JEE Advanced 2022 Paper 1 Online

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

Match the rate expressions in LIST-I for the decomposition of $X$ with the corresponding profiles provided in LIST-II. $X_{\mathrm{s}}$ and $\mathrm{k}$ are constants having appropriate units.

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Considering the following reaction sequence,

the correct option(s) is(are)

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

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LIST-I contains metal species and LIST-II contains their properties.

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The treatment of galena with $\mathrm{HNO}_{3}$ produces a gas that is

The reduction potential $\left(E^{0}\right.$, in $\left.\mathrm{V}\right)$ of $\mathrm{MnO}_{4}^{-}(\mathrm{aq}) / \mathrm{Mn}(\mathrm{s})$ is __________.

[Given: $E_{\left(\mathrm{MnO}_{4}^{-}(\mathrm{aq}) / \mathrm{MnO}_{2}(\mathrm{~s})\...

If the reaction sequence given below is carried out with 15 moles of acetylene, the amount of the product $\mathbf{D}$ formed (in $\mathrm{g}$ ) is ___________ .

The yields of $\mathbf{A}, \mathbf{B}, \mathbf{C}$ and $\mathbf{D}$ are given...

LIST-I contains compounds and LIST-II contains reactions

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A solution is prepared by mixing $0.01 \mathrm{~mol}$ each of $\mathrm{H}_{2} \mathrm{CO}_{3}, \mathrm{NaHCO}_{3}, \mathrm{Na}_{2} \mathrm{CO}_{3}$, and $\mathrm{NaOH}$ in $100 \mathrm{~mL}$ of water. $p \mathrm{H}$ of the resulting solutio...

The electrochemical extraction of aluminum from bauxite ore involves

Dissolving $1.24 \mathrm{~g}$ of white phosphorous in boiling $\mathrm{NaOH}$ 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 ________...

Consider the following reaction.

On estimation of bromine in $1.00 \mathrm{~g}$ of $\mathbf{R}$ using Carius method, the amount of $\mathrm{AgBr}$ formed (in $\mathrm{g}$ ) is ___________.

[Given: Atomic mass of $\mathrm{H}=1, \mathrm{C}=...

The weight percentage of hydrogen in $\mathbf{Q}$, formed in the following reaction sequence, is ________.

[Given: Atomic mass of $\mathrm{H}=1, \mathrm{C}=12, \mathrm{~N}=14, \mathrm{O}=16, \mathrm{~S}=32, \mathrm{Cl}=35$ ]

The treatment of an aqueous solution of $3.74 \mathrm{~g}$ of $\mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2}$ with excess KI results in a brown solution along with the formation of a precipitate. Passing $\mathrm{H}_{2} \mathrm{~S}$ through t...

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

The correct option(s) related to adsorption processes is(are)

$2 \mathrm{~mol} \,\mathrm{of}\, \mathrm{Hg}(\mathrm{g})$ is combusted in a fixed volume bomb calorimeter with excess of $\mathrm{O}_{2}$ at $298 \mathrm{~K}$ and 1 atm into $\mathrm{HgO}(s)$. During the reaction, temperature increases from...

Let \(P_{1}\) and \(P_{2}\) be two planes given by

$$ \begin{aligned} &P_{1}: 10 x+15 y+12 z-60=0 \\\\ &P_{2}:-2 x+5 y+4 z-20=0 \end{aligned} $$

Which of the following straight lines can be an edge of some tetrahedron whose two faces lie ...

Let \(S\) be the reflection of a point \(Q\) with respect to the plane given by

\(\vec{r}=-(t+p) \hat{\imath}+t \hat{\jmath}+(1+p) \hat{k}\)

where \(t, p\) are real parameters and \(\hat{\imath}, \hat{\jmath}, \hat{k}\) are the unit vec...

Let \(A B C\) be the triangle with \(A B=1, A C=3\) and \(\angle B A C=\frac{\pi}{2}\). If a circle of radius \(r>0\) touches the sides \(A B, A C\) and also touches internally the circumcircle of the triangle \(A B C\), then the value of $...

Let \(z\) be a complex number with a non-zero imaginary part. If

\(\frac{2+3 z+4 z^{2}}{2-3 z+4 z^{2}}\)

is a real number, then the value of \(|z|^{2}\) is _________.

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 _________.

Consider the equation
\(\int_{1}^{e} \frac{\left(\log _{\mathrm{e}} x\right)^{1 / 2}}{x\left(a-\left(\log _{\mathrm{e}} x\right)^{3 / 2}\right)^{2}} d x=1, \quad a \in(-\infty, 0) \cup(1, \infty)\)

Which of the following statements is/ar...

