JEE Advanced 2023 · 04 Jun 2023 · Paper 1

Q1.A slide with a frictionless curved surface, which becomes horizontal at its lower end, is fixed on the terrace of a building of height $3h$ from the ground, as shown in the figure. A spherical ball of mass m is released on the slide from rest at a height $h$ from the top of the t …

Q2.A plane polarized blue light ray is incident on a prism such that there is no reflection from the surface of the prism. The angle of deviation of the emergent ray is $\delta =60^{\circ }$ (see Figure-1). The angle of minimum deviation for red light from the same prism is …

Q3.In a circuit shown in the figure, the capacitor $C$ is initially uncharged and the key $K$ is open. In this condition, a current of 1 A flows through the $1\Omega$ resistor. The key is closed at time $t=t_0$. Which of the following statement(s) is(are) correct?
[Given: …

Q4.A bar of mass $M=1.00\mathrm{kg}$ and length $L=0.20\mathrm{m}$ is lying on a horizontal frictionless surface. One end of the bar is pivoted at a point about which it is free to rotate. A small mass $m=0.10\mathrm{kg}$ is moving on the same horizontal surface with …

Q5.A container has a base of 50 cm × 5 cm and height 50 cm, as shown in the figure. It has two parallel electrically conducting walls each of area 50 cm × 50 cm. The remaining walls of the container are thin and non-conducting. The container is being filled with a liquid of dielectr …

Q6.One mole of an ideal gas expands adiabatically from an initial state ($T_{\mathrm{A}},V_0$) to final state ($T_{\mathrm{f}},5V_0$). Another mole of the same gas expands isothermally from a different initial state ($T_{\mathrm{B}},{\mathrm{V}}_0$) to the same final state ( …

Q7.Two satellites P and Q are moving in different circular orbits around the Earth (radius $R$). The heights of P and Q from the Earth surface are $h_{\mathrm{P}}$ and $h_{\mathrm{Q}}$, respectively, where $h_{\mathrm{p}}=\mathrm{R}/3$. The accelerations of P and Q due to Earth's …

Q8.A Hydrogen-like atom has atomic number $Z$. Photons emitted in the electronic transitions from level $n=4$ to level $n=3$ in these atoms are used to perform photoelectric effect experiment on a target metal. The maximum kinetic energy of the photoelectrons generated is 1.95 eV. I …

Q10.In an experiment for determination of the focal length of a thin convex lens, the distance of the object from the lens is 10 ± 0.1 cm and the distance of its real image from the lens is 20 ± 0.2 cm. The error in the determination of focal length of the lens is $n\%$. The value o …

Q11.A closed container contains a homogeneous mixture of two moles of an ideal monatomic gas $(\gamma =5/3)$ and one mole of an ideal diatomic gas $(\gamma =7/5)$. Here, $\gamma$ is the ratio of the specific heats at constant pressure and constant volume of an ideal gas. The gas mi …

Q12.A person of height 1.6 m is walking away from a lamp post of height 4 m along a straight path on the flat ground. The lamp post and the person are always perpendicular to the ground. If the speed of the person is $60\mathrm{cm}{\mathrm{s}}^{-1}$, the speed of the tip of the per …

Q13.Two point-like objects of masses 20 gm and 30 gm are fixed at the two ends of a rigid massless rod of length 10 cm. This system is suspended vertically from a rigid ceiling using a thin wire attached to its center of mass, as shown in the figure. The resulting torsional pendulum …

Q14.List-I shows different radioactive decay processes and List-II provides possible emitted particles. Match each entry in List-I with an appropriate entry from List-II, and choose the correct option.
| (P) | …

Q15.Match the temperature of a black body given in List-I with an appropriate statement in List-II, and choose the correct option.
[Given: Wien's constant as $2.9\times 10^{-3}\mathrm{m}-\mathrm{K}$ and $\frac{\mathrm{hc}}{\mathrm{e}}=1.24\times 10^{-6}\mathrm{V}-\mathrm{m}$] …

Q16.A series LCR circuit is connected to a $45\sin (\omega t)$ Volt source. The resonant angular frequency of the circuit is $10^5\mathrm{rad}{\mathrm{s}}^{-1}$ and current amplitude at resonance is $I_0$. When the angular frequency of the source is …

Q17.A thin conducting rod MN of mass 20 gm, length 25 cm and resistance $10\Omega$ is held on frictionless, long, perfectly conducting vertical rails as shown in the figure. There is a uniform magnetic field ${\mathrm{B}}_0=4\mathrm{T}$ directed perpendicular to the plane of the r …

Q1.The correct statement(s) related to processes involved in the extraction of metals is(are)
(A) Roasting of Malachite produces Cuprite.
(B) Calcination of Calamine produces Zincite.
(C) Copper pyrites is heated with silica in a reverberatory furnace to remove iron.
(D) Impure silv …

Q2.In the following reactions, P, Q, R, and S are the major products. …

Q3.Consider the following reaction scheme and choose the correct option(s) for the major products Q, R and S.

