JEE Advanced 2023 Paper 2 Question Paper

Question 1

Let $f : [1, \infty) 	o \mathbb{R}$ be a differentiable function such that $f(1) = \frac{1}{3}$ and $3\int_{1}^{x} f(t)\,dt = x f(x) - \frac{x^{3}}{3}$, $x \in [1, \infty)$. Let e denote the base of the natural logarithm. Then the value of $f(e)$ is

Accepted Answer

(C) $\frac{4e^{2}}{3}$

Answer

(A) $\frac{e^{2}+4}{3}$

Answer

(B) $\frac{\log_{e} 4 + e}{3}$

Answer

(D) $\frac{e^{2}-4}{3}$

Question 2

Consider an experiment of tossing a coin repeatedly until the outcomes of two consecutive tosses are same. If the probability of a random toss resulting in head is $\frac{1}{3}$, then the probability that the experiment stops with head is

Accepted Answer

(B) $\frac{5}{21}$

Answer

(A) $\frac{1}{3}$

Answer

(C) $\frac{4}{21}$

Answer

(D) $\frac{2}{7}$

Question 3

For any $y \in \mathbb{R}$, let $\cot^{-1}(y) \in (0, \pi)$ and $	an^{-1}(y) \in \left(-\frac{\pi}{2}, \frac{\pi}{2}ight)$. Then the sum of all the solutions of the equation $	an^{-1}\left(\frac{6y}{9-y^{2}}ight) + \cot^{-1}\left(\frac{9-y^{2}}{6y}ight) = \frac{2\pi}{3}$ for $0 < |y| < 3$, is equal to

Accepted Answer

(C) $4\sqrt{3} - 6$

Answer

(A) $2\sqrt{3} - 3$

Answer

(B) $3 - 2\sqrt{3}$

Answer

(D) $6 - 4\sqrt{3}$

Question 4

Let the position vectors of the points $P$, $Q$, $R$ and S be $\vec{a} = \hat{i} + 2\hat{j} - 5\hat{k}$, $\vec{b} = 3\hat{i} + 6\hat{j} + 3\hat{k}$, $\vec{c} = \frac{17}{5}\hat{i} + \frac{16}{5}\hat{j} + 7\hat{k}$ and $\vec{d} = 2\hat{i} + \hat{j} + \hat{k}$, respectively. Then which of the following statements is true?

Accepted Answer

(B) $\frac{\vec{b} + 2\vec{d}}{3}$ is the position vector of a point which divides $PR$ internally in the ratio $5 : 4$

Answer

(A) The points $P$, $Q$, $R$ and S are NOT coplanar

Answer

(C) $\frac{\vec{b} + 2\vec{d}}{3}$ is the position vector of a point which divides $PR$ externally in the ratio $5 : 4$

Answer

(D) The square of the magnitude of the vector $\vec{b} 	imes \vec{d}$ is 95

Question 5

Let M = $(a_{ij})$, $i, j \in \{1, 2, 3\}$, be the $3 	imes 3$ matrix such that $a_{ij} = 1$ if $j + 1$ is divisible by $i$, otherwise $a_{ij} = 0$. Then which of the following statements is(are) true?

Accepted Answer

(B) There exists a nonzero column matrix $\begin{pmatrix} a_{1} \ a_{2} \ a_{3} \end{pmatrix}$ and such that $M \begin{pmatrix} a_{1} \ a_{2} \ a_{3} \end{pmatrix} = \begin{pmatrix} -a_{1} \ -a_{2} \ -a_{3} \end{pmatrix}$

Accepted Answer

(C) The set $\left\{ X \in \mathbb{R}^{3} : MX = \mathbf{0} ight\} 
eq \{\mathbf{0}\}$, where $\mathbf{0} = \begin{pmatrix} 0 \ 0 \ 0 \end{pmatrix}$

Answer

(A) $M$ is invertible

Answer

(D) The matrix $(M - 2I)$ is invertible, where $I$ is the $3 	imes 3$ identity matrix

Question 6

Let $f : (0, 1) 	o \mathbb{R}$ be the function defined as $f(x) = [4x]\left(x - \frac{1}{4}ight)^{2}\left(x - \frac{1}{2}ight)$, where $[x]$ denotes the greatest integer less than or equal to x . Then which of the following statements is(are) true?

