JEE Main 2022 (Online) 29th July Evening Shift

Paper was held on
Fri, Jul 29, 2022 9:30 AM

## Chemistry

Consider the reaction
$$4 \mathrm{HNO}_{3}(1)+3 \mathrm{KCl}(\mathrm{s}) \rightarrow \mathrm{Cl}_{2}(\mathrm{~g})+\mathr

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Given below are the quantum numbers for 4 electrons.
A. $$\mathrm{n}=3,l=2, \mathrm{~m}_{1}=1, \mathrm{~m}_{\mathrm{s}}=

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$$
\begin{aligned}
&\mathrm{C}(\mathrm{s})+\mathrm{O}_{2}(\mathrm{~g}) \rightarrow \mathrm{CO}_{2}(\mathrm{~g})+400 \mat

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$$200 \mathrm{~mL}$$ of $$0.01 \,\mathrm{M} \,\mathrm{HCl}$$ is mixed with $$400 \mathrm{~mL}$$ of $$0.01 \,\mathrm{M} \

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Given below are the critical temperatures of some of the gases:
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.tg t

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In liquation process used for tin (Sn), the metal

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Given below are two statements.
Statement I : Stannane is an example of a molecular hydride.
Statement II : Stannane is

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Portland cement contains 'X' to enhance the setting time. What is 'X' ?

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When borax is heated with $$\mathrm{CoO}$$ on a platinum loop, blue coloured bead formed is largely due to

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Which of the following $$3\mathrm{d}$$-metal ion will give the lowest enthalpy of hydration $$\left(\Delta_{\text {hyd }

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Octahedral complexes of copper(II) undergo structural distortion (Jahn-Teller). Which one of the given copper (II) compl

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Dinitrogen is a robust compound, but reacts at high altitudes to form oxides. The oxide of nitrogen that can damage plan

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Correct structure of $$\gamma$$-methylcyclohexane carbaldehyde is

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Compound 'A' undergoes following sequence of reactions to give compound 'B'.
The correct structure and chirality of comp

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Given below are two statements.
Statement I : The compound is optically active.
Statement II : is mirror image of abov

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When enthanol is heated with conc. $$\mathrm{H}_{2} \mathrm{SO}_{4}$$, a gas is produced. The compound formed, when this

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The Hinsberg reagent is

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Which of the following is NOT a natural polymer?

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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: Amylo

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A compound 'X' is a weak acid and it exhibits colour change at pH close to the equivalence point during neutralization o

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'x' g of molecular oxygen $$\left(\mathrm{O}_{2}\right)$$ is mixed with $$200 \mathrm{~g}$$ of neon (Ne). The total pres

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Consider, $$\mathrm{PF}_{5}, \mathrm{BrF}_{5}, \mathrm{PCl}_{3}, \mathrm{SF}_{6},\left[\mathrm{ICl}_{4}\right]^{-}, \mat

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$$1.80 \mathrm{~g}$$ of solute A was dissolved in $$62.5 \mathrm{~cm}^{3}$$ of ethanol and freezing point of the solutio

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For a cell, $$\mathrm{Cu}(\mathrm{s})\left|\mathrm{Cu}^{2+}(0.001 \,\mathrm{M}) \| \mathrm{Ag}^{+}(0.01 \,\mathrm{M})\ri

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Assuming $$1 \,\mu \mathrm{g}$$ of trace radioactive element X with a half life of 30 years is absorbed by a growing tre

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Sum of oxidation state (magnitude) and coordination number of cobalt in $$\mathrm{Na}\left[\mathrm{Co}(\mathrm{bpy}) \ma

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Consider the following sulphur based oxoacids.
$$\mathrm{H}_{2} \mathrm{SO}_{3}, \mathrm{H}_{2} \mathrm{SO}_{4}, \mathrm

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A 1.84 mg sample of polyhydric alcoholic compound 'X' of molar mass 92.0 g/mol gave 1.344 mL of $$\mathrm{H}_{2}$$ gas a

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The number of stereoisomers formed in a reaction of $$(±)\mathrm{Ph}(\mathrm{C}=\mathrm{O}) \mathrm{C}(\mathrm{OH})(\mat

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The number of chlorine atoms in bithionol is __________.

