JEE Main 2022 (Online) 26th June Morning Shift

Paper was held on
Sun, Jun 26, 2022 3:30 AM

## Chemistry

A commercially sold conc. HCl is 35% HCl by mass. If the density of this commercial acid is 1.46 g/mL, the molarity of t

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An evacuated glass vessel weighs 40.0 g when empty, 135.0 g when filled with a liquid of density 0.95 g mL$$-$$1 and 40.

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If the radius of the 3rd Bohr's orbit of hydrogen atom is r3 and the radius of 4th Bohr's orbit is r4. Then :

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Consider the ions/molecule
O$$_2^ + $$, O2, O$$_2^ - $$, O$$_2^ {2-} $$
For increasing bond order the correct option is

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The $${\left( {{{\partial E} \over {\partial T}}} \right)_P}$$ of different types of half cells are as follows:
.tg {b

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Choose the correct stability order of group 13 elements in their + 1 oxidation state.

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Given below are two statements :
Statement I : According to Ellingham diagram, any metal oxide with higher $$\Delta$$G$$

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Consider the following reaction:
$$2HSO_4^ - (aq)\mathrel{\mathop{\kern0pt\longrightarrow}
\limits_{(2)\,Hydrolysis}^{(1

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The correct order of melting point is :

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The correct order of melting points of hydrides of group 16 elements is :

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Consider the following reaction :
A + alkali $$\to$$ B (Major Product)
If B is an oxoacid of phosphorus with no P-H bond

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Polar stratospheric clouds facilitate the formation of :

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Given below are two statements :
Statement I : In 'Lassaigne's Test', when both nitrogen and sulphur are present in an o

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(C7H5O2)2 $$\buildrel {hv} \over
\longrightarrow $$ [X] $$\to$$ 2C6H5 + 2CO2
Consider the above reaction and identify t

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Consider the above reaction sequence and identify the product B.

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Which will have the highest enol content?

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Among the following structures, which will show the most stable enamine formation? (Where Me is $$-$$CH3)

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Which of the following sets are correct regarding polymer?
(A) Copolymer : Buna-S
(B) Condensation polymer : Nylon-6,6
(

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A chemical which stimulates the secretion of pepsin is :

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Which statement is not true with respect to nitrate ion test?

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For complete combustion of methanol
CH3OH(I) + $${3 \over 2}$$O2(g) $$\to$$ CO2(g) + 2H2O(I)
the amount of heat produced

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A 0.5 percent solution of potassium chloride was found to freeze at $$-$$0.24$$^\circ$$C. The percentage dissociation of

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50 mL of 0.1 M CH3COOH is being titrated against 0.1 M NaOH. When 25 mL of NaOH has been added, the pH of the solution w

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A flask is filled with equal moles of A and B. The half lives of A and B are 100 s and 50 s respectively and are indepen

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2.0 g of H2 gas is adsorbed on 2.5 g of platinum powder at 300 K and 1 bar pressure. The volume of the gas adsorbed per

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The spin-only magnetic moment value of the most basic oxide of vanadium among V2O3, V2O4 and V2O5 is _____________ B.M.

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The spin-only magnetic moment value of an octahedral complex among CoCl3.4NH3, NiCl2.6H2O and PtCl4.2HCl, which upon rea

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On complete combustion 0.30 g of an organic compound gave 0.20 g of carbon dioxide and 0.10 g of water. The percentage o

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Compound 'P' on nitration with dil. HNO3 yields two isomers (A) and (B). These isomers can be separated by steam distill

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The number of oxygens present in a nucleotide formed from a base, that is present only in RNA is ___________.

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## Mathematics

Let $$f(x) = {{x - 1} \over {x + 1}},\,x \in R - \{ 0, - 1,1\} $$. If $${f^{n + 1}}(x) = f({f^n}(x))$$ for all n $$\in$$

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Let $$A = \left\{ {z \in C:\left| {{{z + 1} \over {z - 1}}} \right|

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Let A be a 3 $$\times$$ 3 invertible matrix. If |adj (24A)| = |adj (3 adj (2A))|, then |A|2 is equal to :

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The ordered pair (a, b), for which the system of linear equations
3x $$-$$ 2y + z = b
5x $$-$$ 8y + 9z = 3
2x + y + az =

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The remainder when (2021)2023 is divided by 7 is :

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$$\mathop {\lim }\limits_{x \to {1 \over {\sqrt 2 }}} {{\sin ({{\cos }^{ - 1}}x) - x} \over {1 - \tan ({{\cos }^{ - 1}}x

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Let f, g : R $$\to$$ R be two real valued functions defined as $$f(x) = \left\{ {\matrix{
{ - |x + 3|} & , & {x 1 and

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The sum of the absolute minimum and the absolute maximum values of the function f(x) = |3x $$-$$ x2 + 2| $$-$$ x in the

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Let S be the set of all the natural numbers, for which the line $${x \over a} + {y \over b} = 2$$ is a tangent to the cu

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The area bounded by the curve y = |x2 $$-$$ 9| and the line y = 3 is :

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Let R be the point (3, 7) and let P and Q be two points on the line x + y = 5 such that PQR is an equilateral triangle.

