JEE Main 2023 (Online) 30th January Evening Shift

Paper was held on
Mon, Jan 30, 2023 9:30 AM

## Chemistry

Given below are two statements:
Statement I: During Electrolytic refining, the pure metal is made to act as anode and i

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Formulae for Nessler's reagent is:

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Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: can

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The water quality of a pond was analyzed and its BOD was found to be 4. The pond has

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The most stable carbocation for the following is:

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Chlorides of which metal are soluble in organic solvents:

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Which of the following reaction is correct?

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Match List I with List II:
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The $\mathrm{Cl}-\mathrm{Co}-\mathrm{Cl}$ bond angle values in a fac- $\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{3}

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Decreasing order towards SN 1 reaction for the following compounds is:

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Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason $\mathbf{R}$.
Assert

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$\mathrm{KMnO}_4$ oxidises $\mathrm{I}^{-}$ in acidic and neutral/faintly alkaline solutions, respectively, to

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In the above conversion of compound $(\mathrm{X})$ to product $(\mathrm{Y})$, the sequence of reagents to be used will

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Match List I with List II:
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Maximum number of electrons that can be accommodated in shell with $n=4$ are:

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Bond dissociation energy of "E-H" bond of the "$\mathrm{H}_{2} \mathrm{E}$ " hydrides of group 16 elements (given below)

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Boric acid is solid, whereas $\mathrm{BF}_3$ is gas at room temperature because of

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The correct order of $\mathrm{pK}_{\mathrm{a}}$ values for the following compounds is:

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$1 \mathrm{~L}, 0.02 \mathrm{M}$ solution of $\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{5} \mathrm{SO}_{4}\right]$

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The wave function $(\Psi)$ of $2 \mathrm{~s}$ is given by
$$
\Psi_{2 \mathrm{~s}}=\frac{1}{2 \sqrt{2 \pi}}\left(\frac{1}

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The graph of $\log \frac{x}{m}$ vs $\log \mathrm{p}$ for an adsorption process is a straight line inclined at an angle o

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The strength of 50 volume solution of hydrogen peroxide is ______ $\mathrm{g} / \mathrm{L}$ (Nearest integer).
Given:

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A short peptide on complete hydrolysis produces 3 moles of glycine (G), two moles of leucine (L) and two moles of valine

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Number of compounds from the following which will not dissolve in cold $\mathrm{NaHCO}_{3}$ and $\mathrm{NaOH}$ solution

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An organic compound undergoes first-order decomposition. If the time taken for the $60 \%$ decomposition is $540 \mathrm

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1 mole of ideal gas is allowed to expand reversibly and adiabatically from a temperature of $27^{\circ} \mathrm{C}$. The

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The electrode potential of the following half cell at $298 \mathrm{~K}$
$\mathrm{X}\left|\mathrm{X}^{2+}(0.001 \mathrm{

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Consider the following equation:
$2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g), \Del

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Lead storage battery contains $38 \%$ by weight solution of $\mathrm{H}_{2} \mathrm{SO}_{4}$. The van't Hoff factor is $

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Iron oxide FeO, crystallises in a cubic lattice with a unit cell edge length of 5.0 Å. If density of the $\mathrm{FeO}$

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## Mathematics

A vector $\vec{v}$ in the first octant is inclined to the $x$-axis at $60^{\circ}$, to the $y$-axis at 45 and to the $z$

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Let $a_{1}=1, a_{2}, a_{3}, a_{4}, \ldots .$. be consecutive natural numbers.
Then $\tan ^{-1}\left(\frac{1}{1+a_{1} a_

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For $\alpha, \beta \in \mathbb{R}$, suppose the system of linear equations
$$
\begin{aligned}
& x-y+z=5 \\
& 2 x+2 y+\al

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The number of ways of selecting two numbers $a$ and $b, a \in\{2,4,6, \ldots ., 100\}$ and $b \in\{1,3,5, \ldots . ., 99

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Let $S$ be the set of all values of $a_1$ for which the mean deviation about the mean of 100 consecutive positive intege

