 < P_2$ .

Accepted Answer

(B) When a constant current source of 2 Amp is connected across A and B in both circuits, $P_1 > P_2$.

Accepted Answer

(C) When a voltage source of 6 V is connected across A and B in Circuit-1, $Q_1 > P_1$ .

Answer

(D) When a constant current source of 2 Amp is connected across A and B in both circuits, $Q_2 < Q_1$ .

Question 29

A bubble has surface tension S. The ideal gas inside the bubble has ratio of specific heats $\gamma = \frac{5}{3}$ . The bubble is exposed to the atmosphere and it always retains its spherical shape. When the atmospheric pressure is $P_{\alpha 1}$, the radius of the bubble is found to be $r_1$ and the temperature of the enclosed gas is $T_1$. When the atmospheric pressure is $P_{\alpha 2}$, the radius of the bubble and the temperature of the enclosed gas are $r_2$ and $T_2$ , respectively.
Which of the following statement(s) is(are) correct?

Accepted Answer

(C) If the surface of the bubble is a perfect heat conductor and the change in atmospheric temperature is negligible, then $\left(\frac{r_1}{r_2}\right)^3 = \frac{P_{\alpha 2} + \frac{4S}{r_2}}{P_{\alpha 1} + \frac{4S}{r_1}}$

Accepted Answer

(D) If the surface of the bubble is a perfect heat insulator, then $\left(\frac{T_2}{T_1}\right)^{\frac{5}{2}} = \frac{P_{\alpha 2} + \frac{4S}{r_2}}{P_{\alpha 1} + \frac{4S}{r_1}}$

Answer

(A) If the surface of the bubble is a perfect heat insulator, then $\left(\frac{r_1}{r_2}\right)^5 = \frac{P_{\alpha 2} + \frac{2S}{r_2}}{P_{\alpha 1} + \frac{2S}{r_1}}$

Answer

(B) If the surface of the bubble is a perfect heat insulator, then the total internal energy of the bubble including its surface energy does not change with the external atmospheric pressure.

Question 30

A disk of radius R with uniform positive charge density $\sigma$ is placed on the xy plane with its centre at the origin. The Coulomb potential along the z-axis is
$V(z) = \frac{\sigma}{2\,\epsilon_0}\left(\sqrt{R^2 + z^2} - z\right).$
A particle of positive charge q is placed initially at rest at a point on the z axis with $z = z_0$ and $z_0 > 0$. In addition to the Coulomb force, the particle experiences a vertical force $\vec{F} = -c\hat{k}$ with $c > 0$. Let $\beta = \frac{2c\,\epsilon_0}{q\sigma}$ . Which of the following statements(s) is (are) correct?

Accepted Answer

(A) For $\beta = \frac{1}{4}$ and $z_0 = \frac{25}{7}R$ , the particle reaches the origin.

Accepted Answer

(C) For $\beta = \frac{1}{4}$ and $z_0 = \frac{R}{\sqrt{3}}$ , the particle returns back to $z = z_0$ .

Accepted Answer

(D) For $\beta > 1$ and $z_0 > 0$, the particle always reaches the origin.

Answer

(B) For $\beta = \frac{1}{4}$ and $z_0 = \frac{3}{7}R$ , the particle reaches the origin.

Question 31

A double slit setup is shown in the figure. One of the slits is in medium 2 of refractive index $n_2$ . The other slit is at the interface of this medium with another medium 1 of refractive index $n_1(
eq n_2)$ . The line joining the slits is perpendicular to the interface and the distance between the slits is d . The slit widths are much smaller than d . A monochromatic parallel beam of light is incident on the slits from medium 1. A detector is placed in medium 2 at a large distance from the slits, and at an angle $	heta$ from the line joining them, so that $	heta$ equals the angle of refraction of the beam. Consider two approximately parallel rays from the slits received by the detector.
Which of the following statement(s) is(are) correct?

Accepted Answer

(A) The phase difference between the two rays is independent of d .

Accepted Answer

(B) The two rays interfere constructively at the detector.

Answer

(C) The phase difference between the two rays depends on $n_1$ but is independent of $n_2$ .