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Let C be a circle passing through the points A(2, $$-$$1) and B(3, 4). The line segment AB s not a diameter of C. If r i

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Let the normal at the point on the parabola y2 = 6x pass through the point (5, $$-$$8). If the tangent at P to the parab

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If the two lines $${l_1}:{{x - 2} \over 3} = {{y + 1} \over {-2}},\,z = 2$$ and $${l_2}:{{x - 1} \over 1} = {{2y + 3} \o

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Let the plane 2x + 3y + z + 20 = 0 be rotated through a right angle about its line of intersection with the plane x $$-$

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If $$\overrightarrow a \,.\,\overrightarrow b = 1,\,\overrightarrow b \,.\,\overrightarrow c = 2$$ and $$\overrightarr

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Let a biased coin be tossed 5 times. If the probability of getting 4 heads is equal to the probability of getting 5 head

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The mean of the numbers a, b, 8, 5, 10 is 6 and their variance is 6.8. If M is the mean deviation of the numbers about t

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Let $$f(x) = 2{\cos ^{ - 1}}x + 4{\cot ^{ - 1}}x - 3{x^2} - 2x + 10$$, $$x \in [ - 1,1]$$. If [a, b] is the range of the

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Let $$\Delta$$, $$\nabla $$ $$\in$$ {$$\wedge$$, $$\vee$$} be such that p $$\nabla$$ q $$\Rightarrow$$ ((p $$\Delta$$ q)

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The sum of the cubes of all the roots of the equation $${x^4} - 3{x^3} - 2{x^2} + 3x + 1 = 0$$ is _________.

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There are ten boys B1, B2, ......., B10 and five girls G1, G2, ........, G5 in a class. Then the number of ways of formi

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Let the common tangents to the curves $$4({x^2} + {y^2}) = 9$$ and $${y^2} = 4x$$ intersect at the point Q. Let an ellip

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Let f(x) = max {|x + 1|, |x + 2|, ....., |x + 5|}. Then $$\int\limits_{ - 6}^0 {f(x)dx} $$ is equal to __________.

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Let the solution curve y = y(x) of the differential equation $$(4 + {x^2})dy - 2x({x^2} + 3y + 4)dx = 0$$ pass through t

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If $${\sin ^2}(10^\circ )\sin (20^\circ )\sin (40^\circ )\sin (50^\circ )\sin (70^\circ ) = \alpha - {1 \over {16}}\sin

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Let A = {n $$\in$$ N : H.C.F. (n, 45) = 1} and
Let B = {2k : k $$\in$$ {1, 2, ......., 100}}. Then the sum of all the el

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The value of the integral $${{48} \over {{\pi ^4}}}\int\limits_0^\pi {\left( {{{3\pi {x^2}} \over 2} - {x^3}} \right){{

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Let $$A = \sum\limits_{i = 1}^{10} {\sum\limits_{j = 1}^{10} {\min \,\{ i,j\} } } $$ and $$B = \sum\limits_{i = 1}^{10}

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Let $$S = (0,2\pi ) - \left\{ {{\pi \over 2},{{3\pi } \over 4},{{3\pi } \over 2},{{7\pi } \over 4}} \right\}$$. Let $$y

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## Physics

An expression for a dimensionless quantity P is given by $$P = {\alpha \over \beta }{\log _e}\left( {{{kt} \over {\beta

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A person is standing in an elevator. In which situation, he experiences weight loss?

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An object is thrown vertically upwards. At its maximum height, which of the following quantity becomes zero?

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A ball is released from rest from point P of a smooth semi-spherical vessel as shown in figure. The ratio of the centrip

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A thin circular ring of mass M and radius R is rotating with a constant angular velocity 2 rads$$-$$1 in a horizontal pl

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The variation of acceleration due to gravity (g) with distance (r) from the center of the earth is correctly represented

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The efficiency of a Carnot's engine, working between steam point and ice point, will be :

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Time period of a simple pendulum in a stationary lift is 'T'. If the lift accelerates with $${g \over 6}$$ vertically up

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A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats 1.4. Vessel is moving

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Two capacitors having capacitance C1 and C2 respectively are connected as shown in figure. Initially, capacitor C1 is ch

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Given below two statements : One is labelled as Assertion (A) and other is labelled as Reason (R).
Assertion (A) : Non-p

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The magnetic flux through a coil perpendicular to its plane is varying according to the relation $$\phi = (5{t^3} + 4{t

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An aluminium wire is stretched to make its length, 0.4% larger. The percentage change in resistance is :

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A proton and an alpha particle of the same velocity enter in a uniform magnetic field which is acting perpendicular to t

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If Electric field intensity of a uniform plane electromagnetic wave is given as $$E = - 301.6\sin (kz - \omega t){\wide

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In free space, an electromagnetic wave of 3 GHz frequency strikes over the edge of an object of size $${\lambda \over {

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An electron with speed v and a photon with speed c have the same de-Broglie wavelength. If the kinetic energy and moment

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How many alpha and beta particles are emitted when Uranium 92U238 decays to lead 82Pb206 ?

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The I-V characteristics of a p-n junction diode in forward bias is shown in the figure. The ratio of dynamic resistance,

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Choose the correct statement for amplitude modulation :

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A fighter jet is flying horizontally at a certain altitude with a speed of 200 ms$$-$$1. When it passes directly overhea

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A ball of mass 0.5 kg is dropped from the height of 10 m. The height, at which the magnitude of velocity becomes equal t

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The elastic behaviour of material for linear stress and linear strain, is shown in the figure. The energy density for a

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The elongation of a wire on the surface of the earth is 10$$-$$4 m. The same wire of same dimensions is elongated by 6 $

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A 10 $$\Omega$$, 20 mH coil carrying constant current is connected to a battery of 20 V through a switch. Now after swit

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A light ray is incident, at an incident angle $$\theta$$1, on the system of tow plane mirrors M1 and M2 having an inclin

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In a vernier callipers, each cm on the main scale is divided into 20 equal parts. If tenth vernier scale division coinci

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As per the given circuit, the value of current through the battery will be ____________ A.

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A 110 V, 50 Hz, AC source is connected in the circuit (as shown in figure). The current through the resistance 55 $$\Ome

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An ideal fluid of density 800 kgm$$-$$3, flows smoothly through a bent pipe (as shown in figure) that tapers in cross-se

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