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If a plane passes through the points $(-1, k, 0),(2, k,-1),(1,1,2)$ and is parallel to the line $\frac{x-1}{1}=\frac{2 y

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$\lim\limits_{n \rightarrow \infty} \frac{3}{n}\left\{4+\left(2+\frac{1}{n}\right)^2+\left(2+\frac{2}{n}\right)^2+\ldots

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Consider the following statements:
P : I have fever
Q: I will not take medicine
$\mathrm{R}$ : I will take rest.
The sta

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Let $a, b, c>1, a^3, b^3$ and $c^3$ be in A.P., and $\log _a b, \log _c a$ and $\log _b c$ be in G.P. If the sum of firs

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Let $f, g$ and $h$ be the real valued functions defined on $\mathbb{R}$ as
$f(x)=\left\{\begin{array}{cc}\frac{x}{|x|},

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Let $q$ be the maximum integral value of $p$ in $[0,10]$ for which the roots of the equation $x^2-p x+\frac{5}{4} p=0$ a

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Let $A$ be a point on the $x$-axis. Common tangents are drawn from $A$ to the curves $x^2+y^2=8$ and $y^2=16 x$. If one

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If the functions $f(x)=\frac{x^3}{3}+2 b x+\frac{a x^2}{2}$
and $g(x)=\frac{x^3}{3}+a x+b x^2, a \neq 2 b$ have a commo

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Let $\lambda \in \mathbb{R}, \vec{a}=\lambda \hat{i}+2 \hat{j}-3 \hat{k}, \vec{b}=\hat{i}-\lambda \hat{j}+2 \hat{k}$.
If

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If $P$ is a $3 \times 3$ real matrix such that $P^T=a P+(a-1) I$, where $a>1$, then :

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The parabolas : $a x^2+2 b x+c y=0$ and $d x^2+2 e x+f y=0$ intersect on the line $y=1$. If $a, b, c, d, e, f$ are posit

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Let $\vec{a}$ and $\vec{b}$ be two vectors, Let $|\vec{a}|=1,|\vec{b}|=4$ and $\vec{a} \cdot \vec{b}=2$. If $\vec{c}=(2

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The range of the function $f(x)=\sqrt{3-x}+\sqrt{2+x}$ is :

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The solution of the differential equation
$\frac{d y}{d x}=-\left(\frac{x^2+3 y^2}{3 x^2+y^2}\right), y(1)=0$ is :

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Let $x=(8 \sqrt{3}+13)^{13}$ and $y=(7 \sqrt{2}+9)^9$. If $[t]$ denotes the greatest integer $\leq t$, then :

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Let $A=\{1,2,3,5,8,9\}$. Then the number of possible functions $f: A \rightarrow A$ such that $f(m \cdot n)=f(m) \cdot f

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The $8^{\text {th }}$ common term of the series
$$
\begin{aligned}
& S_1=3+7+11+15+19+\ldots . . \\\\
& S_2=1+6+11+16+21

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The number of seven digits odd numbers, that can
be formed using all theseven digits 1, 2, 2, 2, 3, 3,
5 is ____________

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Let $A$ be the area of the region
$\left\{(x, y): y \geq x^2, y \geq(1-x)^2, y \leq 2 x(1-x)\right\}$.
Then $540 \mathrm

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If the value of real number $a>0$ for which $x^2-5 a x+1=0$ and $x^2-a x-5=0$
have a common real root is $\frac{3}{\sqrt

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Let $P\left(a_1, b_1\right)$ and $Q\left(a_2, b_2\right)$ be two distinct points on a circle with center $C(\sqrt{2}, \s

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Let a line $L$ pass through the point $P(2,3,1)$ and be parallel to the line $x+3 y-2 z-2=0=x-y+2 z$. If the distance of

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A bag contains six balls of different colours. Two balls are drawn in succession with replacement. The probability that

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If $\int \sqrt{\sec 2 x-1} d x=\alpha \log _e\left|\cos 2 x+\beta+\sqrt{\cos 2 x\left(1+\cos \frac{1}{\beta} x\right)}\r

