JEE Main 2021 (Online) 24th February Morning Shift

Paper was held on
Wed, Feb 24, 2021 3:30 AM

## Chemistry

The electrode potential of M2+/M of 3d-series elements shows positive value for :

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Which of the following reagent is used for the following reaction ?
$$
\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{CH}_3 \stackr

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The gas released during anaerobic degradation of vegetation may lead to :

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Which of the following are isostructural pairs ?
A. $$SO_4^{2 - }$$ and $$CrO_4^{2 - }$$
B. SiCl4, and TiCl4
C. NH3 and

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Consider the elements Mg, Al, S, P and Si, the correct increasing order of their first ionization
enthalpy is :

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Out of the following, which type of interaction is reponsible for the stabilisation of $$\alpha $$-helix structure of pr

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The major components in "Gun Metal” are :

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Match List I with List II.
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.tg td{border-color:black;border

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Which of the following compound gives pink colour on reaction with phthalic anhydride in
conc. H2SO4 followed by treatme

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(A) HOCI + H2O2 → H3O+ + Cl- + O2
(B) I2 + H2O2 + 2OH- → 2I- + 2H2O + O2
Choose the correct option.

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Given below are two statements :
Statement I : Colourless cupric metaborate is reduced to cuprous metaborate in a lumino

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Which of the following ore is concentrated using group 1 cyanide salt ?

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In the following reaction the reason why meta-nitro product also formed is :

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What is the major product formed by HI on reaction with

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Al2O3 was leached with alkali to get X. The solution of X on passing of gas Y, forms Z.
X, Y and Z respectively are :

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'A' and 'B' in the following reactions are :

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Identify products A and B.

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In Freundlich adsorption isotherm, slope of AB line is :

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What is the final product (major) 'A' in the given reaction ?

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The product formed in the first step of the reaction of
with excess $$\mathrm{Mg/Et_2O}$$ ($$\mathrm{Et=C_2H_5}$$) is

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Number of amphoteric compounds among the following is ________.
(A) BeO
(B) BaO
(C) Be(OH)2
(D) Sr(OH)2

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The coordination number of an atom in a body-centered cubic structure is _______.
[Assume that the lattice is made up of

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The stepwise formation of $${\left[ {Cu{{\left( {N{H_3}} \right)}_4}} \right]^{2 + }}$$ is given below:
The value of st

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A proton and a Li3+ nucleus are accelerated by the same potential. If $$\lambda _{Li}$$ and $$\lambda _p$$ denote the
de

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At 1990 K and 1 atm pressure, there are equal number of Cl2, molecules and Cl atoms in the
reaction mixture. The value o

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When 9.45 g of CICH2COOH is added to 500 mL of water, its freezing point drops by 0.5°C. The dissociation constant of CI

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4.5 g of compound A (MW = 90) was used to make 250 mL of its aqueous solution. The
molarity of the solution in M is x $$

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The reaction of sulphur in alkaline medium is given below:
The values of 'a' is _______.
(Integer answer)

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For the reaction A(g) $$ \to $$ B(g) the value of the equilibrium constant at 300 K and 1 atm is equal to 100.0. The val

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Gaseous cyclobutene isomerises to butadiene in a first order process which has a 'k' value of 3.3 $$ \times $$ 10-4 s-1

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## Mathematics

If $$\int {{{\cos x - \sin x} \over {\sqrt {8 - \sin 2x} }}} dx = a{\sin ^{ - 1}}\left( {{{\sin x + \cos x} \over b}} \r

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The equation of the plane passing through the point (1, 2, -3) and perpendicular to the
planes 3x + y - 2z = 5 and 2x -

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If f : R $$ \to $$ R is a function defined by f(x)= [x - 1] $$\cos \left( {{{2x - 1} \over 2}} \right)\pi $$, where [.]

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The distance of the point (1, 1, 9) from the point of intersection of the line
$${{x - 3} \over 1} = {{y - 4} \over 2} =

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The population P = P(t) at time 't' of a certain species follows the differential equation
$${{dP} \over {dt}}$$
= 0.5P

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Let f : R → R be defined as f (x) = 2x – 1 and g : R - {1} → R be defined as g(x) =
$${{x - {1 \over 2}} \over {x - 1}}$

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The function
f(x) = $${{4{x^3} - 3{x^2}} \over 6} - 2\sin x + \left( {2x - 1} \right)\cos x$$ :

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$$\mathop {\lim }\limits_{x \to 0} {{\int\limits_0^{{x^2}} {\left( {\sin \sqrt t } \right)dt} } \over {{x^3}}}$$ is equa

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The value of
-15C1 + 2.15C2 – 3.15C3 + ... - 15.15C15 + 14C1 + 14C3 + 14C5 + ...+ 14C11 is :

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A scientific committee is to be formed from 6 Indians and 8 foreigners, which includes at
least 2 Indians and double the

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A man is walking on a straight line. The arithmetic mean
of the reciprocals of the intercepts of this line on the
coordi

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Two vertical poles are 150 m apart and the height of one is three times that of the other. If
from the middle point of t

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Let p and q be two positive numbers such that p + q = 2 and p4+q4 = 272. Then p and q are
roots of the equation :

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The area (in sq. units) of the part of the circle x2 + y2 = 36, which is outside the parabola
y2 = 9x, is :

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If the tangent to the curve y = x3 at the point P(t, t3) meets the curve again at Q, then the
ordinate of the point whic