Accepted Answer

(A) The function $f$ is discontinuous exactly at one point in $(0, 1)$

Accepted Answer

(B) There is exactly one point in $(0, 1)$ at which the function $f$ is continuous but NOT differentiable

Answer

(C) The function f is NOT differentiable at more than three points in $(0, 1)$

Answer

(D) The minimum value of the function f is $-\frac{1}{512}$

Question 7

Let $S$ be the set of all twice differentiable functions f from $\mathbb{R}$ to $\mathbb{R}$ such that $\frac{d^{2}f}{dx^{2}}(x) > 0$ for all $x \in (-1, 1)$. For $f \in S$, let $X_{f}$ be the number of points $x \in (-1, 1)$ for which $f(x) = x$. Then which of the following statements is(are) true?

Accepted Answer

(A) There exists a function $f \in S$ such that $X_{f} = 0$

Accepted Answer

(B) For every function $f \in S$, we have $X_{f} \le 2$

Accepted Answer

(C) There exists a function $f \in S$ such that $X_{f} = 2$

Answer

(D) There does NOT exist any function $f$ in $S$ such that $X_{f} = 1$

Question 8

For $x \in \mathbb{R}$, let $	an^{-1}(x) \in \left(-\frac{\pi}{2}, \frac{\pi}{2}ight)$. Then the minimum value of the function $f : \mathbb{R} 	o \mathbb{R}$ defined by $f(x) = \int_{0}^{x 	an^{-1} x} \frac{e^{(t - \cos t)}}{1 + t^{2023}}\,dt$ is

Accepted Answer

0

Question 9

For $x \in \mathbb{R}$, let $y(x)$ be a solution of the differential equation $(x^{2} - 5)\frac{dy}{dx} - 2xy = -2x(x^{2} - 5)^{2}$ such that $y(2) = 7$. Then the maximum value of the function $y(x)$ is

Accepted Answer

16

Question 10

Let $X$ be the set of all five digit numbers formed using 1, 2, 2, 2, 4, 4, 0. For example, 22240 is in $X$ while 02244 and 44422 are not in $X$. Suppose that each element of $X$ has an equal chance of being chosen. Let $p$ be the conditional probability that an element chosen at random is a multiple of 20 given that it is a multiple of 5. Then the value of $38p$ is equal to

Accepted Answer

31

Question 11

Let $A_{1}$, $A_{2}$, $A_{3}$, ....., $A_{8}$ be the vertices of a regular octagon that lie on a circle of radius 2. Let P be a point on the circle and let $PA_{i}$ denote the distance between the points $P$ and $A_{i}$ for $i = 1, 2, ....., 8$. If $P$ varies over the circle, then the maximum value of the product $PA_{1} \cdot PA_{2} ..... PA_{8}$, is

Accepted Answer

512

Question 12

Let $R = \left\{ \begin{pmatrix} a & 3 & b \ c & 2 & d \ 0 & 5 & 0 \end{pmatrix} : a, b, c, d \in \{0, 3, 5, 7, 11, 13, 17, 19\} ight\}$. Then the number of invertible matrices in R is

Accepted Answer

3780

Question 13

Let $C_{1}$ be the circle of radius 1 with center at the origin. Let $C_{2}$ be the circle of radius $r$ with center at the point $A = (4, 1)$, where $1 < r < 3$. Two distinct common tangents $PQ$ and $ST$ of $C_{1}$ and $C_{2}$ are drawn. The tangent $PQ$ touches $C_{1}$ at $P$ and $C_{2}$ at $Q$. The tangent $ST$ touches $C_{1}$ at $S$ and $C_{2}$ at $T$. Mid points of the line segments $PQ$ and $ST$ are joined to form a line which meets the x-axis at a point $B$. If $AB = \sqrt{5}$, then the value of $r^{2}$ is

Accepted Answer

2

Question 14

Consider an obtuse angled triangle ABC in which the difference between the largest and the smallest angle is $\frac{\pi}{2}$ and whose sides are in arithmetic progression. Suppose that the vertices of this triangle lie on a circle of radius 1. Let $a$ be the area of the triangle $ABC$. Then the value of $(64a)^{2}$ is