Answer

(D) The phase difference between the two rays vanishes only for certain values of d and the angle of incidence of the beam, with $	heta$ being the corresponding angle of refraction.

Question 32

In the given P-V diagram, a monoatomic gas $\left(\gamma = \frac{5}{3}\right)$ is first compressed adiabatically from state A to state B. Then it expands isothermally from state B to state C. [Given : $\left(\frac{1}{3}\right)^{0.6} \simeq 0.5$, $\ln 2 \simeq 0.7$ ].
Which of the following statement(s) is(are) correct?

Accepted Answer

(B) The magnitude of the work done in the process $B \rightarrow C$ is 84kJ .

Accepted Answer

(C) The magnitude of the work done in the process $A \rightarrow B$ is 60kJ .

Accepted Answer

(D) The magnitude of the work done in the process $C \rightarrow A$ is zero.

Answer

(A) The magnitude of the total work done in the process $A \rightarrow B \rightarrow C$ is 144kJ .

Question 33

A flat surface of a thin uniform disk A of radius R is glued to a horizontal table. Another thin uniform disk B of mass M and with the same radius R rolls without slipping on the circumference of A , as shown in the figure. A flat surface of B also lies on the plane of the table. The center of mass of B has fixed angular speed $\omega$ about the vertical axis passing through the center of A . The angular momentum of B is $nM\omega R^2$ with respect to the center of A . Which of the following is the value of n ?

Accepted Answer

(B) 5

Answer

(A) 2

Answer

(C) 7/2

Answer

(D) 9/2

Question 34

When light of a given wavelength is incident on a metallic surface, the minimum potential needed to stop the emitted photoelectrons is 6.0V . This potential drops to 0.6V if another source with wavelength four times that of the first one and intensity half of the first one is used. What are the wavelength of the first source and the work function of the metal, respectively? [Take hc/e $= 1.24 	imes 10^{-6}\,\mathrm{JmC}^{-1}$.]

Accepted Answer

(A) $1.72 	imes 10^{-7}$m, 1.20eV

Answer

(B) $1.72 	imes 10^{-7}$m, 5.60eV

Answer

(C) $3.78 	imes 10^{-7}$m, 5.60eV

Answer

(D) $3.78 	imes 10^{-7}$m, 1.20eV

Question 35

Which one of the following options represents the magnetic field $\vec{B}$ at O due to the current flowing in the given wire segments lying on the xy plane?

Accepted Answer

(C) $\vec{B} = \frac{-\mu_0 I}{L}\left(1 + \frac{1}{4\sqrt{2}\pi}\right)\hat{k}$

Answer

(A) $\vec{B} = \frac{-\mu_0 I}{L}\left(\frac{3}{2} + \frac{1}{4\sqrt{2}\pi}\right)\hat{k}$

Answer

(B) $\vec{B} = -\frac{\mu_0 I}{L}\left(\frac{3}{2} + \frac{1}{2\sqrt{2}\pi}\right)\hat{k}$

Answer

(D) $\vec{B} = \frac{-\mu_0 I}{L}\left(1 + \frac{1}{4\pi}\right)\hat{k}$

Question 36

Concentration of $\mathrm{H_2SO_4}$ and $\mathrm{Na_2SO_4}$ in a solution is 1 M and $1.8 	imes 10^{-2}$ M, respectively. Molar solubility of $\mathrm{PbSO_4}$ in the same solution is $\mathrm{X} 	imes 10^{-\mathrm{Y}}$ M (expressed in scientific notation). The value of Y is____.
[Given : Solubility product of $\mathrm{PbSO_4}\left(\mathrm{K_{sp}}ight) = 1.6 	imes 10^{-8}$. For $\mathrm{H_2SO_4}$, $\mathrm{K_{a_1}}$ is very large and $\mathrm{K_{a_2}} = 1.2 	imes 10^{-2}$]

Accepted Answer

6

Question 37

An aqueous solution is prepared by dissolving 0.1 mol of an ionic salt in 1.8 kg of water at $35^\circ\mathrm{C}$. The salt remains 90% dissociated in the solution. The vapour pressure of the solution is 59.724 mm of Hg. Vapor pressure of water at $35^\circ\mathrm{C}$ is 60.000 mm of Hg. The number of ions present per formula unit of the ionic salt is____.