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## Mathematics

If $$z \neq 0$$ be a complex number such that $$\left|z-\frac{1}{z}\right|=2$$, then the maximum value of $$|z|$$ is :

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Which of the following matrices can NOT be obtained from the matrix $$\left[\begin{array}{cc}-1 & 2 \\ 1 & -1\end{array}

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If the system of equations
$$
\begin{aligned}
&x+y+z=6 \\
&2 x+5 y+\alpha z=\beta \\
&x+2 y+3 z=14
\end{aligned}
$$
has

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$$
\text { Let the function } f(x)=\left\{\begin{array}{cl}
\frac{\log _{e}(1+5 x)-\log _{e}(1+\alpha x)}{x} & ;\text {

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If $$[t]$$ denotes the greatest integer $$\leq t$$, then the value of $$\int_{0}^{1}\left[2 x-\left|3 x^{2}-5 x+2\right|

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$$
\begin{aligned}
&\text { Let }\left\{a_{n}\right\}_{n=0}^{\infty} \text { be a sequence such that } a_{0}=a_{1}=0 \te

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$$\sum\limits_{r=1}^{20}\left(r^{2}+1\right)(r !)$$ is equal to

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For $$I(x)=\int \frac{\sec ^{2} x-2022}{\sin ^{2022} x} d x$$, if $$I\left(\frac{\pi}{4}\right)=2^{1011}$$, then

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If the solution curve of the differential equation $$\frac{d y}{d x}=\frac{x+y-2}{x-y}$$ passes through the points $$(2,

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Let $$y=y(x)$$ be the solution curve of the differential equation $$ \frac{d y}{d x}+\left(\frac{2 x^{2}+11 x+13}{x^{3}+

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Let $$m_{1}, m_{2}$$ be the slopes of two adjacent sides of a square of side a such that $$a^{2}+11 a+3\left(m_{1}^{2}+m

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The number of elements in the set $$S=\left\{x \in \mathbb{R}: 2 \cos \left(\frac{x^{2}+x}{6}\right)=4^{x}+4^{-x}\right\

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Let $$\mathrm{A}(\alpha,-2), \mathrm{B}(\alpha, 6)$$ and $$\mathrm{C}\left(\frac{\alpha}{4},-2\right)$$ be vertices of a

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Let $$Q$$ be the foot of perpendicular drawn from the point $$P(1,2,3)$$ to the plane $$x+2 y+z=14$$. If $$R$$ is a poin

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If $$(2,3,9),(5,2,1),(1, \lambda, 8)$$ and $$(\lambda, 2,3)$$ are coplanar, then the product of all possible values of $

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Bag I contains 3 red, 4 black and 3 white balls and Bag II contains 2 red, 5 black and 2 white balls. One ball is transf

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Let $$\mathrm{S}=\{z=x+i y:|z-1+i| \geq|z|,|z|

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Let $$\vec{a}, \vec{b}, \vec{c}$$ be three coplanar concurrent vectors such that angles between any two of them is same.

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The domain of the function $$f(x)=\sin ^{-1}\left(\frac{x^{2}-3 x+2}{x^{2}+2 x+7}\right)$$ is:

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The statement $$(p \Rightarrow q) \vee(p \Rightarrow r)$$ is NOT equivalent to

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The sum and product of the mean and variance of a binomial distribution are 82.5 and 1350 respectively. Then the number

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Let $$\alpha, \beta(\alpha>\beta)$$ be the roots of the quadratic equation $$x^{2}-x-4=0 .$$ If $$P_{n}=\alpha^{n}-\beta

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Let $$X=\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right]$$ and $$A=\left[\begin{array}{ccc}-1 & 2 & 3 \\ 0 & 1 & 6 \\

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The number of natural numbers lying between 1012 and 23421 that can be formed using the digits $$2,3,4,5,6$$ (repetition

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$$
\text { If } \sum\limits_{k=1}^{10} K^{2}\left(10_{C_{K}}\right)^{2}=22000 L \text {, then } L \text { is equal to }$

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If $$[t]$$ denotes the greatest integer $$\leq t$$, then the number of points, at which the function $$f(x)=4|2 x+3|+9\l

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If the tangent to the curve $$y=x^{3}-x^{2}+x$$ at the point $$(a, b)$$ is also tangent to the curve $$y = 5{x^2} + 2x -

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Let $$A B$$ be a chord of length 12 of the circle $$(x-2)^{2}+(y+1)^{2}=\frac{169}{4}$$. If tangents drawn to the circle