(see reaction scheme)

Q4.In the scheme given below, $\mathbf{X}$ and $\mathbf{Y}$, respectively, are

Metal halide $\stackrel{\text{ aq. }\mathrm{NaOH}}{\to }$ White precipitate (P) + Filtrate (Q) …

Q5.Plotting $1/{\Lambda }_{\mathrm{m}}$ against $\mathrm{c}{\Lambda }_{\mathrm{m}}$ for aqueous solutions of a monobasic weak acid (HX) resulted in a straight line with y-axis intercept of P and slope of S. The ratio P/S is

[${\Lambda }_{\mathrm{m}}=$ molar conductivity …

Q6.On decreasing the $p\mathrm{H}$ from 7 to 2, the solubility of a sparingly soluble salt (MX) of a weak acid (HX) increased from $10^{-4}\mathrm{mol}{\mathrm{L}}^{-1}$ to $10^{-3}\mathrm{mol}{\mathrm{L}}^{-1}$. The $p{\mathrm{K}}_{\mathrm{a}}$ of HX is:

Q7.In the given reaction scheme, $\mathbf{P}$ is a phenyl alkyl ether, $\mathbf{Q}$ is an aromatic compound; $\mathbf{R}$ and $\mathbf{S}$ are the major products. …

Q8.The stoichiometric reaction of 516 g of dimethyldichlorosilane with water results in a tetrameric cyclic product X in 75% yield. The weight (in g) of X obtained is ____.

[Use, molar mass …

Q9.A gas has a compressibility factor of 0.5 and a molar volume of $0.4{\mathrm{dm}}^3{\mathrm{mol}}^{-1}$ at a temperature of 800 K and pressure $\mathbf{x}$ atm. If it shows ideal gas behaviour at the same temperature and pressure, the molar volume will be …

Q10.The plot of $\log {\mathrm{k}}_{\mathrm{f}}$ versus $\frac{1}{\mathrm{T}}$ for a reversible reaction $\mathrm{A}(\mathrm{g})\rightleftharpoons \mathrm{P}(\mathrm{g})$ is shown.

(see plot)

Pre-exponential factors for the forward and backward reactions are …

Q11.One mole of an ideal monoatomic gas undergoes two reversible processes (A → B and B → C) as shown in the given figure:

(see figure)

$\mathrm{A}\to \mathrm{B}$ is an adiabatic process. If the total heat absorbed in the entire process ( …

Q12.In a one-litre flask, 6 moles of A undergoes the reaction A (g) ⇌P (g). The progress of product formation at two temperatures (in Kelvin), ${\mathrm{T}}_1$ and ${\mathrm{T}}_2$, is shown in the figure:

(see figure)

If ${\mathrm{T}}_1=2{\mathrm{T}}_2$ and …

Q13.The total number of ${\mathrm{sp}}^2$ hybridised carbon atoms in the major product P (a non-heterocyclic compound) of the following reaction is ____.

(see reaction scheme)

Q14.Match the reactions (in the given stoichiometry of the reactants) in List-I with one of their products given in List-II and choose the correct option.

List-I
(P) ${\mathrm{P}}_2{\mathrm{O}}_3+3{\mathrm{H}}_2\mathrm{O}\to$
(Q) …

Q15.Match the electronic configurations in List-I with appropriate metal complex ions in List-II and choose the correct option.

[Atomic Number: $\mathrm{Fe}=26,\mathrm{Mn}=25,\mathrm{Co}=27$]

List-I
(P) ${\mathrm{t}}_{2\mathrm{g}}^6{\mathrm{e}}_{\mathrm{g}}^0$
(Q) …

Q16.Match the reactions in List-I with the features of their products in List-II and choose the correct option.

List-I
(P) (-)-1-Bromo-2-ethylpentane (single enantiomer) $\underset{{\mathrm{S}}_{\mathrm{N}}2\text{ reaction }}{\overset{\text{ aq. }\mathrm{NaOH}}{\to }}$
(Q) (-)-2-Bromopentan …

Q17.The major products obtained from the reactions in List-II are the reactants for the named reactions mentioned in List-I. Match List-I with List-II and choose the correct option.

List-I
(P) Etard reaction
(Q) Gattermann reaction
(R) Gattermann-Koch reaction
(S) Rosenmund reductio …

Q1.Let $\mathrm{S}=(0,1)\cup (1,2)\cup (3,4)$ and $\mathrm{T}=\{0,1,2,3\}$. Then which of the following statements is(are) true ?

