JEE Main 2023 (Online) 1st February Morning Shift

Paper was held on
Wed, Feb 1, 2023 3:30 AM

## Chemistry

How can photochemical smog be controlled?

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Which of the following complex will show largest splitting of d-orbitals?

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Which of the following are the example of double salt?
A. $$\mathrm{FeSO}_{4} \cdot\left(\mathrm{NH}_{4}\right)_{2} \mat

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Match List I with List II :
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Match List I with List II
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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: In an

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Highest oxidation state of Mn is exhibited in $$\mathrm{Mn_2O_7}$$. The correct statements about $$\mathrm{Mn_2O_7}$$ ar

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The correct representation in six membered pyranose form for the following sugar [X] is

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But-2-yne is reacted separately with one mole of Hydrogen as shown below :
A. A is more soluble than B.
B. The boiling

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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: Hydrog

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Resonance in carbonate ion $$\left(\mathrm{CO}_{3}{ }^{2-}\right)$$ is
Which of the following is true?

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Which of the following represents the lattice structure of $$\mathrm{A_{0.95}O}$$ containing $$\mathrm{A^{2+},A^{3+}}$$

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Choose the correct statement(s) :
A. Beryllium oxide is purely acidic in nature.
B. Beryllium carbonate is kept in the a

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Match List I with List II
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In the following reaction, 'A' is

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A solution of $$\mathrm{FeCl_3}$$ when treated with $$\mathrm{K_4[Fe(CN)_6]}$$ gives a prussium blue precipitate due to

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Identify the incorrect option from the following

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Given below are two statements:
Statement I: Chlorine can easily combine with oxygen to form oxides; and the product has

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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: Amongs

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Decreasing order of dehydration of the following alcohols is

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25 mL of an aqueous solution of KCl was found to require 20 mL of 1 M $$\mathrm{AgNO_3}$$ solution when titrated using $

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Electrons in a cathode ray tube have been emitted with a velocity of 1000 m s$$^{-1}$$. The number of following statemen

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At what pH, given half cell $$\mathrm{MnO_{4}^{-}(0.1~M)~|~Mn^{2+}(0.001~M)}$$ will have electrode potential of 1.282 V?

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A and B are two substances undergoing radioactive decay in a container. The half life of A is 15 min and that of B is 5

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At $$25^{\circ} \mathrm{C}$$, the enthalpy of the following processes are given :
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Sum of oxidation states of bromine in bromic acid and perbromic acid is ___________.

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Number of isomeric compounds with molecular formula $$\mathrm{C}_{9} \mathrm{H}_{10} \mathrm{O}$$ which (i) do not disso

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The total number of chiral compound/s from the following is ______________.

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(i) $$\mathrm{X}(\mathrm{g}) \rightleftharpoons \mathrm{Y}(\mathrm{g})+\mathrm{Z}(\mathrm{g}) \quad \mathrm{K}_{\mathrm{

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The density of $$3 \mathrm{M}$$ solution of $$\mathrm{NaCl}$$ is $$1.0 \mathrm{~g} \mathrm{~mL}^{-1}$$. Molality of the

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## Mathematics

The value of $$\frac{1}{1 ! 50 !}+\frac{1}{3 ! 48 !}+\frac{1}{5 ! 46 !}+\ldots .+\frac{1}{49 ! 2 !}+\frac{1}{51 ! 1 !}$$

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$$\mathop {\lim }\limits_{n \to \infty } \left[ {{1 \over {1 + n}} + {1 \over {2 + n}} + {1 \over {3 + n}}\, + \,...\, +

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Let $$S$$ be the set of all solutions of the equation $$\cos ^{-1}(2 x)-2 \cos ^{-1}\left(\sqrt{1-x^{2}}\right)=\pi, x \

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The sum of 10 terms of the series
$${1 \over {1 + {1^2} + {1^4}}} + {2 \over {1 + {2^2} + {2^4}}} + {3 \over {1 + {3^2}