Accepted Answer

1008

Question 15

Consider an obtuse angled triangle ABC in which the difference between the largest and the smallest angle is $\frac{\pi}{2}$ and whose sides are in arithmetic progression. Suppose that the vertices of this triangle lie on a circle of radius 1. Then the inradius of the triangle $ABC$ is

Accepted Answer

0.25

Question 16

Consider the $6 	imes 6$ square in the figure. Let $A_{1}$, $A_{2}$, ....., $A_{49}$ be the points of intersections (dots in the picture) in some order. We say that $A_{i}$ and $A_{j}$ are friends if they are adjacent along a row or along a column. Assume that each point $A_{i}$ has an equal chance of being chosen. Let $p_{i}$ be the probability that a randomly chosen point has $i$ many friends, $i = 0, 1, 2, 3, 4$. Let $X$ be a random variable such that for $i = 0, 1, 2, 3, 4$, the probability $P(X = i) = p_{i}$. Then the value of $7E(X)$ is

Accepted Answer

24

Question 17

Consider the $6 	imes 6$ square in the figure. Let $A_{1}$, $A_{2}$, ....., $A_{49}$ be the points of intersections (dots in the picture) in some order. We say that $A_{i}$ and $A_{j}$ are friends if they are adjacent along a row or along a column. Assume that each point $A_{i}$ has an equal chance of being chosen. Two distinct points are chosen randomly out of the points $A_{1}$, $A_{2}$, ....., $A_{49}$. Let $p$ be the probability that they are friends. Then the value of $7p$ is

Accepted Answer

0.5

Question 18

An electric dipole is formed by two charges +q and - q located in xy-plane at (0, 2) mm and (0, -2) mm, respectively, as shown in the figure. The electric potential at point P (100, 100) mm due to the dipole is $V_0$. The charges +q and -q are then moved to the points (-1, 2) mm and (1, -2) mm, respectively. What is the value of electric potential at P due to the new dipole?

Accepted Answer

(B) $V_0/2$

Answer

(A) $V_0/4$

Answer

(C) $V_0 / \sqrt{2}$

Answer

(D) $3V_0/4$

Question 19

Young's modulus of elasticity Y is expressed in terms of three derived quantities, namely, the gravitational constant G, Planck's constant h and the speed of light c, as $Y = c^{\alpha} h^{\beta} G^{\gamma}$. Which of the following is the correct option?

Accepted Answer

(A) $\alpha = 7, \beta = -1, \gamma = -2$

Answer

(B) $\alpha = -7, \beta = -1, \gamma = -2$

Answer

(C) $\alpha = 7, \beta = -1, \gamma = 2$

Answer

(D) $\alpha = -7, \beta = 1, \gamma = -2$

Question 20

An ideal gas is in thermodynamic equilibrium. The number of degrees of freedom of a molecule of the gas is n. The internal energy of one mole of the gas is $U_n$ and the speed of sound in the gas is $v_n$. At a fixed temperature and pressure, which of the following is the correct option ?

Accepted Answer

(C) $v_5 > v_7$ and $U_5 < U_7$

Answer

(A) $v_3 < v_6$ and $U_3 > U_6$

Answer

(B) $v_5 > v_3$ and $U_3 > U_5$

Answer

(D) $v_6 < v_7$ and $U_6 < U_7$

Question 21

A monochromatic light wave is incident normally on a glass slab of thickness d, as shown in the figure. The refractive index of the slab increases linearly from $n_1$ to $n_2$ over the height h. Which of the following statement(s) is(are) true about the light wave emerging out of the slab?

Accepted Answer

(B) It will deflect up by an angle $	an^{-1}\left[\frac{\left(n_2 - n_1ight)d}{h}ight]$.

Accepted Answer

(D) The deflection angle depends only on $(n_2 - n_1)$ and not on the individual values of $n_1$ and $n_2$.

Answer

(A) It will deflect up by an angle $	an^{-1}\left[\frac{\left(n_2^{2} - n_1^{2}ight)d}{2h}ight]$.

