JEE Main 2022 (Online) 27th July Morning Shift

Paper was held on
Wed, Jul 27, 2022 3:30 AM

## Chemistry

$$250 \mathrm{~g}$$ solution of $$\mathrm{D}$$-glucose in water contains $$10.8 \%$$ of carbon by weight. The molality o

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Given below are two statements.
Statement I: $$\mathrm{O}_{2}, \mathrm{Cu}^{2+}$$, and $$\mathrm{Fe}^{3+}$$ are weakly a

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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: Energ

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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 : Acti

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Boiling point of a $$2 \%$$ aqueous solution of a non-volatile solute A is equal to the boiling point of $$8 \%$$ aqueou

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The incorrect statement is

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Which of the following methods are not used to refine any metal?
A. Liquation
B. Calcination
C. Electrolysis
D. Leaching

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Given below are two statements.
Statement I: Hydrogen peroxide can act as an oxidizing agent in both acidic and basic co

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Given below are two statements.
Statement I: The chlorides of $$\mathrm{Be}$$ and $$\mathrm{Al}$$ have Cl-bridged struct

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Which oxoacid of phosphorous has the highest number of oxygen atoms present in its chemical formula?

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Given below are two statements.
Statement I: Iron (III) catalyst, acidified $$\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_

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The total number of $$\mathrm{Mn}=\mathrm{O}$$ bonds in $$\mathrm{Mn}_{2} \mathrm{O}_{7}$$ is __________.

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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: [6]

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In the above reaction product B is :

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Match List I with List II.
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A sugar 'X' dehydrates very slowly under acidic condition to give furfural which on further reaction with resorcinol giv

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Match List I with List II.
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In Carius method of estimation of halogen, $$0.45 \mathrm{~g}$$ of an organic compound gave $$0.36 \mathrm{~g}$$ of $$\m

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$$20 \mathrm{~mL}$$ of $$0.02 \,\mathrm{M} \,\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}$$ solution is used for the ti

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$$2 \mathrm{NO}+2 \mathrm{H}_{2} \rightarrow \mathrm{N}_{2}+2 \mathrm{H}_{2} \mathrm{O}$$
The above reaction has been st

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Amongst the following, the number of oxide(s) which are paramagnetic in nature is
$$\mathrm{Na}_{2} \mathrm{O}, \mathrm{

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The molar heat capacity for an ideal gas at constant pressure is $$20.785 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1

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According to MO theory, number of species/ions from the following having identical bond order is ________.
$$\mathrm{CN}

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At $$310 \mathrm{~K}$$, the solubility of $$\mathrm{CaF}_{2}$$ in water is $$2.34 \times 10^{-3} \mathrm{~g} / 100 \math

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The conductivity of a solution of complex with formula $$\mathrm{CoCl}_{3}\left(\mathrm{NH}_{3}\right)_{4}$$ corresponds

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In the titration of $$\mathrm{KMnO}_{4}$$ and oxalic acid in acidic medium, the change in oxidation number of carbon at

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Optical activity of an enantiomeric mixture is $$+12.6^{\circ}$$ and the specific rotation of $$(+)$$ isomer is $$+30^{\

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In the following reaction
The $$\%$$ yield for reaction I is $$60 \%$$ and that of reaction II is $$50 \%$$. The overal

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## Mathematics

Let $$R_{1}$$ and $$R_{2}$$ be two relations defined on $$\mathbb{R}$$ by
$$a \,R_{1} \,b \Leftrightarrow a b \geq 0$$ a

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Let $$f, g: \mathbb{N}-\{1\} \rightarrow \mathbb{N}$$ be functions defined by $$f(a)=\alpha$$, where $$\alpha$$ is the m

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Let the minimum value $$v_{0}$$ of $$v=|z|^{2}+|z-3|^{2}+|z-6 i|^{2}, z \in \mathbb{C}$$ is attained at $${ }{z}=z_{0}$

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Let $$A=\left(\begin{array}{cc}1 & 2 \\ -2 & -5\end{array}\right)$$. Let $$\alpha, \beta \in \mathbb{R}$$ be such that $

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The remainder when $$(2021)^{2022}+(2022)^{2021}$$ is divided by 7 is