Accepted Answer

5

Question 38

Consider the strong electrolytes $\mathrm{Z_mX_n}$, $\mathrm{U_mY_p}$ and $\mathrm{V_mX_n}$. Limiting molar conductivity $\left(\Lambda^0\right)$ of $\mathrm{U_mY_p}$ and $\mathrm{V_mX_n}$ are 250 and 440 $\mathrm{S\ cm^2\ mol^{-1}}$, respectively. The value of (m + n + p) is____.
The plot of molar conductivity $\left(\Lambda\right)$ of $\mathrm{Z_mX_n}$ vs $\mathrm{c^{1/2}}$ is given below.

Accepted Answer

7

Question 39

The reaction of Xe and $\mathrm{O_2F_2}$ gives a Xe compound $\mathbf{P}$. The number of moles of HF produced by the complete hydrolysis of 1 mol of $\mathbf{P}$ is____.

Accepted Answer

2

Question 40

Thermal decomposition of $\mathrm{AgNO_3}$ produces two paramagnetic gases. The total number of electrons present in the antibonding molecular orbitals of the gas that has the higher number of unpaired electrons is____.

Accepted Answer

6

Question 41

The number of isomeric tetraenes (NOT containing $sp$-hybridized carbon atoms) that can be formed from the following reaction sequence is____.

Accepted Answer

2

Question 42

The number of $-\mathrm{CH_2}-$ (methylene) groups in the product formed from the following reaction sequence is____.

Accepted Answer

0

Question 43

The total number of chiral molecules formed from one molecule of $\mathbf{P}$ on complete ozonolysis $\left(\mathrm{O_3}, \mathrm{Zn}/\mathrm{H_2O}\right)$ is____.

Accepted Answer

2

Question 44

To check the principle of multiple proportions, a series of pure binary compounds $\left(\mathrm{P_mQ_n}\right)$ were analyzed and their composition is tabulated below. The correct option(s) is(are)

Compound | Weight % of P | Weight % of Q
1 | 50 | 50
2 | 44.4 | 55.6
3 | 40 | 60

Accepted Answer

(B) If empirical formula of compound $\mathbf{3}$ is $\mathrm{P_3Q_2}$, and atomic weight of element P is 20, then the atomic weight of Q is 45.

Accepted Answer

(C) If empirical formula of compound $\mathbf{2}$ is PQ, then the empirical formula of compound $\mathbf{1}$ is $\mathrm{P_5Q_4}$.

Answer

(A) If empirical formula of compound $\mathbf{3}$ is $\mathrm{P_3Q_4}$, then the empirical formula of compound $\mathbf{2}$ is $\mathrm{P_3Q_5}$.

Answer

(D) If atomic weight of P and Q are 70 and 35, respectively, then the empirical formula of compound $\mathbf{1}$ is $\mathrm{P_2Q}$.

Question 45

The correct option(s) about entropy (S) is(are)
[R = gas constant, F = Faraday constant, T = Temperature]

Accepted Answer

(B) The cell reaction, $\mathrm{Pt(s)}\,|\,\mathrm{H_2}\,(\mathrm{g},\ 1\,\mathrm{bar})\,|\,\mathrm{H^+}\,(\mathrm{aq},\ 0.01\ \mathrm{M})\,||\,\mathrm{H^+}\,(\mathrm{aq},\ 0.1\ \mathrm{M})\,|\,\mathrm{H_2}\,(\mathrm{g},\ 1\ \mathrm{bar})\,|\,\mathrm{Pt(s)}$, is in an entropy driven process.

Accepted Answer

(C) For racemisation of an optically active compound, $\Delta \mathrm{S} > 0$.

Accepted Answer

(D) $\Delta \mathrm{S} > 0$, for $\left[\mathrm{Ni(H_2O)_6}\right]^{2+} + 3\ \mathrm{en} \longrightarrow \left[\mathrm{Ni(en)_3}\right]^{2+} + 6\mathrm{H_2O}$ (where en = ethylenediamine).