Answer

(C) It will not deflect.

Question 22

An annular disk of mass M, inner radius a and outer radius b is placed on a horizontal surface with coefficient of friction $\mu$, as shown in the figure. At some time, an impulse $J_0\hat{x}$ is applied at a height h above the center of the disk. If $h = h_m$ then the disk rolls without slipping along the x-axis. Which of the following statement(s) is(are) correct?

Accepted Answer

(A) For $\mu 
eq 0$ and $a ightarrow 0$, $h_m = b/2$

Accepted Answer

(B) For $\mu 
eq 0$ and $a ightarrow b$, $h_m = b$

Accepted Answer

(C) For $h = h_m$, the initial angular velocity does not depend on the inner radius a.

Accepted Answer

(D) For $\mu = 0$ and $h = 0$, the wheel always slides without rolling.

Question 23

The electric field associated with an electromagnetic wave propagating in a dielectric medium is given by $\vec{E} = 30\left(2\hat{x} + \hat{y}ight)\sin\left[2\pi\left(5	imes10^{14}t - \frac{10^{7}}{3}zight)ight]$ V m$^{-1}$. Which of the following option(s) is(are) correct ?

[Given: The speed of light in vacuum, c = $3 	imes 10^{8}$ m s$^{-1}$]

Accepted Answer

(A) $B_x = -2	imes10^{-7}\sin\left[2\pi\left(5	imes10^{14}t - \frac{10^{7}}{3}zight)ight]$ Wb m$^{-2}$.

Accepted Answer

(D) The refractive index of the medium is 2.

Answer

(B) $B_y = 2	imes10^{-7}\sin\left[2\pi\left(5	imes10^{14}t - \frac{10^{7}}{3}zight)ight]$ Wb m$^{-2}$.

Answer

(C) The wave is polarized in the xy-plane with polarization angle 30$^{\circ}$ with respect to the x-axis.

Question 24

A thin circular coin of mass 5 gm and radius 4/3 cm is initially in a horizontal xy -plane. The coin is tossed vertically up (+z direction) by applying an impulse of $\sqrt{\frac{\pi}{2}}	imes10^{-2}$ N-s at a distance 2/3 cm from its center. The coin spins about its diameter and moves along the +z direction. By the time the coin reaches back to its initial position, it completes n rotations. The value of n is ________.

[Given: The acceleration due to gravity g = 10 m s$^{-2}$]

Accepted Answer

30

Question 25

A rectangular conducting loop of length 4 cm and width 2 cm is in the xy-plane, as shown in the figure. It is being moved away from a thin and long conducting wire along the direction $\frac{\sqrt{3}}{2}\hat{x} + \frac{1}{2}\hat{y}$ with a constant speed v. The wire is carrying a steady current $I$ = 10 A in the positive x-direction. A current of 10 $\mu$A flows through the loop when it is at a distance d = 4 cm from the wire. If the resistance of the loop is 0.1 $\Omega$, then the value of v is ________ m s$^{-1}$.

[Given: The permeability of free space $\mu_0 = 4\pi	imes10^{-7}$ N A$^{-2}$]

Accepted Answer

4

Question 26

A string of length 1 m and mass $2 	imes 10^{-5}$ kg is under tension $T$. When the string vibrates, two successive harmonics are found to occur at frequencies 750 Hz and 1000 Hz. The value of tension $T$ is _____ Newton.

Accepted Answer

5

Question 27

An incompressible liquid is kept in a container having a weightless piston with a hole. A capillary tube of inner radius 0.1 mm is dipped vertically into the liquid through the airtight piston hole, as shown in the figure. The air in the container is isothermally compressed from its original volume $V_0$ to $\frac{100}{101}V_0$ with the movable piston. Considering air as an ideal gas, the height (h) of the liquid column in the capillary above the liquid level in cm is________.