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Suppose $$a_{1}, a_{2}, \ldots, a_{n}$$, .. be an arithmetic progression of natural numbers. If the ratio of the sum of

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Let $$f: \mathbb{R} \rightarrow \mathbb{R}$$ be a function defined as
$$f(x)=a \sin \left(\frac{\pi[x]}{2}\right)+[2-x],

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Let $$
I=\int_{\pi / 4}^{\pi / 3}\left(\frac{8 \sin x-\sin 2 x}{x}\right) d x
$$. Then

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The area of the smaller region enclosed by the curves $$y^{2}=8 x+4$$ and $$x^{2}+y^{2}+4 \sqrt{3} x-4=0$$ is equal to

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Let $$y=y_{1}(x)$$ and $$y=y_{2}(x)$$ be two distinct solutions of the differential equation $$\frac{d y}{d x}=x+y$$, wi

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Let $$P(a, b)$$ be a point on the parabola $$y^{2}=8 x$$ such that the tangent at $$P$$ passes through the centre of the

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Let $$\vec{a}=\alpha \hat{i}+\hat{j}+\beta \hat{k}$$ and $$\vec{b}=3 \hat{i}-5 \hat{j}+4 \hat{k}$$ be two vectors, such

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$$
\text { Let } \vec{a}=2 \hat{i}-\hat{j}+5 \hat{k} \text { and } \vec{b}=\alpha \hat{i}+\beta \hat{j}+2 \hat{k} \text

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Let $$S$$ be the sample space of all five digit numbers. It $$p$$ is the probability that a randomly selected number fro

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Let a vertical tower $$A B$$ of height $$2 h$$ stands on a horizontal ground. Let from a point $$P%$$ on the ground a ma

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$$(p \wedge r) \Leftrightarrow(p \wedge(\sim q))$$ is equivalent to $$(\sim p)$$ when $$r$$ is

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If the plane $$P$$ passes through the intersection of two mutually perpendicular planes $$2 x+k y-5 z=1$$ and $$3 k x-k

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Let $$A(1,1), B(-4,3), C(-2,-5)$$ be vertices of a triangle $$A B C, P$$ be a point on side $$B C$$, and $$\Delta_{1}$$

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If the circle $$x^{2}+y^{2}-2 g x+6 y-19 c=0, g, c \in \mathbb{R}$$ passes through the point $$(6,1)$$ and its centre li

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Let a function $$f: \mathbb{R} \rightarrow \mathbb{R}$$ be defined as :
$$f(x)= \begin{cases}\int\limits_{0}^{x}(5-|t-3|

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For $$k \in \mathbb{R}$$, let the solutions of the equation $$\cos \left(\sin ^{-1}\left(x \cot \left(\tan ^{-1}\left(\c

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The mean and variance of 10 observations were calculated as 15 and 15 respectively by a student who took by mistake 25 i

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Let the line $$\frac{x-3}{7}=\frac{y-2}{-1}=\frac{z-3}{-4}$$ intersect the plane containing the lines $$\frac{x-4}{1}=\f

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An ellipse $$E: \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$$ passes through the vertices of the hyperbola $$H: \frac{x^{

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Let $$y=y(x)$$ be the solution curve of the differential equation
$$\sin \left( {2{x^2}} \right){\log _e}\left( {\tan {x

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Let $$M$$ and $$N$$ be the number of points on the curve $$y^{5}-9 x y+2 x=0$$, where the tangents to the curve are para

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Let $$f(x)=2 x^{2}-x-1$$ and $$\mathrm{S}=\{n \in \mathbb{Z}:|f(n)| \leq 800\}$$. Then, the value of $$\sum\limits_{n \

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Let $$S$$ be the set containing all $$3 \times 3$$ matrices with entries from $$\{-1,0,1\}$$. The total number of matric

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If the length of the latus rectum of the ellipse $$x^{2}+4 y^{2}+2 x+8 y-\lambda=0$$ is 4 , and $$l$$ is the length of i

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Let $$S=\left\{z \in \mathbb{C}: z^{2}+\bar{z}=0\right\}$$. Then $$\sum\limits_{z \in S}(\operatorname{Re}(z)+\operatorn

