JEE Main 2022 (Online) 28th June Morning Shift

Paper was held on
Tue, Jun 28, 2022 3:30 AM

## Chemistry

The incorrect statement about the imperfections in solids is :

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The Zeta potential is related to which property of colloids?

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Element "E" belongs to the period 4 and group 16 of the periodic table. The valence shell electron configuration of the

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Given are two statements one is labelled as Assertion A and other is labelled as Reason R.
Assertion A : Magnesium can r

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Dihydrogen reacts with CuO to give :

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Nitrogen gas is obtained by thermal decomposition of :

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Given below are two statements :
Statement I : The pentavalent oxide of group-15 element, E2O5, is less acidic than triv

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Which one of the lanthanoids given below is the most stable in divalent form?

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Given below are two statements :
Statement I : [Ni(CN)4]2$$-$$ is square planar and diamagnetic complex, with dsp2 hybri

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Which amongst the following is not a pesticide?

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Which one of the following techniques is not used to spot components of a mixture separated on thin layer chromatographi

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Which of the following structure are aromatic in nature?

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The major product (P) in the reaction
is

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The correct structure of product 'A' formed in the following reaction.
is

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Which one of the following compounds is inactive towards SN1 reaction?

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Identify the major product formed in the following sequence of reactions:

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A primary aliphatic amine on reaction with nitrous acid in cold (273 K) and there after raising temperature of reaction

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Which one of the following is NOT a copolymer?

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Stability of $$\alpha$$-Helix structure of proteins depends upon

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The formula of the purple colour formed in Laissaigne's test for sulphur using sodium nitroprusside is :

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A 2.0 g sample containing MnO2 is treated with HCl liberating Cl2. The Cl2 gas is passed into a solution of KI and 60.0

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If the work function of a metal is 6.63 $$\times$$ 10$$-$$19J, the maximum wavelength of the photon required to remove a

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The hybridization of P exhibited in PF5 is spxdy. The value of y is __________.

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4.0 L of an ideal gas is allowed to expand isothermally into vacuum until the total volume is 2.0 L. The amount of heat

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The vapour pressures of two volatile liquids A and B at 25$$^\circ$$C are 50 Torr and 100 Torr, respectively. If the liq

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The solubility product of a sparingly soluble salt A2X3 is 1.1 $$\times$$ 10$$-$$23. If specific conductance of the solu

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The quantity of electricity in Faraday needed to reduce 1 mol of Cr2O$$_7^{2 - }$$ to Cr3+ is ____________.

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For a first order reaction A $$\to$$ B, the rate constant, k = 5.5 $$\times$$ 10$$-$$14 s$$-$$1. The time required for 6

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Number of complexes which will exhibit synergic bonding amongst, $$[Cr{(CO)_6}]$$, $$[Mn{(CO)_5}]$$ and $$[M{n_2}{(CO)_{

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In the estimation of bromine, 0.5 g of an organic compound gave 0.40 g of silver bromide. The percentage of bromine in t

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## Mathematics

If $$\sum\limits_{k = 1}^{31} {\left( {{}^{31}{C_k}} \right)\left( {{}^{31}{C_{k - 1}}} \right) - \sum\limits_{k = 1}^{3

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Let a function f : N $$\to$$ N be defined by
$$f(n) = \left[ {\matrix{
{2n,} & {n = 2,4,6,8,......} \cr
{n - 1,}

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If the system of linear equations
$$2x + 3y - z = - 2$$
$$x + y + z = 4$$
$$x - y + |\lambda |z = 4\lambda - 4$$
where

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Let A be a matrix of order 3 $$\times$$ 3 and det (A) = 2. Then det (det (A) adj (5 adj (A3))) is equal to _____________

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The total number of 5-digit numbers, formed by using the digits 1, 2, 3, 5, 6, 7 without repetition, which are multiple

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Let A1, A2, A3, ....... be an increasing geometric progression of positive real numbers. If A1A3A5A7 = $${1 \over {1296}

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Let [t] denote the greatest integer less than or equal to t. Then, the value of the integral $$\int\limits_0^1 {[ - 8{x^

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Let f : R $$\to$$ R be defined as
$$f(x) = \left[ {\matrix{
{[{e^x}],} & {x
where a, b, c $$\in$$ R and [t] denotes

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The area of the region S = {(x, y) : y2 $$\le$$ 8x, y $$\ge$$ $$\sqrt2$$x, x $$\ge$$ 1} is

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Let the solution curve $$y = y(x)$$ of the differential equation
$$\left[ {{x \over {\sqrt {{x^2} - {y^2}} }} + {e^{{y \

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Let y = y(x) be the solution of the differential equation $$x(1 - {x^2}){{dy} \over {dx}} + (3{x^2}y - y - 4{x^3}) = 0$$

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The number of real solutions of $${x^7} + 5{x^3} + 3x + 1 = 0$$ is equal to ____________.