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$50^{\text {th }}$ root of a number $x$ is 12 and $50^{\text {th }}$ root of another number $y$ is 18 . Then the remaind

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## Physics

A vehicle travels $4 \mathrm{~km}$ with speed of $3 \mathrm{~km} / \mathrm{h}$ and another $4 \mathrm{~km}$ with speed o

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Match List I with List II:
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An object is allowed to fall from a height $R$ above the earth, where $R$ is the radius of earth. Its velocity when it s

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A force is applied to a steel wire 'A', rigidly clamped at one end. As a result elongation in the wire is $0.2 \mathrm{~

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An electron accelerated through a potential difference $V_{1}$ has a de-Broglie wavelength of $\lambda$. When the potent

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A machine gun of mass $10 \mathrm{~kg}$ fires $20 \mathrm{~g}$ bullets at the rate of 180 bullets per minute with a spee

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The equivalent resistance between $A$ and $B$ is _________.

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Match List I with List II:
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In the given circuit, rms value of current $\left(I_{\mathrm{rms}}\right)$ through the resistor $R$ is:

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A thin prism $P_1$ with an angle $6^{\circ}$ and made of glass of refractive index $1.54$ is combined with another prism

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Given below are two statements: one is labelled as Assertion $\mathbf{A}$ and the other is labelled as Reason $\mathbf{R

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A point source of $100 \mathrm{~W}$ emits light with $5 \%$ efficiency. At a distance of $5 \mathrm{~m}$ from the source

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Given below are two statements: one is labelled as Assertion $\mathbf{A}$ and the other is labelled as Reason $\mathbf{R

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A block of $\sqrt{3} \mathrm{~kg}$ is attached to a string whose other end is attached to the wall. An unknown force $\m

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As shown in the figure, a point charge $Q$ is placed at the centre of conducting spherical shell of inner radius $a$ and

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A flask contains hydrogen and oxygen in the ratio of $2: 1$ by mass at temperature $27^{\circ} \mathrm{C}$. The ratio of

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As shown in the figure, a current of $2 \mathrm{~A}$ flowing in an equilateral triangle of side $4 \sqrt{3} \mathrm{~cm}

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The output $Y$ for the inputs $A$ and $B$ of circuit is given by
Truth table of the shown circuit is:

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A current carrying rectangular loop PQRS is made of uniform wire. The length $P R=Q S=5 \mathrm{~cm}$ and $P Q=R S=100 \

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For a simple harmonic motion in a mass spring system shown, the surface is frictionless. When the mass of the block is $

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In an ac generator, a rectangular coil of 100 turns each having area $14 \times 10^{-2} \mathrm{~m}^{2}$ is rotated at $

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A faulty thermometer reads $5^{\circ} \mathrm{C}$ in melting ice and $95^{\circ} \mathrm{C}$ in stream. The correct temp

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In a Young's double slit experiment, the intensities at two points, for the path differences $\frac{\lambda}{4}$ and $\f

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If the potential difference between $\mathrm{B}$ and $\mathrm{D}$ is zero, the value of $x$ is $\frac{1}{n} \Omega$. The

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A uniform disc of mass $0.5 \mathrm{~kg}$ and radius $r$ is projected with velocity $18 \mathrm{~m} / \mathrm{s}$ at $\m

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The velocity of a particle executing SHM varies with displacement $(x)$ as $4 v^{2}=50-x^{2}$. The time period of oscill

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A body of mass $2 \mathrm{~kg}$ is initially at rest. It starts moving unidirectionally under the influence of a source

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A radioactive nucleus decays by two different process. The half life of the first process is 5 minutes and that of the s

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As shown in figure, a cuboid lies in a region with electric field $E=2 x^{2} \hat{i}-4 y \hat{j}+6 \hat{k} \mathrm{~N} /

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A stone tied to $180 \mathrm{~cm}$ long string at its end is making 28 revolutions in horizontal circle in every minute.

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