JEE Advanced 2023 Paper 2 Online

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) :

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 :

The correct molecular orbital diagram for $\mathrm{F}_2$ molecule in the ground state is :

Among $\left[\mathrm{I}_3\right]^{+},\left[\mathrm{SiO}_4\right]^{4-}, \mathrm{SO}_2 \mathrm{Cl}_2, \mathrm{XeF}_2, \mathrm{SF}_4, \mathrm{ClF}_3, \mathrm{Ni}(\mathrm{CO})_4, \mathrm{XeO}_2 \mathrm{~F}_2,\left[\mathrm{PtCl}_4\right]^{2-}, \...

Consider the following molecules: $\mathrm{Br}_3 \mathrm{O}_8, \mathrm{~F}_2 \mathrm{O}, \mathrm{H}_2 \mathrm{S}_4 \mathrm{O}_6, \mathrm{H}_2 \mathrm{S}_5 \mathrm{O}_6$, and $\mathrm{C}_3 \mathrm{O}_2$. Count the number of atoms existing in...

The number of heteroatoms present in one molecule of $\mathbf{R}$ is _________.
[Use : Molar mass (in $\left.\mathrm{g} \mathrm{mol}^{-1}\right)$ : $\mathrm{H}=1, \mathrm{C}=12, \mathrm{~N}=14, \mathrm{O}=16, \mathrm{Br}=80, \mathrm{Cl}=35....

The total number of carbon atoms and heteroatoms present in one molecule of $\mathbf{S}$ is _________.
[Use : Molar mass (in $\mathrm{g} \mathrm{mol}^{-1}$ ): $\mathrm{H}=1, \mathrm{C}=12, \mathrm{~N}=14, \mathrm{O}=16, \mathrm{Br}=80, \mat...

The complex(es), which can exhibit the type of isomerism shown by $\left[\operatorname{Pt}\left(\mathrm{NH}_3\right)_2 \mathrm{Br}_2\right]$, is(are) :
[en $=\mathrm{H}_2 \mathrm{NCH}_2 \mathrm{CH}_2 \mathrm{NH}_2$ ]

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 :

The reaction of 4-methyloct-1-ene $(\mathbf{P}, 2.52 \mathrm{~g})$ with $\mathrm{HBr}$ in the presence of $\left(\mathrm{C}_6 \mathrm{H}_5 \mathrm{CO}\right)_2 \mathrm{O}_2$ gives two isomeric bromides in a $9: 1$ ratio, with a combined yie...

Atoms of metals $\mathrm{x}, \mathrm{y}$, and $\mathrm{z}$ form face-centred cubic (fcc) unit cell of edge length $\mathrm{L}_{\mathrm{x}}$, body-centred cubic (bcc) unit cell of edge length $\mathrm{L}_y$, and simple cubic unit cell of edg...

$50 \mathrm{~mL}$ of 0.2 molal urea solution (density $=1.012 \mathrm{~g} \mathrm{~mL}^{-1}$ at $300 \mathrm{~K}$ ) is mixed with $250 \mathrm{~mL}$ of a solution containing $0.06 \mathrm{~g}$ of urea. Both the solutions were prepared in th...

$\mathrm{H}_2 \mathrm{S}$ (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...

For $\mathrm{He}^{+}$, a transition takes place from the orbit of radius $105.8 \mathrm{pm}$ to the orbit of radius $26.45 \mathrm{pm}$. The wavelength (in nm) of the emitted photon during the transition is _______.
[Use :
Bohr radius, $\ma...

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)...

The value of entropy change, $S_\beta-S_\alpha$ (in $\mathrm{J} \mathrm{mol}^{-1} \mathrm{~K}^{-1}$ ), at $300 \mathrm{~K}$ is _______.
[Use : $\ln 2=0.69$
Given : $S_\beta-S_\alpha=0$ at $0 \mathrm{~K}$ ]

\(\text { The value of enthalpy change, } \mathrm{H}_\beta-\mathrm{H}_\alpha \text { (in } \mathrm{J} \mathrm{mol}^{-1} \text { ), at } 300 \mathrm{~K} \text { is }\) ________.

