JEE Main 2021 February 24, Shift 2 Question Paper with Solutions

All 90 questions from the JEE Main 2021 (February 24, Shift 2) shift — Physics (30), Chemistry (30) and Mathematics (30) — each with the correct answer (answer key) and a step-by-step solution. Read it free online, or attempt the full paper as a timed mock test.

Physics PYQs 2021 Chemistry PYQs 2021 Mathematics PYQs 2021

Physics30 questions

Q1Single correctUnits and Measurements

The period of oscillation of a simple pendulum is

T = 2 π \frac{L}{g}

. Measured value of L is

1.0 m

from meter scale having a minimum division of

1 mm

and time of one complete oscillation is

1.95 s

measured from stopwatch of

0.01 s

resolution. The percentage error in the determination of g will be:

(A)

1.03%

(B)

1.33%

(C)

1.30%

(D)

1.13%

Q2Single correctWork, Energy and Power

A particle is projected with velocity

v_{0}

along x-axis. A damping force is acting on the particle which is proportional to the square of the distance from the origin i.e.

ma = - α x^{2}

. The distance at which the particle stops:

(A)

(\frac{2 v _{0}}{3 α})^{\frac{1}{3}}

(B)

(\frac{3 m v _{0}^{2}}{2 α})^{\frac{1}{3}}

(C)

(\frac{3 v _{0}^{2}}{2 α})^{\frac{1}{2}}

(D)

(\frac{2 v _{0}^{2}}{3 α})^{\frac{1}{2}}

Q3Single correctRotational Motion

A circular hole of radius

(\frac{a}{2})

is cut out of a circular disc of radius a as shown in figure. The centroid of the remaining circular portion with respect to point O will be:

Circular disc radius a centred at distance a from O on the x-axis, with a circular hole of radius a/2 cut tangent to the right edge.

(A)

\frac{2}{3} a

(B)

\frac{5}{6} a

(C)

\frac{1}{6} a

(D)

\frac{10}{11} a

Q4Single correctGravitation

A body weighs

49 N

on a spring balance at the north pole. What will be its weight recorded on the same weighing machine, if it is shifted to the equator?
[Use

g = \frac{GM}{R ^{2}} = 9.8 m s^{- 2}

and radius of earth,

R = 6400 km

(A)

49.17 N

(B)

48.83 N

(C)

49.83 N

(D)

49 N

Q5Single correctThermodynamics

If one mole of an ideal gas at

(P_{1}, V_{1})

is allowed to expand reversibly and isothermally (A to B) its pressure is reduced to one-half of the original pressure (see figure). This is followed by a constant volume cooling till its pressure is reduced to one-fourth of the initial value (

B \to C

). Then it is restored to its initial state by a reversible adiabatic compression (C to A). The net workdone by the gas is equal to:

P-V cycle: isotherm A(V1,P1) to B(2V1,P1/2), isochore B to C(2V1,P1/4), adiabatic compression C to A.

(A)

0

(B)

RT ln (2)

(C)

- \frac{RT}{2 ( γ - 1 )}

(D)

RT [ln (2) - \frac{1}{2 ( γ - 1 )}]

Q6Single correctKinetic Theory of Gases

On the basis of kinetic theory of gases, the gas exerts pressure because its molecules:

(A)

continuously stick to the walls of container.

(B)

suffer change in momentum when impinge on the walls of container.

(C)

continuously lose their energy till it reaches wall.

(D)

are attracted by the walls of container.

Q7Single correctOscillations and Waves

In the given figure, a body of mass

M

is held between two massless springs, on a smooth inclined plane. The free ends of the springs are attached to firm supports. If each spring has spring constant

k

, the frequency of oscillation of given body is:

Block M on a smooth incline of angle alpha, held between two springs (each constant k) attached to supports at the top and bottom of the incline.

(A)

\frac{1}{2 π} \frac{2 k}{M g sin α}

(B)

\frac{1}{2 π} \frac{k}{M g} sin α

(C)

\frac{1}{2 π} \frac{k}{2 M}

(D)

\frac{1}{2 π} \frac{2 k}{M}

Q8Single correctOscillations and Waves

When a particle executes SHM, the nature of graphical representation of velocity as a function of displacement is:

(A)

straight line

(B)

elliptical

(C)

circular

(D)

parabolic

Q9Single correctOscillations and Waves

Which of the following equations represents a travelling wave?

