JEE Advanced 2022 · 28 Aug 2022 · Paper 1

Q1.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 $M_B=2M_A$. Due to an interaction process, star $A$ loses some of its mass, so th …

Q2.The minimum kinetic energy needed by an alpha particle to cause the nuclear reaction ${}_7^{16}\mathrm{N}+{}_2^4\mathrm{He}\to {}_1^1\mathrm{H}+{}_8^{19}\mathrm{O}$ in a laboratory frame is $n$ (in MeV). Assume that ${}_7^{16}\mathrm{N}$ is at rest …

Q3.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 ____ $\mu C$.

Q4.A rod of length $2cm$ makes an angle $\frac{2\pi }{3}$ rad with the principal axis of a thin convex lens. The lens has a focal length of $10cm$ and is placed at a distance of $\frac{40}{3}cm$ from the object as shown in the figure. The height of the image is …

Q5.At time $t=0$, a disk of radius 1 m starts to roll without slipping on a horizontal plane with an angular acceleration of $\alpha =\frac{2}{3}rad{s}^{-2}$. A small stone is stuck to the disk. At $t=0$, it is at the contact point of the disk and the plane. Later, at time …

Q6.A solid sphere of mass $1kg$ and radius $1m$ rolls without slipping on a fixed inclined plane with an angle of inclination $\theta =30^{\circ }$ from the horizontal. Two forces of magnitude $1N$ each, parallel to the incline, act on the sphere, both at distance …

Q7.Consider an LC circuit, with inductance $L=0.1H$ and capacitance $C=10^{-3}F$, kept on a plane. The area of the circuit is $1m^2$. It is placed in a constant magnetic field of strength $B_0$ which is perpendicular to the plane of the circuit. At time $t=0$, the m …

Q8.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 different region where the effect …

Q9.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 in Figure (a). Now, both the plates …

Q10.The figure shows a circuit having eight resistances of $1\Omega$ each, labelled $R_1$ to $R_8$, and two ideal batteries with voltages ${\epsilon }_1=12V$ and ${\epsilon }_2=6V$.

Which of the following statement(s) is(are) correct?

Q11.An ideal gas of density $\rho =0.2kg{m}^{-3}$ enters a chimney of height h at the rate of $\alpha =0.8kg{s}^{-1}$ from its lower end, and escapes through the upper end as shown in the figure. The cross-sectional area of the lower end is $A_1=0.1m^2$ and the upper end is …

Q12.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 only come out through the same hol …

Q13.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 center O of the hexagon and is bisect …

Q14.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 of a neutron be $E_b^n$ in the nu …

Q15.A small circular loop of area $A$ and resistance $R$ is fixed on a horizontal $xy$-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 $I$ counterclockwise as shown in the fi …

Q16.List I describes four systems, each with two particles $A$ and $B$ in relative motion as shown in figure. List II gives possible magnitudes of their relative velocities (in $m{s}^{-1}$) at time $t=\frac{\pi }{3}s$.
| (I) …

Q17.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.
| (I) | …

Q18.List I contains four combinations of two lenses (1 and 2) whose focal lengths (in cm) are indicated in the figures. In all cases, the object is placed $20cm$ from the first lens on the left, and the distance between the two lenses is $5cm$. List II contains the positions of …

Q1.2 mol of Hg(g) is combusted in a fixed volume bomb calorimeter with excess of ${\mathrm{O}}_2$ at 298 K and 1 atm into HgO(s). During the reaction, temperature increases from 298.0 K to 312.8 K. If heat capacity of the bomb calorimeter and enthalpy of formation of …

Q2.The reduction potential ( $E^0$, in V ) of ${\mathrm{MnO}}_4^{-}(\mathrm{aq})/\mathrm{Mn}(\mathrm{s})$ is ____. …

Q3.A solution is prepared by mixing 0.01 mol each of ${\mathrm{H}}_2{\mathrm{CO}}_3,{\mathrm{NaHCO}}_3,{\mathrm{Na}}_2{\mathrm{CO}}_3$, and NaOH in 100 mL of water. pH of the resulting solution is ____.
[Given : $p{\mathrm{K}}_{\mathrm{a}1}$ and …

Q4.The treatment of an aqueous solution of 3.74 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 this brown solution gives another precipitate X. …

Q5.Dissolving 1.24 g of white phosphorous in boiling 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 ____.
[Given : Atomic mass of …

Q6.Consider the following reaction.