[Given: Surface tension of the liquid is 0.075 N m$^{-1}$, atmospheric pressure is $10^{5}$ N m$^{-2}$, acceleration due to gravity (g) is 10 m s$^{-2}$, density of the liquid is $10^{3}$ kg m$^{-3}$ and contact angle of capillary surface with the liquid is zero]

Accepted Answer

25

Question 28

In a radioactive decay process, the activity is defined as $A = -\frac{dN}{dt}$, where N(t) is the number of radioactive nuclei at time t. Two radioactive sources, $S_1$ and $S_2$ have same activity at time $t$ = 0. At a later time, the activities of $S_1$ and $S_2$ are $A_1$ and $A_2$, respectively. When $S_1$ and $S_2$ have just completed their 3$^{rd}$ and 7$^{th}$ half-lives, respectively, the ratio $A_1/A_2$ is ___________.

Accepted Answer

16

Question 29

One mole of an ideal gas undergoes two different cyclic processes I and II, as shown in the P-V diagrams below. In cycle I, processes a, b, c and d are isobaric, isothermal, isobaric and isochoric, respectively. In cycle II, processes a$'$, b$'$, c$'$ and d$'$ are isothermal, isochoric, isobaric and isochoric, respectively. The total work done during cycle I is $W_I$ and that during cycle II is $W_{II}$. The ratio $W_I / W_{II}$ is ________.

Accepted Answer

2

Question 30

$S_1$ and $S_2$ are two identical sound sources of frequency 656 Hz. The source $S_1$ is located at O and $S_2$ moves anti-clockwise with a uniform speed $4\sqrt{2}$ m s$^{-1}$ on a circular path around O, as shown in the figure. There are three points P, Q and R on this path such that P and R are diametrically opposite while Q is equidistant from them. A sound detector is placed at point $P$. The source $S_1$ can move along direction OP.

[Given: The speed of sound in air is 324 m s$^{-1}$]

When only $S_2$ is emitting sound and it is at Q, the frequency of sound measured by the detector in Hz is _________.

Accepted Answer

648

Question 31

$S_1$ and $S_2$ are two identical sound sources of frequency 656 Hz. The source $S_1$ is located at O and $S_2$ moves anti-clockwise with a uniform speed $4\sqrt{2}$ m s$^{-1}$ on a circular path around O, as shown in the figure. There are three points P, Q and R on this path such that P and R are diametrically opposite while Q is equidistant from them. A sound detector is placed at point $P$. The source $S_1$ can move along direction OP.

[Given: The speed of sound in air is 324 m s$^{-1}$]

Consider both sources emitting sound. When $S_2$ is at R and $S_1$ approaches the detector with a speed 4 m s$^{-1}$, the beat frequency measured by the detector is ________Hz.

Accepted Answer

8.2

Question 32

A cylindrical furnace has height (H) and diameter (D) both 1 m. It is maintained at temperature 360 K. The air gets heated inside the furnace at constant pressure $P_{a}$ and its temperature becomes T = 360 K. The hot air with density $\rho$ rises up a vertical chimney of diameter d = 0.1 m and height h = 9 m above the furnace and exits the chimney (see the figure). As a result, atmospheric air of density $\rho_{a}$ = 1.2 kg m$^{-3}$, pressure $P_{a}$ and temperature $T_{a}$ = 300 K enters the furnace. Assume air as an ideal gas, neglect the variations in $\rho$ and T inside the chimney and the furnace. Also ignore the viscous effects.

[Given: The acceleration due to gravity g = 10 m s$^{-2}$ and $\pi$ = 3.14]

Considering the air flow to be streamline, the steady mass flow rate of air exiting the chimney is ________ gm s$^{-1}$.

Accepted Answer

49.61

Question 33

A cylindrical furnace has height (H) and diameter (D) both 1 m. It is maintained at temperature 360 K. The air gets heated inside the furnace at constant pressure $P_{a}$ and its temperature becomes T = 360 K. The hot air with density $\rho$ rises up a vertical chimney of diameter d = 0.1 m and height h = 9 m above the furnace and exits the chimney (see the figure). As a result, atmospheric air of density $\rho_{a}$ = 1.2 kg m$^{-3}$, pressure $P_{a}$ and temperature $T_{a}$ = 300 K enters the furnace. Assume air as an ideal gas, neglect the variations in $\rho$ and T inside the chimney and the furnace. Also ignore the viscous effects.