(A)

y = A sin (15 x - 2 t)

(B)

y = A e^{x} cos (ω t - θ)

(C)

y = A e^{- x^{2}} (v t + θ)

(D)

y = A sin x cos ω t

Q10Single correctElectrostatics

Two electrons each are fixed at a distance

2 d

. A third charge proton placed at the midpoint is displaced slightly by a distance

x (x ≪ d)

perpendicular to the line joining the two fixed charges. Proton will execute simple harmonic motion having angular frequency:
(

m =

mass of charged particle)

(A)

(\frac{π ε _{0} m d ^{3}}{2 q ^{2}})^{\frac{1}{2}}

(B)

(\frac{2 π ε _{0} m d ^{3}}{q ^{2}})^{\frac{1}{2}}

(C)

(\frac{q ^{2}}{2 π ε _{0} m d ^{3}})^{\frac{1}{2}}

(D)

(\frac{2 q ^{2}}{π ε _{0} m d ^{3}})^{\frac{1}{2}}

Q11Single correctMagnetic Effects of Current and Magnetism

A soft ferromagnetic material is placed in an external magnetic field. The magnetic domains:

(A)

have no relation with external magnetic field.

(B)

decrease in size and changes orientation.

(C)

increase in size but no change in orientation.

(D)

may increase or decrease in size and change its orientation.

Q12Single correctElectromagnetic Induction and Alternating Currents

The figure shows a circuit that contains four identical resistors with resistance

R = 2.0 Ω

, two identical inductors with inductance

L = 2.0 mH

and an ideal battery with E.M.F.

E = 9 V

. The current i just after the switch S is closed will be:

9 V battery with switch S feeding three parallel branches (R; L in series with R; R in series with L) and a series R in the bottom rail.

(A)

9 A

(B)

3.37 A

(C)

2.25 A

(D)

3.0 A

Q13Single correctDual Nature of Matter and Radiation

An X-ray tube is operated at

1.24

million volt. The shortest wavelength of the produced photon will be:

(A)

1 0^{- 3} nm

(B)

1 0^{- 2} nm

(C)

1 0^{- 4} nm

(D)

1 0^{- 1} nm

Q14Single correctElectromagnetic Waves

Match List - I with List - II.

List-I	List-II
(a). Source of microwave frequency	(i). Radioactive decay of nucleus
(b). Source of infrared frequency	(ii). Magnetron
(c). Source of Gamma Rays	(iii). Inner shell electrons
(d). Source of X-rays	(iv). Vibration of atoms and molecules
	(v). LASER
	(vi). RC circuit

(A)

(a)-(ii), (b)-(iv), (c)-(vi), (d)-(iii)

(B)

(a)-(vi), (b)-(iv), (c)-(i), (d)-(v)

(C)

(a)-(vi), (b)-(v), (c)-(i), (d)-(iv)

(D)

(a)-(ii), (b)-(iv), (c)-(i), (d)-(iii)

Q15Single correctOptics

If the source of light used in a Young's double slit experiment is changed from red to violet:

(A)

consecutive fringe lines will come closer.

(B)

the fringes will become brighter.

(C)

the central bright fringe will become a dark

(D)

the intensity of minima will increase.

Q16Single correctDual Nature of Matter and Radiation

The de Broglie wavelength of a proton and

α

-particle are equal. The ratio of their velocities is

(A)

4 : 1

(B)

4 : 3

(C)

1 : 4

(D)

4 : 2

Q17Single correctAtoms and Nuclei

According to Bohr atom model, in which of the following transitions will the frequency be maximum?

(A)

n = 3

n = 2

(B)

n = 5

n = 4

(C)

n = 4

n = 3

(D)

n = 2

n = 1

Q18Single correctElectronic Devices

The logic circuit shown above is equivalent to :

A and (B through a NOT gate) feed an OR gate whose output passes through a NOT gate to C.

(A)

(B)

(C)

(D)

Q19Single correctElectronic Devices

Zener breakdown occurs in a

p - n

junction having

p

and

n

both:

(A)

lightly doped and have narrow depletion layer.

(B)

heavily doped and have wide depletion layer.

(C)

lightly doped and have wide depletion layer.

(D)

heavily doped and have narrow depletion layer.

Q20Single correctElectronic Devices

Given below are two statements:
Statement I :

p - n

junction diodes can be used to function as a transistor, simply by connecting two diodes, back to back, which acts as the base terminal
Statement II: In the study of transistors, the amplification factor

β

indicates ratio of the collector current to the base current.
In the light of the above statements, choose the correct answer from the options given below.