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Let $$R$$ be a relation on $$1\mathbb{R}$$, given by $$R=\{(a, b): 3 a-3 b+\sqrt{7}$$ is an irrational number $$\}$$. Th

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The shortest distance between the lines $${{x - 5} \over 1} = {{y - 2} \over 2} = {{z - 4} \over { - 3}}$$ and $${{x + 3

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Let $$S$$ denote the set of all real values of $$\lambda$$ such that the system of equations
$$\lambda x+y+z=1$$
$$x+\la

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The combined equation of the two lines $$ax+by+c=0$$ and $$a'x+b'y+c'=0$$ can be written as
$$(ax+by+c)(a'x+b'y+c')=0$$

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In a binomial distribution $$B(n,p)$$, the sum and the product of the mean and the variance are 5 and 6 respectively, th

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Let $$S = \left\{ {x:x \in \mathbb{R}\,\mathrm{and}\,{{(\sqrt 3 + \sqrt 2 )}^{{x^2} - 4}} + {{(\sqrt 3 - \sqrt 2 )}^{{

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If the center and radius of the circle $$\left| {{{z - 2} \over {z - 3}}} \right| = 2$$ are respectively $$(\alpha,\beta

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The mean and variance of 5 observations are 5 and 8 respectively. If 3 observations are 1, 3, 5, then the sum of cubes o

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Let $$f(x) = 2x + {\tan ^{ - 1}}x$$ and $$g(x) = {\log _e}(\sqrt {1 + {x^2}} + x),x \in [0,3]$$. Then

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The negation of the expression $$q \vee \left( {( \sim \,q) \wedge p} \right)$$ is equivalent to

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For a triangle $$ABC$$, the value of $$\cos 2A + \cos 2B + \cos 2C$$ is least. If its inradius is 3 and incentre is M, t

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Let $$f(x) = \left| {\matrix{
{1 + {{\sin }^2}x} & {{{\cos }^2}x} & {\sin 2x} \cr
{{{\sin }^2}x} & {1 + {{\cos }

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The area enclosed by the closed curve $$\mathrm{C}$$ given by the differential equation $$\frac{d y}{d x}+\frac{x+a}{y-2

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Let the image of the point $$P(2,-1,3)$$ in the plane $$x+2 y-z=0$$ be $$Q$$. Then the distance of the plane $$3 x+2 y+z

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If the orthocentre of the triangle, whose vertices are (1, 2), (2, 3) and (3, 1) is $$(\alpha,\beta)$$, then the quadrat

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If $$y=y(x)$$ is the solution curve of the differential equation $$\frac{d y}{d x}+y \tan x=x \sec x, 0 \leq x \leq \fra

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If $$\int_\limits{0}^{1}\left(x^{21}+x^{14}+x^{7}\right)\left(2 x^{14}+3 x^{7}+6\right)^{1 / 7} d x=\frac{1}{l}(11)^{m /

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Let $$a_{1}=8, a_{2}, a_{3}, \ldots, a_{n}$$ be an A.P. If the sum of its first four terms is 50 and the sum of its last

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Let $$f: \mathbb{R} \rightarrow \mathbb{R}$$ be a differentiable function such that $$f^{\prime}(x)+f(x)=\int_\limits{0}

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The remainder, when $$19^{200}+23^{200}$$ is divided by 49 , is ___________.

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The number of 3-digit numbers, that are divisible by either 2 or 3 but not divisible by 7, is ____________.

