JEE Main 2021 (Online) 17th March Evening Shift

Paper was held on
Wed, Mar 17, 2021 9:30 AM

## Chemistry

$${C_{12}}{H_{22}}{O_{11}} + {H_2}O\buildrel {Enzyme\,A} \over
\longrightarrow \mathop {{C_6}{H_{12}}{O_6}}\limits_{Glu

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Choose the correct statement regarding the formation of carbocations A and B given.

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Nitrogen can be estimated by Kjeldahl's method for which of the following compound?

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The set of elements that differ in mutual relationship from those of the other sets is :

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Amongst the following, the linear species is :

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The correct pair(s) of the ambident nucleophiles is(are)(A) AgCN/KCN(B) RCOOAg/RCOOK(C) AgNO2/KNO2(D) AgI/KI

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Given below are two statements :Statement I : 2-methylbutane on oxidation with KMnO4 gives 2-methylbutan-2-ol.Statement

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Match List - I with List - II :
List - I
List - II
(a)
Haematite
(i)
$$A{l

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The set that represents the pair of neutral oxides of nitrogen is :

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During which of the following processes, does entropy decrease?(A) Freezing of water to ice at 0$$^\circ$$C(B) Freezing

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For the coagulation of a negative sol, the species below, that has the highest flocculating power is :

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In the above reaction, the structural formula of (A), ''X'' and ''Y'' respectively are :

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Primary, secondary and tertiary amines can be separated using:

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Which of the following statement(s) is (are) incorrect reason for eutrophication?(A) excess usage of fertilisers(B) exce

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Match List - I with List - II.
List - IChemical Compound
List - IIUsed as
(a)
Sucr

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Match List - I with List - II :
List - I
List - II
(a)
$$[Co{(N{H_3})_6}][Cr{(CN)_

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The functional groups that are responsible for the ion-exchange property of cation and anion exchange resins, respective

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One of the by-products formed during the recovery of NH3 from Solvay process is :

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Fructose is an example of :

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The common positive oxidation states for an element with atomic number 24, are :

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A KCl solution of conductivity 0.14 S m$$-$$1 shows a resistance of 4.19$$\Omega$$ in a conductivity cell. If the same c

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On complete reaction of FeCl3 with oxalic acid in aqueous solution containing KOH, resulted in the formation of product

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The number of chlorine atoms in 20 mL of chlorine gas at STP is _________ 1021. (Round off to the Nearest Integer).[Assu

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KBr is doped with 10$$-$$5 mole percent of SrBr2. The number of cationic vacancies in 1g of KBr crystal is ____________

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Consider the above reaction. The percentage yield of amide product is __________. (Round off to the Nearest Integer).(Gi

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The reaction 2A + B2 $$ \to $$ 2AB is an elementary reaction.For a certain quantity of reactants, if the volume of the r

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Consider the reaction $$N_{2}O_{4}\left( g\right) \rightleftharpoons 2NO_{2}\left( g\right) $$The temperature at whic

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In the ground state of atomic Fe(Z = 26), the spin-only magnetic moment is ____________ $$\times$$ 10$$-$$1 BM. (Round o

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A 1 molal K4Fe(CN)6 solution has a degree of dissociation of 0.4. Its boiling point is equal to that of another solution

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The total number of C-C sigma bond/s in mesityl oxide (C6H10O) is __________. (Round off to the Nearest Integer).

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## Mathematics

The number of solutions of the equation x + 2tanx = $${\pi \over 2}$$ in the interval [0, 2$$\pi$$] is :

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If the sides AB, BC and CA of a triangle ABC have 3, 5 and 6 interior points respectively, then the total number of tria

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Let a computer program generate only the digits 0 and 1 to form a string of binary numbers with probability of occurrenc

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Let f : R $$ \to $$ R be defined as f(x) = e$$-$$xsinx. If F : [0, 1] $$ \to $$ R is a differentiable function with that

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Let S1, S2 and S3 be three sets defined asS1 = {z$$\in$$C : |z $$-$$ 1| $$ \le $$ $$\sqrt 2 $$}S2 = {z$$\in$$C : Re((1 $

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Let the tangent to the circle x2 + y2 = 25 at the point R(3, 4) meet x-axis and y-axis at points P and Q, respectively.