[Given: The acceleration due to gravity g = 10 m s$^{-2}$ and $\pi$ = 3.14]

When the chimney is closed using a cap at the top, a pressure difference $\Delta$P develops between the top and the bottom surfaces of the cap. If the changes in the temperature and density of the hot air, due to the stoppage of air flow, are negligible then the value of $\Delta$P is ________ N m$^{-2}$.

Accepted Answer

20

Question 34

The correct molecular orbital diagram for $\mathrm{F_2}$ molecule in the ground state is

Accepted Answer

(C) (C)

Answer

(A) (A)

Answer

(B) (B)

Answer

(D) (D)

Question 35

Consider the following statements related to colloids.
(I) Lyophobic colloids are not formed by simple mixing of dispersed phase and dispersion medium.
(II) For emulsions, both the dispersed phase and the dispersion medium are liquid.
(III) Micelles are produced by dissolving a surfactant in any solvent at any temperature.
(IV) Tyndall effect can be observed from a colloidal solution with dispersed phase having the same refractive index as that of the dispersion medium.

The option with the correct set of statements is

Accepted Answer

(A) (I) and (II)

Answer

(B) (II) and (III)

Answer

(C) (III) and (IV)

Answer

(D) (II) and (IV)

Question 36

In the following reactions, $\mathbf{P}$, $\mathbf{Q}$, $\mathbf{R}$, and $\mathbf{S}$ are the major products.

The correct statement about $\mathbf{P}$, $\mathbf{Q}$, $\mathbf{R}$, and $\mathbf{S}$ is

Accepted Answer

(B) $\mathbf{Q}$ undergoes Kolbe's electrolysis to give an eight-carbon product.

Answer

(A) $\mathbf{P}$ is a primary alcohol with four carbons.

Answer

(C) $\mathbf{R}$ has six carbons and it undergoes Cannizzaro reaction.

Answer

(D) $\mathbf{S}$ is a primary amine with six carbons.

Question 37

A disaccharide $\mathbf{X}$ cannot be oxidised by bromine water. The acid hydrolysis of $\mathbf{X}$ leads to a laevorotatory solution. The disaccharide $\mathbf{X}$ is

Accepted Answer

(A) (A)

Answer

(B) (B)

Answer

(C) (C)

Answer

(D) (D)

Question 38

The complex(es), which can exhibit the type of isomerism shown by $[\mathrm{Pt(NH_3)_2Br_2}]$, is(are)
$[\mathrm{en} = \mathrm{H_2NCH_2CH_2NH_2}]$

Accepted Answer

(C) $[\mathrm{Pt(NH_3)_2Cl_4}]$

Accepted Answer

(D) $[\mathrm{Cr(en)_2(H_2O)(SO_4)}]^{+}$

Answer

(A) $[\mathrm{Pt(en)(SCN)_2}]$

Answer

(B) $[\mathrm{Zn(NH_3)_2Cl_2}]$

Question 39

Atoms of metals x, y, and z form face-centred cubic (fcc) unit cell of edge length $L_x$, body-centred cubic (bcc) unit cell of edge length $L_y$, and simple cubic unit cell of edge length $L_z$, respectively.
If $r_z = \frac{\sqrt{3}}{2} r_y$ ; $r_y = \frac{8}{\sqrt{3}} r_x$ ; $M_z = \frac{3}{2} M_y$ and $M_Z = 3M_x$.
then the correct statement(s) is(are)
[Given: $M_x$, $M_y$, and $M_z$ are molar masses of metals x, y, and z, respectively.
$r_x$, $r_y$, and $r_z$ are atomic radii of metals x, y, and z, respectively.]

Accepted Answer

(A) Packing efficiency of unit cell of x > Packing efficiency of unit cell of y > Packing efficiency of unit cell of z

Accepted Answer

(B) $L_y > L_z$

Accepted Answer

(D) Density of x > Density of y

Answer

(C) $L_x > L_y$

Question 40

In the following reactions, $\mathbf{P}$, $\mathbf{Q}$, $\mathbf{R}$, and $\mathbf{S}$ are the major products.

The correct statement(s) about $\mathbf{P}$, $\mathbf{Q}$, $\mathbf{R}$, and $\mathbf{S}$ is(are)

Accepted Answer

(C) Compounds $\mathbf{Q}$ and $\mathbf{R}$ are the same.

