JEE Advanced 2023 Paper 1 Online

Consider the following reaction scheme and choose the correct option(s) for the major products $\mathbf{Q}$, $\mathbf{R}$ and $\mathbf{S}$.

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.
The correct statement about $\mathbf{S}$ is :

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) :

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.

.tg {border-collapse:collapse;border-spacing:0;width:100%}
....

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

.tg {border-collapse:collapse;border-spacing:0;width:100%}
.tg td{border-color:black;border-style:solid;border-width:1px;font-fami...

The plot of $\log k_f$ versus $1 / T$ for a reversible reaction $\mathrm{A}(\mathrm{g}) \rightleftharpoons \mathrm{P}(\mathrm{g})$ is shown.
Pre-exponential factors for the forward and backward reactions are $10^{15} \mathrm{~s}^{-1}$ and $...

The total number of $s p^2$ hybridised carbon atoms in the major product $\mathbf{P}$ (a non-heterocyclic compound) of the following reaction is ______.

Match the electronic configurations in List-I with appropriate metal complex ions in List-II and choose the correct option.
[Atomic Number: $\mathrm{Fe}=26, \mathrm{Mn}=25, \mathrm{Co}=27$ ]
.tg {border-collapse:collapse;border-spacing:0;w...

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

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

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 $800 \mathrm{~K}$ and pressure $\mathbf{x}$ atm. If it shows ideal gas behaviour at the same temperature and pressur...

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}_{\mat...

The correct statement(s) related to processes involved in the extraction of metals is(are) :

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.

.tg {border-collapse:collapse;border-spacing:0;width:100%}
.tg td{border-color:black;bo...

The stoichiometric reaction of $516 \mathrm{~g}$ of dimethyldichlorosilane with water results in a tetrameric cyclic product $\mathbf{X}$ in $75 \%$ yield. The weight (in g) of $\mathbf{X}$ obtained is _______.

[Use, molar mass $\left(\mat...

One mole of an ideal monoatomic gas undergoes two reversible processes $(\mathrm{A} \rightarrow \mathrm{B}$ and $\mathrm{B} \rightarrow \mathrm{C})$ as shown in the given figure:

$\mathrm{A} \rightarrow \mathrm{B}$ is an adiabatic process....

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

Let $\ell_1$ and $\ell_2$ be the lines $\vec{r}_1=\lambda(\hat{i}+\hat{j}+\hat{k})$ and $\vec{r}_2=(\hat{j}-\hat{k})+\mu(\hat{i}+\hat{k})$, respectively. Let $X$ be the set of all the planes $H$ that contain the line $\ell_1$. For a plane $...

Let $Q$ be the cube with the set of vertices $\left\{\left(x_1, x_2, x_3\right) \in \mathbb{R}^3: x_1, x_2, x_3 \in\{0,1\}\right\}$. Let $F$ be the set of all twelve lines containing the diagonals of the six faces of the cube $Q$. Let $S$ b...

Let $n \geq 2$ be a natural number and $f:[0,1] \rightarrow \mathbb{R}$ be the function defined by
$$
f(x)= \begin{cases}n(1-2 n x) & \text { if } 0 \leq x \leq \frac{1}{2 n} \\\\ 2 n(2 n x-1) & \text { if } \frac{1}{2 n} \leq x \leq \frac{...

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

Let $z$ be a complex number satisfying $|z|^3+2 z^2+4 \bar{z}-8=0$, 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.

.tg {border-...

Let $f:(0,1) \rightarrow \mathbb{R}$ be the function defined as $f(x)=\sqrt{n}$ if $x \in\left[\frac{1}{n+1}, \frac{1}{n}\right)$ where $n \in \mathbb{N}$. Let $g:(0,1) \rightarrow \mathbb{R}$ be a function such that $\int\limits_{x^2}^x \s...

Let $T_1$ and $T_2$ be two distinct common tangents to the ellipse $E: \frac{x^2}{6}+\frac{y^2}{3}=1$ and the parabola $P: y^2=12 x$. Suppose that the tangent $T_1$ touches $P$ and $E$ at the points $A_1$ and $A_2$, respectively and the tan...