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The number of words, with or without meaning, that can be formed using all the letters of the word ASSASSINATION so that

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Let $$\vec{v}=\alpha \hat{i}+2 \hat{j}-3 \hat{k}, \vec{w}=2 \alpha \hat{i}+\hat{j}-\hat{k}$$ and $$\vec{u}$$ be a vector

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Let $$A$$ be the area bounded by the curve $$y=x|x-3|$$, the $$x$$-axis and the ordinates $$x=-1$$ and $$x=2$$. Then $$1

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$$A(2,6,2), B(-4,0, \lambda), C(2,3,-1)$$ and $$D(4,5,0),|\lambda| \leq 5$$ are the vertices of a quadrilateral $$A B C

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If $$f(x)=x^{2}+g^{\prime}(1) x+g^{\prime \prime}(2)$$ and $$g(x)=f(1) x^{2}+x f^{\prime}(x)+f^{\prime \prime}(x)$$, the

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## Physics

Let $$\sigma$$ be the uniform surface charge density of two infinite thin plane sheets shown in figure. Then the electri

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'$$n$$' polarizing sheets are arranged such that each makes an angle $$45^{\circ}$$ with the preceeding sheet. An unpola

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Match List - I with List - II :
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Match List I with List II:
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Find the magnetic field at the point $$\mathrm{P}$$ in figure. The curved portion is a semicircle connected to two long

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Which of the following frequencies does not belong to FM broadcast.

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The equivalent resistance between $$A$$ and $$B$$ of the network shown in figure;

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If earth has a mass nine times and radius twice to that of a planet P. Then $$\frac{v_{e}}{3} \sqrt{x} \mathrm{~ms}^{-1}

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A steel wire with mass per unit length $$7.0 \times 10^{-3} \mathrm{~kg} \mathrm{~m}^{-1}$$ is under tension of $$70 \ma

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An object moves with speed $$v_1,v_2$$ and $$v_3$$ along a line segment AB, BC and CD respectively as shown in figure. W

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A child stands on the edge of the cliff $$10 \mathrm{~m}$$ above the ground and throws a stone horizontally with an init

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A proton moving with one tenth of velocity of light has a certain de Broglie wavelength of $$\lambda$$. An alpha particl

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Given below are two statements:
Statement I: Acceleration due to gravity is different at different places on the surface

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A sample of gas at temperature $$T$$ is adiabatically expanded to double its volume. The work done by the gas in the pro

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A block of mass $$5 \mathrm{~kg}$$ is placed at rest on a table of rough surface. Now, if a force of $$30 \mathrm{~N}$$

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Match List I with List II :
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The mass of proton, neutron and helium nucleus are respectively $$1.0073~u,1.0087~u$$ and $$4.0015~u$$. The binding ener

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$$\left(P+\frac{a}{V^{2}}\right)(V-b)=R T$$ represents the equation of state of some gases. Where $$P$$ is the pressure,

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The average kinetic energy of a molecule of the gas is

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A mercury drop of radius $$10^{-3}~\mathrm{m}$$ is broken into 125 equal size droplets. Surface tension of mercury is $$

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Two equal positive point charges are separated by a distance $$2 a$$. The distance of a point from the centre of the lin

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In an experiment to find emf of a cell using potentiometer, the length of null point for a cell of emf $$1.5 \mathrm{~V}

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A charge particle of $$2 ~\mu \mathrm{C}$$ accelerated by a potential difference of $$100 \mathrm{~V}$$ enters a region

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A light of energy $$12.75 ~\mathrm{eV}$$ is incident on a hydrogen atom in its ground state. The atom absorbs the radiat

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A thin cylindrical rod of length $$10 \mathrm{~cm}$$ is placed horizontally on the principle axis of a concave mirror of

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A small particle moves to position $$5 \hat{i}-2 \hat{j}+\hat{k}$$ from its initial position $$2 \hat{i}+3 \hat{j}-4 \ha

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A series LCR circuit is connected to an ac source of $$220 \mathrm{~V}, 50 \mathrm{~Hz}$$. The circuit contain a resista

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A solid cylinder is released from rest from the top of an inclined plane of inclination $$30^{\circ}$$ and length $$60 \

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The amplitude of a particle executing SHM is $$3 \mathrm{~cm}$$. The displacement at which its kinetic energy will be $$

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A certain pressure '$$\mathrm{P}$$' is applied to 1 litre of water and 2 litre of a liquid separately. Water gets compre

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