JEE Advanced 2022 Paper 2 Online

Treatment of D-glucose with aqueous $\mathrm{NaOH}$ results in a mixture of monosaccharides, which are

The reaction of $\mathrm{Xe}$ and $\mathrm{O}_{2}{F}_{2}$ gives a $\mathrm{Xe}$ compound $\mathbf{P}$. The number of moles of $\mathrm{HF}$ produced by the complete hydrolysis of $1 \mathrm{~mol}$ of $\mathbf{P}$ is __________.

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 ____________.

Consider the strong electrolytes $Z_{m} X_{n}, U_{m} Y_{p}$ and $V_{m} X_{n}$. Limiting molar conductivity ( $\Lambda^{0}$ ) of $\mathrm{U}_{\mathrm{m}} \mathrm{Y}_{\mathrm{p}}$ and $\mathrm{V}_{\mathrm{m}} \mathrm{X}_{\mathrm{n}}$ are 250 ...

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

The number of $-\mathrm{CH}_{2}-$ (methylene) groups in the product formed from the following reaction sequence is _________.

The total number of chiral molecules formed from one molecule of $\mathbf{P}$ on complete ozonolysis $\left(\mathrm{O}_{3}, \mathrm{Zn} / \mathrm{H}_{2} \mathrm{O}\right)$ is _________.

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

Concentration of $\mathrm{H}_{2} \mathrm{SO}_{4}$ and $\mathrm{Na}_{2} \mathrm{SO}_{4}$ in a solution is $1 \mathrm{M}$ and $1.8 \times 10^{-2} \mathrm{M}$, respectively. Molar solubility of $\mathrm{PbSO}_{4}$ in the same solution is $\mat...

The correct option(s) related to the extraction of iron from its ore in the blast furnace operating in the temperature range $900-1500 \mathrm{~K}$ is(are)

The compound(s) which react(s) with $\mathrm{NH}_{3}$ to give boron nitride (BN) is(are)

The reaction of $\mathrm{HClO}_{3}$ with $\mathrm{HCl}$ gives a paramagnetic gas, which upon reaction with $\mathrm{O}_{3}$ produces

The reaction of $\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}$ and $\mathrm{NaCl}$ in water produces a precipitate that dissolves upon the addition of $\mathrm{HCl}$ of appropriate concentration. The dissolution of the precipitate is due to ...

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

Atom $\mathrm{X}$ occupies the fcc lattice sites as well as alternate tetrahedral voids of the same lattice. The packing efficiency (in %) of the resultant solid is closest to

An aqueous solution is prepared by dissolving $0.1 \mathrm{~mol}$ of an ionic salt in $1.8 \mathrm{~kg}$ of water at $35^{\circ} \mathrm{C}$. The salt remains $90 \%$ dissociated in the solution. The vapour pressure of the solution is $59.7...

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

.tg {b...

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

Let

\(\alpha=\sum\limits_{k = 1}^\infty {{{\sin }^{2k}}\left( {{\pi \over 6}} \right)}\)

Let $g:[0,1] \rightarrow \mathbb{R}$ be the function defined by

\(g(x)=2^{\alpha x}+2^{\alpha(1-x)} .\)

Then, which of the following stateme...

Consider the functions $f, g: \mathbb{R} \rightarrow \mathbb{R}$ defined by

$$
f(x)=x^{2}+\frac{5}{12} \quad \text { and } \quad g(x)= \begin{cases}2\left(1-\frac{4|x|}{3}\right), & |x| \leq \frac{3}{4} \\ 0, & |x|>\frac{3}{4}\end{cases}
$...

Let $G$ be a circle of radius $R>0$. Let $G_{1}, G_{2}, \ldots, G_{n}$ be $n$ circles of equal radius $r>0$. Suppose each of the $n$ circles $G_{1}, G_{2}, \ldots, G_{n}$ touches the circle $G$ externally. Also, for $i=1,2, \ldots, n-1$, th...

Let $\bar{z}$ 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

\((\bar{z})^{2}+\frac{1}{z^{2}}\)

are integers, then which of the following is/are possib...

The greatest integer less than or equal to

\(\int_{1}^{2} \log _{2}\left(x^{3}+1\right) d x+\int_{1}^{\log _{2} 9}\left(2^{x}-1\right)^{\frac{1}{3}} d x\)

is ___________.