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Let the eccentricity of the hyperbola $$H:{{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$ be $$\sqrt {{5 \over 2

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If the tangents drawn at the points $$O(0,0)$$ and $$P\left( {1 + \sqrt 5 ,2} \right)$$ on the circle $${x^2} + {y^2} -

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If two distinct point Q, R lie on the line of intersection of the planes $$ - x + 2y - z = 0$$ and $$3x - 5y + 2z = 0$$

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The acute angle between the planes P1 and P2, when P1 and P2 are the planes passing through the intersection of the plan

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Let the plane $$P:\overrightarrow r \,.\,\overrightarrow a = d$$ contain the line of intersection of two planes $$\over

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The probability, that in a randomly selected 3-digit number at least two digits are odd, is :

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Let AB and PQ be two vertical poles, 160 m apart from each other. Let C be the middle point of B and Q, which are feet o

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Let p, q, r be three logical statements. Consider the compound statements
$${S_1}:(( \sim p) \vee q) \vee (( \sim p) \ve

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Let R1 and R2 be relations on the set {1, 2, ......., 50} such that
R1 = {(p, pn) : p is a prime and n $$\ge$$ 0 is an i

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The number of real solutions of the equation $${e^{4x}} + 4{e^{3x}} - 58{e^{2x}} + 4{e^x} + 1 = 0$$ is ___________.

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The mean and standard deviation of 15 observations are found to be 8 and 3 respectively. On rechecking it was found that

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

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A ray of light passing through the point P(2, 3) reflects on the x-axis at point A and the reflected ray passes through

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Let l be a line which is normal to the curve y = 2x2 + x + 2 at a point P on the curve. If the point Q(6, 4) lies on the

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Let A = {1, a1, a2 ....... a18, 77} be a set of integers with 1 1 2 18 Let the set A + A = {x + y : x, y $$\in$$ A} cont

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The number of positive integers k such that the constant term in the binomial expansion of $${\left( {2{x^3} + {3 \over

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The number of elements in the set {z = a + ib $$\in$$ C : a, b $$\in$$ Z and 1

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Let the lines $$y + 2x = \sqrt {11} + 7\sqrt 7 $$ and $$2y + x = 2\sqrt {11} + 6\sqrt 7 $$ be normal to a circle $$C:{

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## Physics

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

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A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration (a) is var

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Motion of a particle in x-y plane is described by a set of following equations $$x = 4\sin \left( {{\pi \over 2} - \ome

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Match List-I with List-II
.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border-style:soli

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Two planets A and B of equal mass are having their period of revolutions TA and TB such that TA = 2TB. These planets are

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A water drop of diameter 2 cm is broken into 64 equal droplets. The surface tension of water is 0.075 N/m. In this proce

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Given below are two statements :
Statement I : When $$\mu$$ amount of an ideal gas undergoes adiabatic change from state

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Given below are two statements :
Statement I : A point charge is brought in an electric field. The value of electric fie

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The three charges q/2, q and q/2 are placed at the corners A, B and C of a square of side 'a' as shown in figure. The ma

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An infinitely long hollow conducting cylinder with radius R carries a uniform current along its surface.
Choose the corr

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A radar sends an electromagnetic signal of electric field (E0) = 2.25 V/m and magnetic field (B0) = 1.5 $$\times$$ 10$$-

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The refracting angle of a prism is A and refractive index of the material of the prism is cot (A/2). Then the angle of m

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The aperture of the objective is 24.4 cm. The resolving power of this telescope, if a light of wavelength 2440 $$\mathop

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The de Broglie wavelengths for an electron and a photon are $$\lambda$$e and $$\lambda$$p respectively. For the same kin

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The Q-value of a nuclear reaction and kinetic energy of the projectile particle, Kp are related as :

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In the following circuit, the correct relation between output (Y) and inputs A and B will be :

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For using a multimeter to identify diode from electrical components, choose the correct statement out of the following 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 : n-p

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Match List-I with List-II
.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border-style:soli

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The velocity of sound in a gas, in which two wavelengths 4.08 m and 4.16 m produce 40 beats in 12s, will be :

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A pendulum is suspended by a string of length 250 cm. The mass of the bob of the pendulum is 200 g. The bob is pulled as

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A meter bridge setup is shown in the figure. It is used to determine an unknown resistance R using a given resistor of 1

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Current measured by the ammeter (A) in the reported circuit when no current flows through 10 $$\Omega$$ resistance, will

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An AC source is connected to an inductance of 100 mH, a capacitance of 100 $$\mu$$F and a resistance of 120 $$\Omega$$ a

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The position vector of 1 kg object is $$\overrightarrow r = \left( {3\widehat i - \widehat j} \right)m$$ and its veloci

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A man of 60 kg is running on the road and suddenly jumps into a stationary trolly car of mass 120 kg. Then, the trolly c

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A hanging mass M is connected to a four times bigger mass by using a string-pulley arrangement, as shown in the figure.

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The total internal energy of two mole monoatomic ideal gas at temperature T = 300 K will be _____________ J. (Given R =

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A singly ionized magnesium atom (A = 24) ion is accelerated to kinetic energy 5 keV, and is projected perpendicularly in

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A telegraph line of length 100 km has a capacity of 0.01 $$\mu$$F/km and it carries an alternating current at 0.5 kilo c

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