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The number of solutions of the equation $${\sin ^{ - 1}}\left[ {{x^2} + {1 \over 3}} \right] + {\cos ^{ - 1}}\left[ {{x^

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If the equation of plane passing through the mirror image of a point (2, 3, 1) with respect to line $${{x + 1} \over 2}

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If the curve y = y(x) is the solution of the differential equation $$2({x^2} + {x^{5/4}})dy - y(x + {x^{1/4}})dx = {2x^{

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Two tangents are drawn from a point P to the circle x2 + y2 $$-$$ 2x $$-$$ 4y + 4 = 0, such that the angle between these

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Let O be the origin. Let $$\overrightarrow {OP} = x\widehat i + y\widehat j - \widehat k$$ and $$\overrightarrow {OQ}

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If the Boolean expression $$(p \wedge q) \odot (p \otimes q)$$ is a tautology, then $$ \odot $$ and $$ \otimes $$ are re

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If the integral
$$\int_0^{10} {{{[\sin 2\pi x]} \over {{e^{x - [x]}}}}} dx = \alpha {e^{ - 1}} + \beta {e^{ - {1 \over

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The value of the limit $$\mathop {\lim }\limits_{\theta \to 0} {{\tan (\pi {{\cos }^2}\theta )} \over {\sin (2\pi {{\si

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Consider the function f : R $$ \to $$ R defined by
$$f(x) = \left\{ \matrix{
\left( {2 - \sin \left( {{1 \over x}} \r

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Let L be a tangent line to the parabola y2 = 4x $$-$$ 20 at (6, 2). If L is also a tangent to the ellipse $${{{x^2}} \ov

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The value of $$\mathop {\lim }\limits_{n \to \infty } {{[r] + [2r] + ... + [nr]} \over {{n^2}}}$$, where r is a non-zero

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If x, y, z are in arithmetic progression with common difference d, x $$\ne$$ 3d, and the determinant of the matrix $$\le

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The value of $$\sum\limits_{r = 0}^6 {\left( {{}^6{C_r}\,.\,{}^6{C_{6 - r}}} \right)} $$ is equal to :

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Let y = y(x) be the solution of the differential equation $$\cos x(3\sin x + \cos x + 3)dy = (1 + y\sin x(3\sin x + \cos

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Let $$A = \left[ {\matrix{
a & b \cr
c & d \cr
} } \right]$$ and $$B = \left[ {\matrix{
\alpha

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Let the coefficients of third, fourth and fifth terms in the expansion of $${\left( {x + {a \over {{x^2}}}} \right)^n},x

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Let tan$$\alpha$$, tan$$\beta$$ and tan$$\gamma$$; $$\alpha$$, $$\beta$$, $$\gamma$$ $$\ne$$ $${{(2n - 1)\pi } \over 2}$

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Let $$\overrightarrow x $$ be a vector in the plane containing vectors $$\overrightarrow a = 2\widehat i - \widehat j +

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Let $${I_n} = \int_1^e {{x^{19}}{{(\log |x|)}^n}} dx$$, where n$$\in$$N. If (20)I10 = $$\alpha$$I9 + $$\beta$$I8, for na

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If 1, log10(4x $$-$$ 2) and log10$$\left( {{4^x} + {{18} \over 5}} \right)$$ are in arithmetic progression for a real nu

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Consider a set of 3n numbers having variance 4. In this set, the mean of first 2n numbers is 6 and the mean of the remai

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Let P be an arbitrary point having sum of the squares of the distances from the planes x + y + z = 0, lx $$-$$ nz = 0 an

