JEE Main 2022 (Online) 29th June Evening Shift

Paper was held on
Wed, Jun 29, 2022 9:30 AM

## Chemistry

Using the rules for significant figures, the correct answer for the expression $${{0.02858 \times 0.112} \over {0.5702}}

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Which of the following is the correct plot for the probability density $${\psi ^2}$$ (r) as a function of distance 'r' o

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Consider the species CH4, NH$$_4^ + $$ and BH$$_4^ - $$. Choose the correct option with respect to the these species.

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4.0 moles of argon and 5.0 moles of PCl5 are introduced into an evacuated flask of 100 litre capacity at 610 K. The syst

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A 42.12% (w/v) solution of NaCl causes precipitation of a certain sol in 10 hours. The coagulating value of NaCl for the

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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 : The

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Match List I with List II.
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Given below are two statements.
$$\bullet$$ Statement I : In CuSO4 . 5H2O, Cu-O bonds are present.
$$\bullet$$ Statement

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Amongst baking soda, caustic soda and washing soda, carbonate anion is present in :

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Number of lone pair(s) of electrons on central atom and the shape BrF3 molecule respectively, are

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Aqueous solution of which of the following boron compounds will be strongly basic in nature?

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Sulphur dioxide is one of the components of polluted air. SO2 is also a major contributor to acid rain. The correct and

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Which of the following carbocations is most stable?

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The stable carbocation formed in the above reaction is

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Two isomers (A) and (B) with Molar mass 184 g/mol and elemental composition C, 52.2%; H, 4.9% and Br 42.9% gave benzoic

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In Friedel-Crafts alkylation of aniline, one gets

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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 : Dac

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The structure of protein that is unaffected by heating is

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The mixture of chloroxylenol and terpineol is an example of

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A white precipitate was formed when BaCl2 was added to water extract of an inorganic salt. Further, a gas 'X' with chara

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A box contains 0.90 g of liquid water in equilibrium with water vapour at 27$$^\circ$$C. The equilibrium vapour pressure

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2.2 g of nitrous oxide (N2O) gas is cooled at a constant pressure of 1 atm from 310 K to 270 K causing the compression o

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Elevation in boiling point for 1.5 molal solution of glucose in water is 4 K. The depression in freezing point for 4.5 m

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The cell potential for the given cell at 298 K
Pt| H2 (g, 1 bar) | H+ (aq) || Cu2+ (aq) | Cu(s)
is 0.31 V. The pH of the

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The equation k = (6.5 $$\times$$ 1012s$$-$$1)e$$-$$26000K/T is followed for the decomposition of compound A. The activat

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Spin only magnetic moment of [MnBr6]4$$-$$ is _________ B.M. (round off to the closest integer)

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For the reaction given below :
CoCl3 . xNH3 + AgNO3 (aq) $$\to$$
If two equivalents of AgCl precipitate out, then the va

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The number of chiral alcohol(s) with molecular formula C4H10O is ________.

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In the given reaction,
the number of sp2 hybridised carbon(s) in compound 'X' is ________.

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In the given reaction,
The number of $$\pi$$ electrons present in the product 'P' is _________.

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## Mathematics

Let $$\alpha$$ be a root of the equation 1 + x2 + x4 = 0. Then, the value of $$\alpha$$1011 + $$\alpha$$2022 $$-$$ $$\al

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Let arg(z) represent the principal argument of the complex number z. Then, |z| = 3 and arg(z $$-$$ 1) $$-$$ arg(z + 1) =

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Let $$A = \left( {\matrix{
2 & { - 1} \cr
0 & 2 \cr
} } \right)$$. If $$B = I - {}^5{C_1}(adj\,A) + {}^5{C_2

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The sum of the infinite series $$1 + {5 \over 6} + {{12} \over {{6^2}}} + {{22} \over {{6^3}}} + {{35} \over {{6^4}}} +

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The value of $$\mathop {\lim }\limits_{x \to 1} {{({x^2} - 1){{\sin }^2}(\pi x)} \over {{x^4} - 2{x^3} + 2x - 1}}$$ is e

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Let f : R $$\to$$ R be a function defined by f(x) = (x $$-$$ 3)n1 (x $$-$$ 5)n2, n1, n2 $$\in$$ N. Then, which of the fo

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Let f be a real valued continuous function on [0, 1] and $$f(x) = x + \int\limits_0^1 {(x - t)f(t)dt} $$.
Then, which of

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If $$\int\limits_0^2 {\left( {\sqrt {2x} - \sqrt {2x - {x^2}} } \right)dx = \int\limits_0^1 {\left( {1 - \sqrt {1 - {y^

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If y = y(x) is the solution of the differential equation $$\left( {1 + {e^{2x}}} \right){{dy} \over {dx}} + 2\left( {1 +

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Let P : y2 = 4ax, a > 0 be a parabola with focus S. Let the tangents to the parabola P make an angle of $${\pi \over 4}

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Let a triangle ABC be inscribed in the circle $${x^2} - \sqrt 2 (x + y) + {y^2} = 0$$ such that $$\angle BAC = {\pi \ov

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Let $${{x - 2} \over 3} = {{y + 1} \over { - 2}} = {{z + 3} \over { - 1}}$$ lie on the plane $$px - qy + z = 5$$, for so

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The distance of the origin from the centroid of the triangle whose two sides have the equations $$x - 2y + 1 = 0$$ and $

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Let Q be the mirror image of the point P(1, 2, 1) with respect to the plane x + 2y + 2z = 16. Let T be a plane passing t

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Let A, B, C be three points whose position vectors respectively are
$$\overrightarrow a = \widehat i + 4\widehat j + 3\