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

[Given : Atomic mass of $\mathrm{H}=1,\mathrm{C}=12,\mathrm{O}=16,\mathrm{P}=31,\mathrm{Br}=80,\mathrm{Ag}=108$ ]

Q7.The weight percentage of hydrogen in $\mathbf{Q}$, formed in the following reaction sequence, is ____.

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

Q8.If the reaction sequence given below is carried out with 15 moles of acetylene, the amount of the product D formed (in g) is ____.

The yields of $\mathbf{A},\mathbf{B},\mathbf{C}$ and $\mathbf{D}$ are given in parentheses.
[Given : Atomic mass of …

Q9.For diatomic molecules, the correct statement(s) about the molecular orbitals formed by the overlap to two $2p_{\mathrm{z}}$ orbitals is(are)

Q10.The correct option(s) related to adsorption processes is(are)

Q11.The electrochemical extraction of aluminum from bauxite ore involves.

Q12.The treatment of galena with ${\mathrm{HNO}}_3$ produces a gas that is

Q13.Considering the reaction sequence given below, the correct statement(s) is(are)

Q14.Consider the following reaction sequence,

the correct option(s) is(are)

Q15.Match the rate expressions in LIST-I for the decomposition of X with the corresponding profiles provided in LIST-II. ${\mathrm{X}}_{\mathrm{s}}$ and k constants having appropriate units.

List-I
(I) rate $=\frac{\mathrm{k}[\mathrm{X}]}{{\mathrm{X}}_{\mathrm{s}}+[\mathrm{X}]}$ und …

Q16.LIST-I contains compounds and LIST-II contains reaction
| (II) $\mathrm{Mg}(\mathrm{OH}{)}_2$ | (Q) …

Q17.LIST-I contains metal species and LIST-II contains their properties.
| (II) ${\left[{\mathrm{RuCl}}_6\right]}^{2-}$ | (Q) …

Q18.Match the compounds in LIST-I with the observation in LIST-II, and choose the correct option.
| (I) Aniline | (P) Sodium fusion extract of the compound on boiling with ${\mathrm{FeSO}}_4$, followed by acidification with conc. …

Q1.Considering only the principal values of the inverse trigonometric functions, the value of

is ____.

Q2.Let $\alpha$ be a positive real number. Let $f:\mathbb{R}\to \mathbb{R}$ and $g:(\alpha ,\infty )\to \mathbb{R}$ be the functions defined by …

Q3.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 cough or both,
350 persons had symptom of cough …

Q4.Let $z$ be a complex number with non-zero imaginary part. If

is a real number, then the value of $|z{|}^2$ is ____.

Q5.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

is ____.

Q6.Let $l_1,l_2,\dots ,l_{100}$ be consecutive terms of an arithmetic progression with common difference $d_1$, and let $w_1,w_2,\dots ,w_{100}$ be consecutive terms of another arithmetic progression with common difference $d_2$, where $d_1{d}_2=10$. For each …

Q7.The number of 4-digit integers in the closed interval [2022, 4482] formed by using the digits $0,2,3,4,6,7$ is ____.

Q8.Let $ABC$ be the triangle with $AB=1,AC=3$ and $\angle BAC=\frac{\pi }{2}$. If a circle of radius $r>0$ touches the sides $AB,AC$ and also touches internally the circumcircle of the triangle $ABC$, then the value of $r$ is ____.

Q9.Consider the equation

Which of the following statements is/are TRUE ?

Q10.Let $a_1,a_2,a_3,\dots$ be an arithmetic progression with $a_1=7$ and common difference 8. Let $T_1,T_2,T_3,\dots$ be such that $T_1=3$ and $T_{n+1}-T_n=a_n$ for $n\ge 1$. Then, which of the following is/are TRUE ?

Q11.Let $P_1$ and $P_2$ be two planes given by


Which of the following straight lines can be an edge of some tetrahedron whose two faces lie on $P_1$ and $P_2$ ?

Q12.Let $S$ be the reflection of a point $Q$ with respect to the plane given by

where $t,p$ are real parameters and $\hat{i},\hat{j},\hat{k}$ are the unit vectors along the three positive coordinate axes. If the position vectors of …

Q13.Consider the parabola $y^2=4x$. 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 lines $S{P}_1$ and $S{P}_2$ respectively such that …

Q14.Let $|M|$ denote the determinant of a square matrix $M$. Let $g:\left[0,\frac{\pi }{2}\right]\to \mathbb{R}$ be the function defined by

where …

Q15.Consider the following lists:
| (II) | …

Q16.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 die rolled by $P_1$ and $P_2$, respectively. I …

Q17.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




| List-I | | Lis …

Q18.Consider the ellipse

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 $F$ respectively, in the first quadrant. The tangent t …