JEE Main 2021 (Online) 20th July Morning Shift

Paper was held on
Tue, Jul 20, 2021 3:30 AM

## Chemistry

According to the valence bond theory the hybridization of central metal atom is dsp2 for which one of the following comp

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The correct structure of Rhumann's Purple, the compound formed in the reaction of ninhydrin with proteins is :

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Green chemistry in day-to-day life is in the use of :

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The correct order of intensity of colors of the compounds is :

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The set in which compounds have different nature is :

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The species given below that does NOT show disproportionation reaction is :

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

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Orlon fibres are made up of :

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

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Chemical nature of the nitrogen oxide compound obtained from a reaction of concentrated nitric acid and P4O10 (in 4 : 1

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An inorganic Compound 'X' on treatment with concentrated H2SO4 produces brown fumes and gives dark brown ring with FeSO4

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Among the given species the Resonance stabilised carbocations are :

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A s-block element (M) reacts with oxygen to form an oxide of the formula MO2. The oxide is pale yellow in colour and par

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In the given reaction
3-Bromo-2, 2-dimethyl butane $$\buildrel {{C_2}{H_5}OH} \over
\longrightarrow \mathop {'A'}\limi

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The metal that can be purified economically by fractional distillation method is :

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Compound A is converted to B on reaction with CHCl3 and KOH. The compound B is toxic and can be decomposed by C. A, B an

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The conditions given below are in the context of observing Tyndall effect in colloidal solutions :(A) The diameter of th

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Identify the incorrect statement from the following

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Which among the above compound/s does/do not form Silver mirror when treated with Tollen's reagent?

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For above chemical reactions, identify the correct statement from the following :

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The number of lone pairs of electrons on the central I atom in I$$_3^ - $$ is ____________.

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250 mL of 0.5 M NaOH was added to 500 mL of 1 M HCl. The number of unreacted HCl molecules in the solution after complet

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The Azimuthal quantum number for the valence electrons of Ga+ ion is ___________.(Atomic number of Ga = 31)

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The spin-only magnetic moment value for the complex [Co(CN)6]4$$-$$ is __________ BM.[At. no. of Co = 27]

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2SO2(g) + O2(g) $$\rightleftharpoons$$ 2SO3(g)In an equilibrium mixture, the partial pressures are PSO3 = 43 kPa; PO2 =

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The number of nitrogen atoms in a semicarbazone molecule of acetone is ______________.

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To synthesize 1.0 mole of 2-methylpropan-2-ol from Ethylethanoate ___________ equivalents of CH3MgBr Reagent will be req

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The inactivation rate of a viral preparation is proportional to the amount of virus. In the first minute after preparati

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An average person needs about 10000 kJ energy per day. The amount of glucose (molar mass = 180.0 g mol$$-$$1) needed to

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At 20$$^\circ$$ C, the vapour pressure of benzene is 70 torr and that of methyl benzene is 20 torr. The mole fraction of

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## Mathematics

The Boolean expression $$(p \wedge \sim q) \Rightarrow (q \vee \sim p)$$ is equivalent to :

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Let a be a positive real number such that $$\int_0^a {{e^{x - [x]}}} dx = 10e - 9$$ where [ x ] is the greatest integer

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The mean of 6 distinct observations is 6.5 and their variance is 10.25. If 4 out of 6 observations are 2, 4, 5 and 7, th

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The value of the integral $$\int\limits_{ - 1}^1 {{{\log }_e}(\sqrt {1 - x} + \sqrt {1 + x} )dx} $$ is equal to:

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If $$\alpha$$ and $$\beta$$ are the distinct roots of the equation $${x^2} + {(3)^{1/4}}x + {3^{1/2}} = 0$$, then the va

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Let $$A = \left[ {\matrix{
2 & 3 \cr
a & 0 \cr
} } \right]$$, a$$\in$$R be written as P + Q where P

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If z and $$\omega$$ are two complex numbers such that $$\left| {z\omega } \right| = 1$$ and $$\arg (z) - \arg (\omega )

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If in a triangle ABC, AB = 5 units, $$\angle B = {\cos ^{ - 1}}\left( {{3 \over 5}} \right)$$ and radius of circumcircle

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Let [ x ] denote the greatest integer $$\le$$ x, where x $$\in$$ R. If the domain of the real valued function $$f(x) = \

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Let y = y(x) be the solution of the differential equation $$x\tan \left( {{y \over x}} \right)dy = \left( {y\tan \left(

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The coefficient of x256 in the expansion of (1 $$-$$ x)101 (x2 + x + 1)100 is :

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Let $$A = [{a_{ij}}]$$ be a 3 $$\times$$ 3 matrix, where $${a_{ij}} = \left\{ {\matrix{
1 & , & {if\,i = j}

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

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The number of real roots of the equation $${\tan ^{ - 1}}\sqrt {x(x + 1)} + {\sin ^{ - 1}}\sqrt {{x^2} + x + 1} = {\pi

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

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Let 'a' be a real number such that the function f(x) = ax2 + 6x $$-$$ 15, x $$\in$$ R is increasing in $$\left( { - \inf

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Let a function f : R $$\to$$ R be defined as $$f(x) = \left\{ {\matrix{
{\sin x - {e^x}} & {if} & {x \le 0}

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Words with or without meaning are to be formed using all the letters of the word EXAMINATION. The probability that the l