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Let $$\vec{a}$$ and $$\vec{b}$$ be two vectors such that $$|\vec{a}+\vec{b}|^{2}=|\vec{a}|^{2}+2|\vec{b}|^{2}, \vec{a} \

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$$\text { Let } S=\left\{(x, y) \in \mathbb{N} \times \mathbb{N}: 9(x-3)^{2}+16(y-4)^{2} \leq 144\right\}$$ and
$$T=\lef

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## Physics

Two identical metallic spheres $$\mathrm{A}$$ and $$\mathrm{B}$$ when placed at certain distance in air repel each other

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Match List I with List II.
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Two identical thin metal plates has charge $$q_{1}$$ and $$q_{2}$$ respectively such that $$q_{1}>q_{2}$$. The plates we

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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: Alloy

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A $$1 \mathrm{~m}$$ long wire is broken into two unequal parts $$\mathrm{X}$$ and $$\mathrm{Y}$$. The $$\mathrm{X}$$ par

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A wire X of length $$50 \mathrm{~cm}$$ carrying a current of $$2 \mathrm{~A}$$ is placed parallel to a long wire $$\math

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A juggler throws balls vertically upwards with same initial velocity in air. When the first ball reaches its highest pos

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A circuit element $$\mathrm{X}$$ when connected to an a.c. supply of peak voltage $$100 \mathrm{~V}$$ gives a peak curre

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An unpolarised light beam of intensity $$2 I_{0}$$ is passed through a polaroid P and then through another polaroid Q wh

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An $$\alpha$$ particle and a proton are accelerated from rest through the same potential difference. The ratio of linear

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Read the following statements :
(A) Volume of the nucleus is directly proportional to the mass number.
(B) Volume of the

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An object of mass $$1 \mathrm{~kg}$$ is taken to a height from the surface of earth which is equal to three times the ra

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A ball is released from a height h. If $$t_{1}$$ and $$t_{2}$$ be the time required to complete first half and second ha

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Two bodies of masses $$m_{1}=5 \mathrm{~kg}$$ and $$m_{2}=3 \mathrm{~kg}$$ are connected by a light string going over a

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If momentum of a body is increased by 20%, then its kinetic energy increases by

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The torque of a force $$5 \hat{i}+3 \hat{j}-7 \hat{k}$$ about the origin is $$\tau$$. If the force acts on a particle wh

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A thermodynamic system is taken from an original state D to an intermediate state E by the linear process shown in the f

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The vertical component of the earth's magnetic field is $$6 \times 10^{-5} \mathrm{~T}$$ at any place where the angle of

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The root mean square speed of smoke particles of mass $$5 \times 10^{-17} \mathrm{~kg}$$ in their Brownian motion in air

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Light enters from air into a given medium at an angle of $$45^{\circ}$$ with interface of the air-medium surface. After

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A tube of length $$50 \mathrm{~cm}$$ is filled completely with an incompressible liquid of mass $$250 \mathrm{~g}$$ and

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Nearly 10% of the power of a $$110 \mathrm{~W}$$ light bulb is converted to visible radiation. The change in average int

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A metal wire of length $$0.5 \mathrm{~m}$$ and cross-sectional area $$10^{-4} \mathrm{~m}^{2}$$ has breaking stress $$5

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The velocity of a small ball of mass $$0.3 \mathrm{~g}$$ and density $$8 \mathrm{~g} / \mathrm{cc}$$ when dropped in a c

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A modulating signal $$2 \sin \left(6.28 \times 10^{6}\right) t$$ is added to the carrier signal $$4 \sin \left(12.56 \ti

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The speed of a transverse wave passing through a string of length $$50 \mathrm{~cm}$$ and mass $$10 \mathrm{~g}$$ is $$6

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The metallic bob of simple pendulum has the relative density 5. The time period of this pendulum is $$10 \mathrm{~s}$$.

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A $$8 \mathrm{~V}$$ Zener diode along with a series resistance $$\mathrm{R}$$ is connected across a $$20 \mathrm{~V}$$ s

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Two radioactive materials A and B have decay constants $$25 \lambda$$ and $$16 \lambda$$ respectively. If initially they

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A capacitor of capacitance 500 $$\mu$$F is charged completely using a dc supply of 100 V. It is now connected to an indu

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