Q2.Let ${\mathrm{T}}_1$ and ${\mathrm{T}}_2$ be two distinct common tangents to the ellipse $\mathrm{E}:\frac{{\mathrm{x}}^2}{6}+\frac{{\mathrm{y}}^2}{3}=1$ and the parabola $\mathrm{P}:{\mathrm{y}}^2=12\mathrm{x}$. Suppose that the tangent ${\mathrm{T}}_1$ touches P and E at the …

Q3.Let $\mathrm{f}:[0,1]\to [0,1]$ be the function defined by $\mathrm{f}(\mathrm{x})=\frac{{\mathrm{x}}^3}{3}-{\mathrm{x}}^2+\frac{5}{9}\mathrm{x}+\frac{17}{36}$. Consider the square region $\mathrm{S}=[0,1]\times [0,1]$. Let …

Q4.Let $\mathrm{f}:(0,1)\to \mathbb{R}$ be the functions defined as $\mathrm{f}(\mathrm{x})=\sqrt{\mathrm{n}}$ if $\mathrm{x}\in \left[\frac{1}{\mathrm{n}+1},\frac{1}{\mathrm{n}}\right)$ where $\mathrm{n}\in \mathrm{N}$. Let $\mathrm{g}:(0,1)\to \mathbb{R}$ be a …

Q5.Let Q be the cube with the set of vertices $\left\{\left({\mathrm{x}}_1,{\mathrm{x}}_2,{\mathrm{x}}_3\right)\in {\mathbb{R}}^3:{\mathrm{x}}_1,{\mathrm{x}}_2,{\mathrm{x}}_3\{0,1\}\right\}$. Let F be the set of all twelve lines containing the diagonals of the six faces of the …

Q6.Let $\mathrm{X}=\{(x,y)\in \mathbb{Z}\times \mathbb{Z}:\frac{x^2}{8}+\frac{y^2}{20}<1$ and $y^2<5x\}$. Three distinct points P, Q and R are randomly chosen from X. Then the probability that P, Q and R form a triangle whose area is a positive integer, is

Q7.Let P be a point on the parabola ${\mathrm{y}}^2=4\mathrm{ax}$, where $\mathrm{a}>0$. The normal to the parabola at P meets the x-axis at a point Q. The area of the triangle PFQ, where F is the focus of the parabola, is 120. If the slope m of the normal and a are both positive i …

Q8.Let ${\tan }^{-1}(\mathrm{x})\in \left(-\frac{\pi }{2},\frac{\pi }{2}\right)$, for $\mathrm{x}\in \mathbb{R}$. Then the number of real solutions of the equation $\sqrt{1+\cos (2x)}=\sqrt{2}{\tan }^{-1}(\tan x)$ in the set …

Q9.Let $\mathrm{n}\ge 2$ be a natural number and $\mathrm{f}:[0,1]\to \mathbb{R}$ be the function defined by …

Q10.Let $\mathrm{75...57}$ denote the $(\mathrm{r}+2)$ digit number where the first and the last digits are 7 and the remaining r digits are 5. Consider the sum $\mathrm{S}=77+757+7557+\dots +75\dots 57$. If $\mathrm{S}=\frac{75\dots 57+\mathrm{m}}{\mathrm{n}}$, where m and n are natur …

Q11.Let $\mathrm{A}=\left\{\frac{1967+1686\mathrm{i}\sin \theta }{7-3\mathrm{i}\cos \theta }:\theta \in \mathbb{R}\right\}$. If A contains exactly one positive integer n, then the value of n is

Q12.Let P be the plane $\sqrt{3}\mathrm{x}+2\mathrm{y}+3\mathrm{z}=16$ and let $\mathrm{S}=\{\alpha \hat{\mathrm{i}}+\beta \hat{\mathrm{j}}+\gamma \hat{\mathrm{k}}:{\alpha }^2+{\beta }^2+{\gamma }^2=1$ and the distance of $(\alpha ,\beta ,\gamma )$ from the plane P is …

Q13.Let a and b be two nonzero real numbers. If the coefficient of ${\mathrm{x}}^5$ in the expansion of ${\left({\mathrm{ax}}^2+\frac{70}{27\mathrm{bx}}\right)}^4$ is equal to the coefficient of $x^{-5}$ is equal to the coefficient of ${\left(ax-\frac{1}{b{x}^2}\right)}^7$, then t …

Q14.Let $\alpha ,\beta$ and $\gamma$ be real numbers. consider the following system of linear equations

Match each entry in List - I to the correct entries in List-II

List-I
(P) If …

Q15.Consider the given data with frequency distribution

Match each entry in List-I to the correct entries in List-II.

List-I
(P) The mean of …

Q16.Let ${\ell }_1$ and ${\ell }_2$ be the lines ${\overrightarrow{\mathrm{r}}}_1=\lambda (\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}})$ and ${\overrightarrow{\mathrm{r}}}_2=(\hat{\mathrm{j}}-\hat{\mathrm{k}})+\mu (\hat{\mathrm{i}}+\hat{\mathrm{k}})$, respectively. Let X be the se …

Q17.Let z be complex number satisfying $|z{|}^3+2z^2+4\bar{z}-8=0$, where $\bar{z}$ denotes the complex conjugate of z. Let the imaginary part of z be nonzero.
Match each entry in List-I to the correct entries in List-II.

List-I
(P) $|z{|}^2$ is equal to
(Q) $|z-\bar{z}{|}^2$ is …