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

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

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

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

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

View Question The incorrect statement is

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

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

View Question Given below are two statements: one is labelled as Assertion A and, the other is labelled as Reason R.
Assertion A: [6]

View Question
In the above reaction product B is :

View Question A sugar 'X' dehydrates very slowly under acidic condition to give furfural which on further reaction with resorcinol giv

View Question In Carius method of estimation of halogen, $$0.45 \mathrm{~g}$$ of an organic compound gave $$0.36 \mathrm{~g}$$ of $$\m

View Question Match List I with List II.
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View Question $$20 \mathrm{~mL}$$ of $$0.02 \,\mathrm{M} \,\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}$$ solution is used for the ti

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

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

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

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

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

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

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

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

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

View Question ## 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

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

View Question 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}$

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

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

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

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

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

View Question 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

View Question 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

View Question 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

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

View Question 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 $$\Delta_{1}$$

View Question 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

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

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

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

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

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

View Question 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 \

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

View Question 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

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

View Question ## Physics

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

View Question 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

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

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

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

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

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

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

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

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

View Question 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

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

View Question