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The probability of selecting integers a$$\in$$[$$-$$ 5, 30] such that x2 + 2(a + 4)x $$-$$ 5a + 64 > 0, for all x$$\i

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Let the tangent to the parabola S : y2 = 2x at the point P(2, 2) meet the x-axis at Q and normal at it meet the parabola

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Let $$\overrightarrow a $$, $$\overrightarrow b $$, $$\overrightarrow c $$ be three mutually perpendicular vectors of th

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Let $$A = \left( {\matrix{
1 & { - 1} & 0 \cr
0 & 1 & { - 1} \cr
0 & 0 & 1 \cr

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Let P be a plane passing through the points (1, 0, 1), (1, $$-$$2, 1) and (0, 1, $$-$$2). Let a vector $$\overrightarrow

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The number of rational terms in the binomial expansion of $${\left( {{4^{{1 \over 4}}} + {5^{{1 \over 6}}}} \right)^{120

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If the shortest distance between the lines $$\overrightarrow {{r_1}} = \alpha \widehat i + 2\widehat j + 2\widehat k +

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Let T be the tangent to the ellipse E : x2 + 4y2 = 5 at the point P(1, 1). If the area of the region bounded by the tang

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Let a, b, c, d in arithmetic progression with common difference $$\lambda$$. If $$\left| {\matrix{
{x + a - c} &

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There are 15 players in a cricket team, out of which 6 are bowlers, 7 are batsman and 2 are wicketkeepers. The number of

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Let y = mx + c, m > 0 be the focal chord of y2 = $$-$$ 64x, which is tangent to (x + 10)2 + y2 = 4. Then, the value o

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If the value of $$\mathop {\lim }\limits_{x \to 0} {(2 - \cos x\sqrt {\cos 2x} )^{\left( {{{x + 2} \over {{x^2}}}} \righ

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## Physics

A deuteron and an alpha particle having equal kinetic energy enter perpendicularly into a magnetic field. Let rd and r$$

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For the circuit shown below, calculate the value of Iz :

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A current of 5 A is passing through a non-linear magnesium wire of cross-section 0.04 m2. At every point the direction o

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The normal reaction 'N' for a vehicle of 800 kg mass, negotiating a turn on a 30$$^\circ$$ banked road at maximum possib

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Consider a mixture of gas molecule of types A, B and C having masses mA < mB < mC. The ratio of their root mean sq

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The amount of heat needed to raise the temperature of 4 moles of rigid diatomic gas from 0$$^\circ$$ C to 50$$^\circ$$

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A butterfly is flying with a velocity $$4\sqrt 2 $$ m/s in North-East direction. Wind is slowly blowing at 1 m/s from No

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A certain charge Q is divided into two parts q and (Q $$-$$ q). How should the charges Q and q be divided so that q and

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The arm PQ of a rectangular conductor is moving from x = 0 to x = 2b outwards and then inwards from x = 2b to x = 0 as s

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The value of current in the 6 $$\Omega$$ resistance is :

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A radioactive material decays by simultaneous emissions of two particles with half lives of 1400 years and 700 years res

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A steel block of 10 kg rests on a horizontal floor as shown. When three iron cylinders are placed on it as shown, the bl

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A nucleus of mass M emits $$\gamma$$ -ray photon of frequency 'v'. The loss of internal energy by the nucleus is :[Take

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The radiation corresponding to 3 $$\to$$ 2 transition of a hydrogen atom falls on a gold surface to generate photoelectr

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If $$\overrightarrow A $$ and $$\overrightarrow B $$ are two vectors satisfying the relation $$\overrightarrow A $$ . $$

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The entropy of any system is given by $$S = {\alpha ^2}\beta \ln \left[ {{{\mu kR} \over {J{\beta ^2}}} + 3} \right]$$ w

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AC voltage V(t) = 20 sin$$\omega$$t of frequency 50 Hz is applied to a parallel plate capacitor. The separation between

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Region I and II are separated by a spherical surface of radius 25 cm. An object is kept in region I at a distance of 40

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A person whose mass is 100 kg travels from Earth to Mars in a spaceship. Neglect all other objects in sky and take acce

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The value of tension in a long thin metal wire has been changed from T1 to T2. The lengths of the metal wire at two diff

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A body having specific charge 8 $$\mu$$C/g is resting on a frictionless plane at a distance 10 cm from the wall (as show

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In a spring gun having spring constant 100 N/m a small ball 'B' of mass 100 g is put in its barrel (as shown in figure)

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A carrier wave Vc(t) = 160 sin(2$$\pi$$ $$\times$$ 106t) volts is made to vary between Vmax = 200 V and Vmin = 120 V by

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An object viewed from a near point distance of 25 cm, using a microscopic lens with magnification '6', gives an unresolv

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The frequency of a car horn encountered a change from 400 Hz to 500 Hz, when the car approaches a vertical wall. If the

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A circular disc reaches from top to bottom of an inclined plane of length 'L'. When it slips down the plane, it makes ti

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The amplitude of wave disturbance propagating in the positive x-direction is given by $$y = {1 \over {{{(1 + x)}^2}}}$$

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In an LCR series circuit, an inductor 30 mH and a resistor 1 $$\Omega$$ are connected to an AC source of angular frequen

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A rod of mass M and length L is lying on a horizontal frictionless surface. A particle of mass 'm' travelling along the

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In the reported figure, heat energy absorbed by a system in going through a cyclic process is ___________ $$\pi$$J.

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