Accepted Answer

(D) $\mathbf{R}$ does not undergo aldol condensation and $\mathbf{S}$ does not undergo Cannizzaro reaction.

Answer

(A) $\mathbf{P}$ and $\mathbf{Q}$ are monomers of polymers dacron and glyptal, respectively.

Answer

(B) $\mathbf{P}$, $\mathbf{Q}$, and $\mathbf{R}$ are dicarboxylic acids.

Question 41

$\mathrm{H_2S}$ (5 moles) reacts completely with acidified aqueous potassium permanganate solution. In this reaction, the number of moles of water produced is $\mathbf{x}$, and the number of moles of electrons involved is $\mathbf{y}$. The value of $(\mathbf{x} + \mathbf{y})$ is ____.

Accepted Answer

18

Question 42

Among $[\mathrm{I_3}]^{+}$, $[\mathrm{SiO_4}]^{4-}$, $\mathrm{SO_2Cl_2}$, $\mathrm{XeF_2}$, $\mathrm{SF_4}$, $\mathrm{ClF_3}$, $\mathrm{Ni(CO)_4}$, $\mathrm{XeO_2F_2}$, $[\mathrm{PtCl_4}]^{2-}$, $\mathrm{XeF_4}$, and $\mathrm{SOCl_2}$, the total number of species having $sp^3$ hybridised central atom is ______.

Accepted Answer

5

Question 43

Consider the following molecules: $\mathrm{Br_3O_8}$, $\mathrm{F_2O}$, $\mathrm{H_2S_4O_6}$, $\mathrm{H_2S_5O_6}$, and $\mathrm{C_3O_2}$.
Count the number of atoms existing in their zero oxidation state in each molecule. Their sum is____.

Accepted Answer

06

Question 44

For $\mathrm{He^{+}}$, a transition takes place from the orbit of radius 105.8 pm to the orbit of radius 26.45 pm. The wavelength (in nm) of the emitted photon during the transition is ___.
[Use:
Bohr radius, a = 52.9 pm
Rydberg constant, $R_H = 2.2 	imes 10^{-18}$ J
Planck's constant, h = $6.6 	imes 10^{-34}$ J s
Speed of light, c = $3 	imes 10^{8}$ m s$^{-1}$]

Accepted Answer

30

Question 45

50 mL of 0.2 molal urea solution (density = 1.012 g mL$^{-1}$ at 300 K) is mixed with 250 mL of a solution containing 0.06 g of urea. Both the solutions were prepared in the same solvent. The osmotic pressure (in Torr) of the resulting solution at 300 K is ___.
[Use: Molar mass of urea = 60 g mol$^{-1}$; gas constant, R = 62 L Torr K$^{-1}$ mol$^{-1}$ ;
Assume, $\Delta_{\mathrm{mix}} H = 0$, $\Delta_{\mathrm{mix}} V = 0$]

Accepted Answer

682

Question 46

The reaction of 4-methyloct-1-ene ($\mathbf{P}$, 2.52 g) with HBr in the presence of $(\mathrm{C_6H_5CO})_2\mathrm{O_2}$ gives two isomeric bromides in a 9 : 1 ratio, with a combined yield of 50%. Of these, the entire amount of the primary alkyl bromide was reacted with an appropriate amount of diethylamine followed by treatment with aq. $\mathrm{K_2CO_3}$ to give a non-ionic product $\mathbf{S}$ in 100% yield.
The mass (in mg) of $\mathbf{S}$ obtained is ___.
[Use molar mass (in g mol$^{-1}$): H = 1, C = 12, N = 14, Br = 80]

Accepted Answer

1791

Question 47

PARAGRAPH I

The entropy versus temperature plot for phases $\alpha$ and $\beta$ at 1 bar pressure is given.
$S_T$ and $S_0$ are entropies of the phases at temperatures T and 0 K, respectively.