Let $A_1, A_2, A_3, \ldots, A_8$ 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 $P A_i$ denote the distance between the points $P$ and $A_i$ for $i=1,2, \ldots, 8$. If $P$ va...

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 $P Q$ and $S T$ of $C_1$ and $C_2$ are drawn. The tange...

For $x \in \mathbb{R}$, let $\tan ^{-1}(x) \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$. Then the minimum value of the function $f: \mathbb{R} \rightarrow \mathbb{R}$ defined by $f(x)=\int\limits_0^{x \tan ^{-1} x} \frac{e^{(t-\cos t)}}{1...

Let $f:[1, \infty) \rightarrow \mathbb{R}$ be a differentiable function such that $f(1)=\frac{1}{3}$ and $3 \int\limits_1^x f(t) d t=x f(x)-\frac{x^3}{3}, x \in[1, \infty)$. Let $e$ denote the base of the natural logarithm. Then the value o...

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

Let $S$ be the set of all twice differentiable functions $f$ from $\mathbb{R}$ to $\mathbb{R}$ such that $\frac{d^2 f}{d x^2}(x)>0$ for all $x \in(-1,1)$. For $f \in S$, let $X_f$ be the number of points $x \in(-1,1)$ for which $f(x)=x$. Th...

For any $y \in \mathbb{R}$, let $\cot ^{-1}(y) \in(0, \pi)$ and $\tan ^{-1}(y) \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$. Then the sum of all the solutions of the equation $\tan ^{-1}\left(\frac{6 y}{9-y^2}\right)+\cot ^{-1}\left(\frac...

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

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

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

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 :

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 pro...

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 $7 E(X)$ is :

Two distinct points are chosen randomly out of the points $A_1, A_2, \ldots, A_{49}$. Let $p$ be the probability that they are friends. Then the value of $7 p$ is :

\(\text { Let } a \text { be the area of the triangle } A B C \text {. Then the value of }(64 a)^2 \text { is }\) :

\(\text { Then the inradius of the triangle } A B C \text { is }\) :

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 $\vec{d}=2 \hat{i}+\hat{j}+\hat{k}$,...

In a radioactive decay process, the activity is defined as $A=-\frac{d N}{d t}$, 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 a...

The electric field associated with an electromagnetic wave propagating in a dielectric medium is given by $\vec{E}=30(2 \hat{x}+\hat{y}) \sin \left[2 \pi\left(5 \times 10^{14} t-\frac{10^7}{3} z\right)\right] \mathrm{Vm}^{-1}$. Which of the...

An electric dipole is formed by two charges $+q$ and $-q$ located in $x y$-plane at $(0,2) \mathrm{mm}$ and $(0,-2) \mathrm{mm}$, respectively, as shown in the figure. The electric potential at point $P(100,100) \mathrm{mm}$ due to the dipo...

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(ar...

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 $\mathrm{v}_n$. At a fixed temperature ...

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...

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

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, ...

A particle of mass $m$ is moving in the $x y$-plane such that its velocity at a point $(x, y)$ is given as $\overrightarrow{\mathrm{v}}=\alpha(y \hat{x}+2 x \hat{y})$, where $\alpha$ is a non-zero constant. What is the force $\vec{F}$ actin...

A rectangular conducting loop of length $4 \mathrm{~cm}$ and width $2 \mathrm{~cm}$ is in the $x y$-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}+\...

An incompressible liquid is kept in a container having a weightless piston with a hole. A capillary tube of inner radius $0.1 \mathrm{~mm}$ is dipped vertically into the liquid through the airtight piston hole, as shown in the figure. The a...

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 cen...

A thin circular coin of mass $5 \mathrm{gm}$ and radius $4 / 3 \mathrm{~cm}$ is initially in a horizontal $x y$-plane. The coin is tossed vertically up ( $+z$ direction) by applying an impulse of $\sqrt{\frac{\pi}{2}} \times 10^{-2} \mathrm...

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 c...

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

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