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## Physics

A torque meter is calibrated to reference standards of mass, length and time each with $$5 \%$$ accuracy. After calibrat

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A bullet is shot vertically downwards with an initial velocity of $$100 \mathrm{~m} / \mathrm{s}$$ from a certain height

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Sand is being dropped from a stationary dropper at a rate of $$0.5 \,\mathrm{kgs}^{-1}$$ on a conveyor belt moving with

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A bag is gently dropped on a conveyor belt moving at a speed of $$2 \mathrm{~m} / \mathrm{s}$$. The coefficient of frict

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Two cylindrical vessels of equal cross-sectional area $$16 \mathrm{~cm}^{2}$$ contain water upto heights $$100 \mathrm{~

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Two satellites $$\mathrm{A}$$ and $$\mathrm{B}$$, having masses in the ratio $$4: 3$$, are revolving in circular orbits

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If $$K_{1}$$ and $$K_{2}$$ are the thermal conductivities, $$L_{1}$$ and $$L_{2}$$ are the lengths and $$A_{1}$$ and $$A

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Read the following statements :
A. When small temperature difference between a liquid and its surrounding is doubled, th

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Same gas is filled in two vessels of the same volume at the same temperature. If the ratio of the number of molecules is

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Two identical positive charges $$Q$$ each are fixed at a distance of '2a' apart from each other. Another point charge $$

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Two sources of equal emfs are connected in series. This combination is connected to an external resistance R. The intern

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Two bar magnets oscillate in a horizontal plane in earth's magnetic field with time periods of $$3 \mathrm{~s}$$ and $$4

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A magnet hung at $$45^{\circ}$$ with magnetic meridian makes an angle of $$60^{\circ}$$ with the horizontal. The actual

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A direct current of $$4 \mathrm{~A}$$ and an alternating current of peak value $$4 \mathrm{~A}$$ flow through resistance

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A beam of light travelling along $$X$$-axis is described by the electric field $$E_{y}=900 \sin \omega(\mathrm{t}-x / c)

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A microscope was initially placed in air (refractive index 1). It is then immersed in oil (refractive index 2). For a li

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An electron (mass $$\mathrm{m}$$) with an initial velocity $$\vec{v}=v_{0} i\left(v_{0}>0\right)$$ is moving in an elect

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What is the half-life period of a radioactive material if its activity drops to $$1 / 16^{\text {th }}$$ of its initial

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A logic gate circuit has two inputs A and B and output Y. The voltage waveforms of A, B and Y are shown below.
The logi

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At a particular station, the TV transmission tower has a height of 100 m. To triple its coverage range, height of the to

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In a meter bridge experiment, for measuring unknown resistance 'S', the null point is obtained at a distance $$30 \mathr

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The one division of main scale of Vernier callipers reads $$1 \mathrm{~mm}$$ and 10 divisions of Vernier scale is equal

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Two beams of light having intensities I and 4I interfere to produce a fringe pattern on a screen. The phase difference b

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To light, a $$50 \mathrm{~W}, 100 \mathrm{~V}$$ lamp is connected, in series with a capacitor of capacitance $$\frac{50}

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A $$1 \mathrm{~m}$$ long copper wire carries a current of $$1 \mathrm{~A}$$. If the cross section of the wire is $$2.0 \

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A long cylindrical volume contains a uniformly distributed charge of density $$\rho \,\mathrm{Cm}^{-3}$$. The electric f

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A mass $$0.9 \mathrm{~kg}$$, attached to a horizontal spring, executes SHM with an amplitude $$\mathrm{A}_{1}$$. When th

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A square aluminum (shear modulus is $$25 \times 10^{9}\, \mathrm{Nm}^{-2}$$) slab of side $$60 \mathrm{~cm}$$ and thickn

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A pulley of radius $$1.5 \mathrm{~m}$$ is rotated about its axis by a force $$F=\left(12 \mathrm{t}-3 \mathrm{t}^{2}\rig

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A ball of mass m is thrown vertically upward. Another ball of mass $$2 \mathrm{~m}$$ is thrown at an angle $$\theta$$ wi

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