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If
$${e^{\left( {{{\cos }^2}x + {{\cos }^4}x + {{\cos }^6}x + ...\infty } \right){{\log }_e}2}}$$
satisfies the equation

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An ordinary dice is rolled for a certain number of times. If the probability of getting an odd
number 2 times is equal t

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The locus of the mid-point of the line segment joining the focus of the parabola y2 = 4ax to a
moving point of the parab

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The system of linear equations
3x - 2y - kz = 10
2x - 4y - 2z = 6
x+2y - z = 5m
is inconsistent if :

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The statement among the following that is a tautology is :

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Let P = $$\left[ {\matrix{
3 & { - 1} & { - 2} \cr
2 & 0 & \alpha \cr
3 & { - 5} &

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The minimum value of $$\alpha $$ for which the equation $${4 \over {\sin x}} + {1 \over {1 - \sin x}} = \alpha $$
has a

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If the least and the largest real values of a, for which the equation z + $$\alpha $$|z – 1| + 2i = 0
(z $$ \in $$ C and

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Let three vectors $$\overrightarrow a ,\overrightarrow b $$ and $$\overrightarrow c $$ be such that $$\overrightarr

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$$\mathop {\lim }\limits_{n \to \infty } \tan \left\{ {\sum\limits_{r = 1}^n {{{\tan }^{ - 1}}\left( {{1 \over {1 + r +

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Let A = {n $$ \in $$ N: n is a 3-digit number}
B = {9k + 2: k $$ \in $$

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If one of the diameters of the circle x2 + y2 - 2x - 6y + 6 = 0 is a chord of another circle 'C',
whose center is at (2,

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If $$\int\limits_{ - a}^a {\left( {\left| x \right| + \left| {x - 2} \right|} \right)} dx = 22$$, (a > 2) and [x] den

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Let M be any 3 $$ \times $$ 3 matrix with entries from the set {0, 1, 2}. The maximum number of such matrices, for which

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Let Bi (i = 1, 2, 3) be three independent events in a sample space. The probability that only B1 occur is $$\alpha $$, o

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## Physics

A cube of side 'a' has point charges +Q located at each of its vertices except at the origin where the charge is $$-$$Q.

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In the given figure, a mass M is attached to a horizontal spring which is fixed on one side to a rigid support. The spri

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A current through a wire depends on time as i = $$\alpha$$0t + $$\beta$$t2where $$\alpha$$0 = 20 A/s and $$\beta$$ = 8 A

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Match List I with List II.
List I
List II
(a)
Isothermal
(i)
Pressure cons

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n mole of a perfect gas undergoes a cyclic process ABCA (see figure) consisting of the following processes.A $$ \to $$ B

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Each side of a box made of metal sheet in cubic shape is 'a' at room temperature 'T', the coefficient of linear expansio

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A cell E1 of emf 6V and internal resistance 2$$\Omega$$ is connected with another cell E2 of emf 4V and internal resista

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The focal length f is related to the radius of curvature r of the spherical convex mirror by :

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In a Young's double slit experiment, the width of the one of the slit is three times the other slit. The amplitude of th

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Four identical particles of equal masses 1 kg made to move along the circumference of a circle of radius 1 m under the a

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Consider two satellites S1 and S2 with periods of revolution 1 hr. and 8 hr. respectively revolving around a planet in c

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If Y, K and $$\eta $$ are the values of Young's modulus, bulk modulus and modulus of rigidity of any material respective

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If the velocity-time graph has the shape AMB, what would be the shape of the corresponding acceleration-time graph?

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In the given figure, the energy levels of hydrogen atom have been shown along with some transitions marked A, B, C, D an

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The work done by a gas molecule in an isolated system is given by, $$W = \alpha {\beta ^2}{e^{ - {{{x^2}} \over {\alpha

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Two stars of masses m and 2m at a distance d rotate about their common centre of mass in free space. The period of revol

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If an emitter current is changed by 4 mA, the collector current changes by 3.5 mA. The value of $$\beta$$ will be :

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Two equal capacitors are first connected in series and then in parallel. The ratio of the equivalent capacities in the t

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Moment of inertia (M. I.) of four bodies, having same mass and radius, are reported as; I1 = M.I. of thin circular ring

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An unpolarised light beam is incident on the polarizer of a polarization experiment and the intensity of light beam emer

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A ball with a speed of 9 m/s collides with another identical ball at rest. After the collision, the direction of each ba

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An audio signal vm = 20 sin 2$$\pi$$(1500t) amplitude modulates a carrier vc = 80 sin 2$$\pi$$(100,000t).The value of pe

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An electromagnetic wave of frequency 5 GHz, is travelling in a medium whose relative electric permittivity and relative

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A hydraulic press can lift 100 kg when a mass 'm' is placed on the smaller piston. It can lift ___________ kg when the d

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An inclined plane is bent in such a way that the vertical cross-section is given by $$y = {{{x^2}} \over 4}$$ where y is

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A common transistor radio set requires 12 V (D.C.) for its operation. The D.C. source is constructed by using a transfor

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The coefficient of static friction between a wooden block of mass 0.5 kg and a vertical rough wall is 0.2. The magnitude

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A resonance circuit having inductance and resistance 2 $$\times$$ 10$$-$$4 H and 6.28$$\Omega$$ respectively oscillates

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In connection with the circuit drawn below, the value of current flowing through 2 k$$\Omega$$ resistor is _________ $$\

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Given below are two statements : Statement I : Two photons having equal linear momenta have equal wavelengths.Statement

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