The transition temperature for $\alpha$ to $\beta$ phase change is 600 K and $C_{p,\beta} - C_{p,\alpha} = 1$ J mol$^{-1}$ K$^{-1}$. Assume $(C_{p,\beta} - C_{p,\alpha})$ is independent of temperature in the range of 200 to 700 K. $C_{p,\alpha}$ and $C_{p,\beta}$ are heat capacities of $\alpha$ and $\beta$ phases, respectively.

The value of entropy change, $S_\beta - S_\alpha$ (in J mol$^{-1}$ K$^{-1}$), at 300 K is ___.
[Use: ln2 = 0.69
Given: $S_\beta - S_\alpha = 0$ at 0 K]

Accepted Answer

0.31

Question 48

PARAGRAPH I

The entropy versus temperature plot for phases $\alpha$ and $\beta$ at 1 bar pressure is given.
$S_T$ and $S_0$ are entropies of the phases at temperatures T and 0 K, respectively.

The transition temperature for $\alpha$ to $\beta$ phase change is 600 K and $C_{p,\beta} - C_{p,\alpha} = 1$ J mol$^{-1}$ K$^{-1}$. Assume $(C_{p,\beta} - C_{p,\alpha})$ is independent of temperature in the range of 200 to 700 K. $C_{p,\alpha}$ and $C_{p,\beta}$ are heat capacities of $\alpha$ and $\beta$ phases, respectively.

The value of enthalpy change, $H_\beta - H_\alpha$ (in J mol$^{-1}$), at 300 K is ___.

Accepted Answer

300

Question 49

PARAGRAPH II

A trinitro compound, 1,3,5-tris-(4-nitrophenyl)benzene, on complete reaction with an excess of Sn/HCl gives a major product, which on treatment with an excess of $\mathrm{NaNO_2}$/HCl at $0^\circ$C provides $\mathbf{P}$ as the product. $\mathbf{P}$, upon treatment with excess of $\mathrm{H_2O}$ at room temperature, gives the product $\mathbf{Q}$. Bromination of $\mathbf{Q}$ in aqueous medium furnishes the product $\mathbf{R}$. The compound $\mathbf{P}$ upon treatment with an excess of phenol under basic conditions gives the product $\mathbf{S}$.
The molar mass difference between compounds $\mathbf{Q}$ and $\mathbf{R}$ is 474 g mol$^{-1}$ and between compounds $\mathbf{P}$ and $\mathbf{S}$ is 172.5 g mol$^{-1}$.

The number of heteroatoms present in one molecule of $\mathbf{R}$ is ______ .
[Use: Molar mass (in g mol-1): H = 1, C = 12, N = 14, O = 16, Br = 80, Cl = 35.5
Atoms other than C and H are considered as heteroatoms]

Accepted Answer

9

Question 50

PARAGRAPH II

A trinitro compound, 1,3,5-tris-(4-nitrophenyl)benzene, on complete reaction with an excess of Sn/HCl gives a major product, which on treatment with an excess of $\mathrm{NaNO_2}$/HCl at $0^\circ$C provides $\mathbf{P}$ as the product. $\mathbf{P}$, upon treatment with excess of $\mathrm{H_2O}$ at room temperature, gives the product $\mathbf{Q}$. Bromination of $\mathbf{Q}$ in aqueous medium furnishes the product $\mathbf{R}$. The compound $\mathbf{P}$ upon treatment with an excess of phenol under basic conditions gives the product $\mathbf{S}$.
The molar mass difference between compounds $\mathbf{Q}$ and $\mathbf{R}$ is 474 g mol$^{-1}$ and between compounds $\mathbf{P}$ and $\mathbf{S}$ is 172.5 g mol$^{-1}$.

The total number of carbon atoms and heteroatoms present in one molecule of $\mathbf{S}$ is ______ .
[Use: Molar mass (in g mol$^{-1}$): H = 1, C = 12, N = 14, O = 16, Br = 80, Cl = 35.5
Atoms other than C and H are considered as heteroatoms]

Accepted Answer

51

JEE Advanced 2023 Paper 2 Question Paper with Answers

Physics — JEE Advanced 2023 Paper 2

Chemistry — JEE Advanced 2023 Paper 2

Mathematics — JEE Advanced 2023 Paper 2

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Attempt JEE Advanced 2023 Paper 2 under exam timing.