Answer

(A) For the reaction, $\mathrm{M(s)} + 2\mathrm{H^+(aq)} \longrightarrow \mathrm{H_2(g)} + \mathrm{M^{2+}(aq)}$, if $\dfrac{\mathrm{dE_{cell}}}{\mathrm{dT}} = \dfrac{\mathrm{R}}{\mathrm{F}}$, then the entropy change of the reaction is R (assume that entropy and internal energy changes are temperature independent).

Question 46

The compound(s) which react(s) with $\mathrm{NH_3}$ to give boron nitride (BN) is(are)

Accepted Answer

(A) B

Accepted Answer

(B) $\mathrm{B_2H_6}$

Accepted Answer

(C) $\mathrm{B_2O_3}$

Answer

(D) $\mathrm{HBF_4}$

Question 47

The correct option(s) related to the extraction of iron from its ore in the blast furnace operating in the temperature range 900 – 1500 K is(are)

Accepted Answer

(A) Limestone is used to remove silicate impurity.

Accepted Answer

(B) Pig iron obtained from blast furnace contains about 4% carbon.

Accepted Answer

(C) Coke (C) converts $\mathrm{CO_2}$ to CO.

Answer

(D) Exhaust gases consist of $\mathrm{NO_2}$ and CO.

Question 48

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

Accepted Answer

(A) Compound $\mathbf{P}$ and $\mathbf{Q}$ are carboxylic acids.

Accepted Answer

(C) Compounds $\mathbf{P}$ and $\mathbf{S}$ react with hydroxylamine to give the corresponding oximes.

Answer

(B) Compound $\mathbf{S}$ decolorizes bromine water.

Answer

(D) Compound $\mathbf{R}$ reacts with dialkylcadmium to give the corresponding tertiary alcohol.

Question 49

Among the following, the correct statement(s) about polymers is(are)

Accepted Answer

(B) Teflon is prepared from tetrafluoroethene by heating it with persulphate catalyst at high pressures.

Accepted Answer

(C) PVC are thermoplastic polymers.

Answer

(A) The polymerization of chloroprene gives natural rubber.

Answer

(D) Ethene at 350 – 570 K temperature and 1000-2000 atm pressure in the presence of a peroxide initiator yields high density polythene.

Question 50

Atom X occupies the fcc lattice sites as well as alternate tetrahedral voids of the same lattice. The packing efficiency (in %) of the resultant solid is closed to

Accepted Answer

(B) 35

Answer

(A) 25

Answer

(C) 55

Answer

(D) 75

Question 51

The reaction of $\mathrm{HClO_3}$ with HCl gives a paramagnetic gas, which upon reaction with $\mathrm{O_3}$ produces

Accepted Answer

(C) $\mathrm{Cl_2O_6}$

Answer

(A) $\mathrm{Cl_2O}$

Answer

(B) $\mathrm{ClO_2}$

Answer

(D) $\mathrm{Cl_2O_7}$

Question 52

The reaction of $\mathrm{Pb\left(NO_3\right)_2}$ and NaCl in water produces a precipitate that dissolves upon the addition of HCl of appropriate concentration. The dissolution of the precipitate is due to the formation of

Accepted Answer

(C) $\left[\mathrm{PbCl_4}\right]^{2-}$

Answer

(A) $\mathrm{PbCl_2}$

Answer

(B) $\mathrm{PbCl_4}$

Answer

(D) $\left[\mathrm{PbCl_6}\right]^{2-}$

Question 53

Treatment of D-glucose with aqueous NaOH results in a mixture of monosaccharides, which are

Accepted Answer

(C) (C)

Answer

(A) (A)

Answer

(B) (B)

Answer

(D) (D)

JEE Advanced 2022 Paper 2 Question Paper with Answers

Physics — JEE Advanced 2022 Paper 2

Chemistry — JEE Advanced 2022 Paper 2

Mathematics — JEE Advanced 2022 Paper 2

Chapters tested in this paper

Attempt JEE Advanced 2022 Paper 2 under exam timing.