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

Let $f:[0,1] \rightarrow[0,1]$ be the function defined by $f(x)=\frac{x^3}{3}-x^2+\frac{5}{9} x+\frac{17}{36}$. Consider the square region $S=[0,1] \times[0,1]$. Let $G=\{(x, y) \in S: y>f(x)\}$ be called the green region and $R=\{(x, y) \i...

Let $\tan ^{-1}(x) \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$, for $x \in \mathbb{R}$. Then the number of real solutions of the equation $\sqrt{1+\cos (2 x)}=\sqrt{2} \tan ^{-1}(\tan x)$ in the set $\left(-\frac{3 \pi}{2},-\frac{\pi}{2}...

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

Let $\alpha, \beta$ and $\gamma$ be real numbers. Consider the following system of linear equations
$$ \begin{aligned} & x+2 y+z=7 \\\\ & x+\alpha z=11 \\\\ & 2 x-3 y+\beta z=\gamma \end{aligned} $$
Match each entry in List-I to the correct...

Let $P$ be a point on the parabola $y^2=4 a x$, where $a>0$. The normal to the parabola at $P$ meets the $x$-axis at a point $Q$. The area of the triangle $P F Q$, where $F$ is the focus of the parabola, is 120 . If the slope $m$ of the nor...

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

Let $7 \overbrace{5 \cdots 5}^r 7$ denote the $(r+2)$ digit number where the first and the last digits are 7 and the remaining $r$ digits are 5 . Consider the sum $S=77+757+7557+\cdots+7 \overbrace{5 \cdots 5}^{98}7$. If $S=\frac{7 \overbra...

Consider the given data with frequency distribution
$$ \begin{array}{ccccccc} x_i & 3 & 8 & 11 & 10 & 5 & 4 \\ f_i & 5 & 2 & 3 & 2 & 4 & 4 \end{array} $$
Match each entry in List-I to the correct entries in List-II.

.tg {border-collapse:c...

Let $P$ be the plane $\sqrt{3} x+2 y+3 z=16$ and let
$S=\left\{\alpha \hat{i}+\beta \hat{j}+\gamma \hat{k}: \alpha^2+\beta^2+\gamma^2=1\right.$ and the distance of $(\alpha, \beta, \gamma)$ from the plane $P$ is $\left.\frac{7}{2}\right\}$....

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 s...

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.

.tg {border-collapse:collapse;border-spa...

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 $1 \mathrm{~A}$ flows through the $1 \Omega$ resistor. The key is closed at time $t=t_0$. Which of the follo...

A container has a base of $50 \mathrm{~cm} \times 5 \mathrm{~cm}$ and height $50 \mathrm{~cm}$, as shown in the figure. It has two parallel electrically conducting walls each of area $50 \mathrm{~cm} \times 50 \mathrm{~cm}$. The remaining w...

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 th...

A thin conducting rod $M N$ of mass $20 ~\mathrm{gm}$, length $25 \mathrm{~cm}$ and resistance $10 ~\Omega$ is held on frictionless, long, perfectly conducting vertical rails as shown in the figure. There is a uniform magnetic field $B_0=4 ...

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...

An optical arrangement consists of two concave mirrors $M_1$ and $M_2$, and a convex lens $L$ with a common principal axis, as shown in the figure. The focal length of $\mathrm{L}$ is $10 \mathrm{~cm}$. The radii of curvature of $M_1$ and $...

Two satellites $\mathrm{P}$ and $\mathrm{Q}$ are moving in different circular orbits around the Earth (radius $R$ ). The heights of $\mathrm{P}$ and $\mathrm{Q}$ from the Earth surface are $h_{\mathrm{P}}$ and $h_{\mathrm{Q}}$, respectively...

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

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 con...

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{h c}{e}=1.24 \times 10^{-6} \ma...

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

A person of height $1.6 \mathrm{~m}$ is walking away from a lamp post of height $4 \mathrm{~m}$ 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...

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 th...

Two point-like objects of masses $20 ~\mathrm{gm}$ and $30 ~\mathrm{gm}$ are fixed at the two ends of a rigid massless rod of length $10 \mathrm{~cm}$. This system is suspended vertically from a rigid ceiling using a thin wire attached to i...