Consider the ellipse

\($ \frac{x^{2}}{4}+\frac{y^{2}}{3}=1\)$

Let $H(\alpha, 0), 0<\alpha<2$, be a point. A straight line drawn through $H$ parallel to the $y$-axis crosses the ellipse and its auxiliary circle at points $E$ and $F$ respe...

Let \(|M|\) denote the determinant of a square matrix \(M\). Let \(g:\left[0, \frac{\pi}{2}\right] \rightarrow \mathbb{R}\) be the function defined by
\(g(\theta)=\sqrt{f(\theta)-1}+\sqrt{f\left(\frac{\pi}{2}-\theta\right)-1}\)
where
$$
f...

Considering only the principal values of the inverse trigonometric functions, the value of

\(\frac{3}{2} \cos ^{-1} \sqrt{\frac{2}{2+\pi^{2}}}+\frac{1}{4} \sin ^{-1} \frac{2 \sqrt{2} \pi}{2+\pi^{2}}+\tan ^{-1} \frac{\sqrt{2}}{\pi}\)

is

Let \(\alpha\) be a positive real number. Let \(f: \mathbb{R} \rightarrow \mathbb{R}\) and \(g:(\alpha, \infty) \rightarrow \mathbb{R}\) be the functions defined by

$$
f(x)=\sin \left(\frac{\pi x}{12}\right) \quad \text { and } \quad g(x)=...

Let \(p, q, r\) be nonzero real numbers that are, respectively, the \(10^{\text {th }}, 100^{\text {th }}\) and \(1000^{\text {th }}\) terms of a harmonic progression. Consider the system of linear equations
$$$
\begin{gathered}
x+y+z=1 \\...

Consider the parabola \(y^{2}=4 x\). Let \(S\) be the focus of the parabola. A pair of tangents drawn to the parabola from the point \(P=(-2,1)\) meet the parabola at \(P_{1}\) and \(P_{2}\). Let \(Q_{1}\) and \(Q_{2}\) be points on the lin...

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

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 coug...

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 di...

Let \(l_{1}, l_{2}, \ldots, l_{100}\) be consecutive terms of an arithmetic progression with common difference \(d_{1}\), and let \(w_{1}, w_{2}, \ldots, w_{100}\) be consecutive terms of another arithmetic progression with common differenc...

Let \(a_{1}, a_{2}, a_{3}, \ldots\) be an arithmetic progression with \(a_{1}=7\) and common difference 8. Let \(T_{1}, T_{2}, T_{3}, \ldots\) be such that \(T_{1}=3\) and \(T_{n+1}-T_{n}=a_{n}\) for \(n \geq 1\). Then, which of the followi...

Consider the following lists :

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The minimum kinetic energy needed by an alpha particle to cause the nuclear reaction ${ }_{7}^{16} \mathrm{~N}+$ ${ }_{2}^{4} \mathrm{He} \rightarrow{ }_{1}^{1} \mathrm{H}+{ }_{8}^{19} \mathrm{O}$ in a laboratory frame is $n$ (in $M e V$. A...

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 o...

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 i...

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 ____________ $\mu C$.

The figure shows a circuit having eight resistances of $1 \Omega$ each, labelled $R_{1}$ to $R_{8}$, and two ideal batteries with voltages $\varepsilon_{1}=12 \mathrm{~V}$ and $\varepsilon_{2}=6 \mathrm{~V}$.

Which of the following stateme...

Consider an LC circuit, with inductance $L=0.1 \,\mathrm{H}$ and capacitance $C=10^{-3} \mathrm{~F}$, kept on a plane. The area of the circuit is $1 \mathrm{~m}^{2}$. It is placed in a constant magnetic field of strength $B_{0}$ which is pe...

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...

A rod of length $2 \mathrm{~cm}$ makes an angle $\frac{2 \pi}{3} \mathrm{rad}$ with the principal axis of a thin convex lens. The lens has a focal length of $10 \mathrm{~cm}$ and is placed at a distance of $\frac{40}{3} \mathrm{~cm}$ from t...

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 $\theta$ and can ...

List I contains four combinations of two lenses (1 and 2) whose focal lengths (in $\mathrm{cm}$ ) are indicated in the figures. In all cases, the object is placed $20 \mathrm{~cm}$ from the first lens on the left, and the distance between t...

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 som...

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.

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A small circular loop of area $A$ and resistance $R$ is fixed on a horizontal $x y$-plane with the center of the loop always on the axis $\hat{n}$ of a long solenoid. The solenoid has $m$ turns per unit length and carries current $I$ counte...

A projectile is fired from horizontal ground with speed $v$ and projection angle $\theta$. 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 d...