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Let f : [$$-$$1, 1] $$ \to $$ R be defined as f(x) = ax2 + bx + c for all x$$\in$$[$$-$$1, 1], where a, b, c$$\in$$R suc

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Let f : [$$-$$3, 1] $$ \to $$ R be given as $$f(x) = \left\{ \matrix{
\min \,\{ (x + 6),{x^2}\}, - 3 \le x \le 0 \hfil

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## Physics

A sound wave of frequency 245 Hz travels with the speed of 300 ms$$-$$1 along the positive x-axis. Each point of the wav

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Which one of the following will be the output of the given circuit?

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A carrier signal C(t) = 25 sin(2.512 $$\times$$ 1010t) is amplitude modulated by a message signal m(t) = 5 sin(1.57 $$\t

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Match List - I with List - II
List - I
List - II
(a)
Phase difference between curr

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The atomic hydrogen emits a line spectrum consisting of various series. Which series of hydrogen atomic spectra is lying

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A hairpin like shape as shown in figure is made by bending a long current carrying wire. What is the magnitude of a magn

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Two identical photocathodes receive the light of frequencies f1 and f2 respectively. If the velocities of the photo-elec

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If one mole of the polyatomic gas is having two vibrational modes and $$\beta$$ is the ratio of molar specific heats for

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Two cells of emf 2E and E with internal resistance r1 and r2 respectively are connected in series to an external resisto

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What happens to the inductive reactance and the current in a purely inductive circuit if the frequency is halved?

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A sphere of mass 2 kg and radius 0.5 m is rolling with an initial speed of 1 ms-1 goes up an inclined plane which makes

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Two particles A and B of equal masses are suspended from two massless springs of spring constants K1 and K2 respectively

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The velocity of a particle is v = v0 + gt + Ft2. Its position is x = 0 at t = 0; then its displacement after time (t = 1

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A block of mass 1 kg attached to a spring is made to oscillate with an initial amplitude of 12 cm. After 2 minutes the a

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A rubber ball is released from a height of 5 m above the floor. It bounces back repeatedly, always rising to $${{81} \ov

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The four arms of a Wheatstone bridge have resistances as shown in the figure. A galvanometer of 15$$\Omega$$ resistance

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Which one is the correct option for the two different thermodynamic processes?

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Two identical blocks A and B each of mass m resting on the smooth horizontal floor are connected by a light spring of na

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A geostationary satellite is orbiting around an arbitrary planet 'P' at a height of 11R above the surface of 'P', R bein

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An object is located at 2 km beneath the surface of the water. If the fractional compression $${{\Delta V} \over V}$$ is

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Suppose you have taken a dilute solution of oleic acid in such a way that its concentration becomes 0.01 cm3 of oleic ac

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The disc of mass M with uniform surface mass density $$\sigma$$ is shown in the figure. The centre of mass of the quarte

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The image of an object placed in air formed by a convex refracting surface is at a distance of 10 m behind the surface.

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The electric field intensity produced by the radiation coming from a 100 W bulb at a distance of 3 m is E. The electric

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The electric field in a region is given by $$\overrightarrow E = {2 \over 5}{E_0}\widehat i + {3 \over 5}{E_0}\widehat

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A 2$$\mu$$F capacitor C1 is first charged to a potential difference of 10V using a battery. Then the battery is removed

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A boy of mass 4 kg is standing on a piece of wood having mass 5 kg. If the coefficient of friction between the wood and

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A body of mass 1 kg rests on a horizontal floor with which it has a coefficient of static friction $${1 \over {\sqrt 3 }

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A particle of mass m moves in a circular orbit in a central potential field U(r) = U0r4. If Bohr's quantization conditio

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Seawater at a frequency f = 9 $$\times$$ 102 Hz, has permittivity $$\varepsilon $$ = 80$$\varepsilon $$0 and resistivity

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