If $y(x)$ is the solution of the differential equation

\(x d y-\left(y^{2}-4 y\right) d x=0 \text { for } x > 0, y(1)=2,\)

and the slope of the curve $y=y(x)$ is never zero, then the value of $10 y(\sqrt{2})$ is

For $x \in \mathbb{R}$, let the function $y(x)$ be the solution of the differential equation

\(\frac{d y}{d x}+12 y=\cos \left(\frac{\pi}{12} x\right), \quad y(0)=0\)

Then, which of the following statements is/are TRUE ?

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 $\angle S P S_{1}=\alpha$, with $\alp...

If
\(\beta=\lim \limits_{x \to 0} \frac{e^{x^{3}}-\left(1-x^{3}\right)^{\frac{1}{3}}+\left(\left(1-x^{2}\right)^{\frac{1}{2}}-1\right) \sin x}{x \sin ^{2} x},\)

then the value of $6 \beta$ is ___________.

For positive integer $n$, define

\(f(n)=n+\frac{16+5 n-3 n^{2}}{4 n+3 n^{2}}+\frac{32+n-3 n^{2}}{8 n+3 n^{2}}+\frac{48-3 n-3 n^{2}}{12 n+3 n^{2}}+\cdots+\frac{25 n-7 n^{2}}{7 n^{2}} .\)

Then, the value of $$\mathop {\lim }\limits_{n \to...

Let $\beta$ be a real number. Consider the matrix

$$ A=\left(\begin{array}{ccc} \beta & 0 & 1 \\ 2 & 1 & -2 \\ 3 & 1 & -2 \end{array}\right) $$

If $A^{7}-(\beta-1) A^{6}-\beta A^{5}$ is a singular matrix, then the value of $9 \beta$ is __...

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

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 bal...

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 ...

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 __________.

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

$$
\left(\frac{\s...

Let $P Q R S$ be a quadrilateral in a plane, where $Q R=1, \angle P Q R=\angle Q R S=70^{\circ}, \angle P Q S=15^{\circ}$ and $\angle P R S=40^{\circ}$. If $\angle R P S=\theta^{\circ}, P Q=\alpha$ and $P S=\beta$, then the interval(s) that...

Let $\hat{\imath}, \hat{\jmath}$ and $\hat{k}$ be the unit vectors along the three positive coordinate axes. Let

$$
\begin{aligned}
& \vec{a}=3 \hat{\imath}+\hat{\jmath}-\hat{k} \text {, } \\
& \vec{b}=\hat{\imath}+b_{2} \hat{\jmath}+b_{3}...

In a radioactive decay chain reaction, ${ }_{90}^{230} \mathrm{Th}$ nucleus decays into ${ }_{84}^{214} \mathrm{Po}$ nucleus. The ratio of the number of $\alpha$ to number of $\beta^{-}$particles emitted in this process is ________.

Two resistances $R_{1}=X \Omega$ and $R_{2}=1 \Omega$ are connected to a wire $A B$ of uniform resistivity, as shown in the figure. The radius of the wire varies linearly along its axis from $0.2 \mathrm{~mm}$ at $A$ to $1 \mathrm{~mm}$ at ...

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 $\mathrm{S}_{1}$ and $\mathrm{S}_{2}...

When light of a given wavelength is incident on a metallic surface, the minimum potential needed to stop the emitted photoelectrons is $6.0 \mathrm{~V}$. This potential drops to $0.6 \mathrm{~V}$ if another source with wavelength four times...

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{n q}{6 \epsilon_...

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 $\rho_{A}=k r$, where $k$ is positive. In the spheric...

A disk of radius $\mathrm{R}$ with uniform positive charge density $\sigma$ is placed on the $x y$ plane with its center at the origin. The Coulomb potential along the $z$-axis is

$$
V(z)=\frac{\sigma}{2 \epsilon_{0}}\left(\sqrt{R^{2}+z^{2...

Consider a configuration of $n$ identical units, each consisting of three layers. The first layer is a column of air of height $h=\frac{1}{3} \mathrm{~cm}$, and the second and third layers are of equal thickness $d=$ $\frac{\sqrt{3}-1}{2} \...

An object and a concave mirror of focal length $f=10 \mathrm{~cm}$ both move along the principal axis of the mirror with constant speeds. The object moves with speed $V_{0}=15 \mathrm{~cm} \mathrm{~s}^{-1}$ towards the mirror with respect t...

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} ...

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

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_{a...

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 fla...

A particle of mass $1 \mathrm{~kg}$ is subjected to a force which depends on the position as $\vec{F}=$ $-k(x \hat{\imath}+y \hat{\jmath}) \mathrm{kg}\, \mathrm{m} \mathrm{s}^{-2}$ with $k=1 \mathrm{~kg} \mathrm{~s}^{-2}$. At time $t=0$, th...