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The probability that a relation R from {x, y} to {x, y} is both symmetric and transitive, is equal to :

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The number of values of a $$\in$$ N such that the variance of 3, 7, 12, a, 43 $$-$$ a is a natural number is :

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From the base of a pole of height 20 meter, the angle of elevation of the top of a tower is 60$$^\circ$$. The pole subte

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Negation of the Boolean statement (p $$\vee$$ q) $$\Rightarrow$$ (($$\sim$$ r) $$\vee$$ p) is equivalent to :

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Let n $$\ge$$ 5 be an integer. If 9n $$-$$ 8n $$-$$ 1 = 64$$\alpha$$ and 6n $$-$$ 5n $$-$$ 1 = 25$$\beta$$, then $$\alph

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Let $$\overrightarrow a = \widehat i - 2\widehat j + 3\widehat k$$, $$\overrightarrow b = \widehat i

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Let y = y(x), x > 1, be the solution of the differential equation $$(x - 1){{dy} \over {dx}} + 2xy = {1 \over {x - 1}}$$

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Let 3, 6, 9, 12, ....... upto 78 terms and 5, 9, 13, 17, ...... upto 59 terms be two series. Then, the sum of the terms

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The number of solutions of the equation $$\sin x = {\cos ^2}x$$ in the interval (0, 10) is _________.

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For real numbers a, b (a > b > 0), let
Area $$\left\{ {(x,y):{x^2} + {y^2} \le {a^2}\,and\,{{{x^2}} \over {{a^2}}} + {{{

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Let f and g be twice differentiable even functions on ($$-$$2, 2) such that $$f\left( {{1 \over 4}} \right) = 0$$, $$f\l

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Let the coefficients of x$$-$$1 and x$$-$$3 in the expansion of $${\left( {2{x^{{1 \over 5}}} - {1 \over {{x^{{1 \over 5

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The total number of four digit numbers such that each of first three digits is divisible by the last digit, is equal to

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Let $$M = \left[ {\matrix{
0 & { - \alpha } \cr
\alpha & 0 \cr
} } \right]$$, where $$\alpha$$ is a non-zer

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Let f(x) and g(x) be two real polynomials of degree 2 and 1 respectively. If $$f(g(x)) = 8{x^2} - 2x$$ and $$g(f(x)) = 4

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## Physics

A small toy starts moving from the position of rest under a constant acceleration. If it travels a distance of 10m in t

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At what temperature a gold ring of diameter 6.230 cm be heated so that it can be fitted on a wooden bangle of diameter 6

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Two point charges Q each are placed at a distance d apart. A third point charge q is placed at a distance x from mid-poi

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The speed of light in media 'A' and 'B' are $$2.0 \times {10^{10}}$$ cm/s and $$1.5 \times {10^{10}}$$ cm/s respectively

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In the following nuclear reaction,
$$D\buildrel \alpha \over
\longrightarrow {D_1}\buildrel {{\beta ^ - }} \over
\lon

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The electric field at a point associated with a light wave is given by
E = 200 [sin (6 $$\times$$ 1015)t + sin (9 $$\tim

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A capacitor is discharging through a resistor R. Consider in time t1, the energy stored in the capacitor reduces to half

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Starting with the same initial conditions, an ideal gas expands from volume V1 to V2 in three different ways. The work d

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Two long current carrying conductors are placed to each other at a distance of 8 cm between them. The magnitude of magne

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The time period of a satellite revolving around earth in a given orbit is 7 hours. If the radius of orbit is increased t

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The TV transmission tower at a particular station has a height of 125 m. For doubling the coverage of its range, the hei

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The motion of a simple pendulum executing S.H.M. is represented by the following equation.
$$y = A\sin (\pi t + \phi )$$

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A vessel contains 16g of hydrogen and 128g of oxygen at standard temperature and pressure. The volume of the vessel in c

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Given below are two statements :
Statement I : The electric force changes the speed of the charged particle and hence ch

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A block of mass 40 kg slides over a surface, when a mass of 4 kg is suspended through an inextensible massless string pa

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In the given figure, the block of mass m is dropped from the point 'A'. The expression for kinetic energy of block when

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A block of mass M placed inside a box descends vertically with acceleration 'a'. The block exerts a force equal to one-f

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If the electric potential at any point (x, y, z) m in space is given by V = 3x2 volt. The electric field at the point (1

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The combination of two identical cells, whether connected in series or parallel combination provides the same current th

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A person can throw a ball upto a maximum range of 100 m. How high above the ground he can throw the same ball?

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The Vernier constant of Vernier callipers is 0.1 mm and it has zero error of ($$-$$0.05) cm. While measuring diameter of

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A small spherical ball of radius 0.1 mm and density 104 kg m$$-$$3 falls freely under gravity through a distance h befo

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In an experiment to determine the velocity of sound in air at room temperature using a resonance tube, the first resonan

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Two resistors are connected in series across a battery as shown in figure. If a voltmeter of resistance 2000 $$\Omega$$

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A potential barrier of 0.4 V exists across a p-n junction. An electron enters the junction from the n-side with a speed

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The displacement current of 4.425 $$\mu$$A is developed in the space between the plates of parallel plate capacitor when

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The moment of inertia of a uniform thin rod about a perpendicular axis passing through one end is I1. The same rod is be

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The half life of a radioactive substance is 5 years. After x years a given sample of the radioactive substance gets redu

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In a double slit experiment with monochromatic light, fringes are obtained on a screen placed at some distance from the

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An inductor of 0.5 mH, a capacitor of 200 $$\mu$$F and a resistor of 2 $$\Omega$$ are connected in series with a 220 V a

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