(A)

Both Statement I and Statement II are false

(B)

Statement I is true but Statement II is false

(C)

Statement I is false but Statement II is true

(D)

Both Statement I and Statement II are true

Q21NumericalWork, Energy and Power

Two solids A and B of mass

1

kg and

2

kg respectively are moving with equal linear momentum. The ratio of their kinetic energies

(K . E .)_{A} : (K . E .)_{B}

will be

\frac{A}{1}

, so the value of A will be __________.

Q22NumericalRotational Motion

A uniform thin bar of mass

6

kg and length

2.4

meter is bent to make an equilateral hexagon. The moment of inertia about an axis passing through the centre of mass and perpendicular to the plane of hexagon is __________

\times 1 0^{- 1} kg m^{2}

Q23NumericalProperties of Solids and Liquids

A uniform metallic wire is elongated by

0.04

m when subjected to a linear force F. The elongation, if its length and diameter is doubled and subjected to the same force will be __________ cm.

Q24NumericalKinetic Theory of Gases

The root-mean-square speed of molecules of a given mass of a gas at

27^{\circ} C

and

1

atmosphere pressure is

200 m s^{- 1}

. The root-mean-square speed of molecules of the gas at

127^{\circ} C

and

2

atmosphere pressure is

\frac{x}{3} m s^{- 1}

. The value of x will be __________.

Q25NumericalOscillations and Waves

Two cars are approaching each other at an equal speed of

7.2 km hr^{- 1}

. When they see each other, both blow horns having a frequency of

676

Hz. The beat frequency heard by each driver will be __________ Hz. [Velocity of sound in air is

340 m s^{- 1}

Q26NumericalElectrostatics

A point charge of

+ 12 μ C

is at a distance

6

cm vertically above the centre of a square of side

12

cm as shown in figure. The magnitude of the electric flux through the square will be __________

\times 1 0^{3} N m^{2} C^{- 1}

A +q point charge 6 cm vertically above the centre of a square of side 12 cm shown in perspective.

Q27NumericalCurrent Electricity

A cylindrical wire of radius

0.5

mm and conductivity

5 \times 1 0^{7} S m^{- 1}

is subjected to an electric field of

10

m^{- 1}

. The expected value of current in the wire will be

x^{3} π

mA. The value of x is __________.

Q28NumericalElectromagnetic Induction and Alternating Currents

A series LCR circuit is designed to resonate at an angular frequency

ω_{0} = 1 0^{5} rad s^{- 1}

. The circuit draws

16

W power from

120

V source at resonance. The value of resistance R in the circuit is __________

Ω

Q29NumericalElectromagnetic Waves

An electromagnetic wave of frequency

3

GHz enters a dielectric medium of relative electric permittivity

2.25

from vacuum. The wavelength of this wave in that medium will be __________

\times 1 0^{- 2}

cm.

Q30NumericalElectromagnetic Waves

A signal of

0.1

kW is transmitted in a cable. The attenuation of cable is

- 5

dB per km and cable length is

20

km. The power received at the receiver is

1 0^{- x}

W. The value of x is __________. [Gain in dB

= 10 lo g_{10} (\frac{P _{O}}{P _{i}})

]

Chemistry30 questions

Q31Single correctAtomic Structure

According to Bohr's atomic theory:
(A) Kinetic energy of electron is

\propto \frac{Z ^{2}}{n ^{2}}

.
(B) The product of velocity (v) of electron and principal quantum number (n),

v n \propto Z^{2}

.
(C) Frequency of revolution of electron in an orbit is

\propto \frac{Z ^{3}}{n ^{3}}

.
(D) Coulombic force of attraction on the electron is

\propto \frac{Z ^{3}}{n ^{4}}

.
Choose the most appropriate answer from the options given below:

(A)

(A), (C) and (D) only

(B)

(A) and (D) only

(C)

(C) only

(D)

(A) only

Q32Single correctChemical Bonding and Molecular Structure

The correct set from the following in which both pairs are in correct order of melting point is:

(A)

LiF > LiCl; NaCl > MgO

(B)

LiCl > LiF; MgO > NaCl

(C)

LiCl > LiF; NaCl > MgO

(D)

LiF > LiCl; MgO > NaCl

Q33Single correctChemical Bonding and Molecular Structure

The correct shape and

I - I - I

bond angles respectively in

I_{3}^{-}

ion are:

(A)

T-shaped; 18 0^{\circ} and 9 0^{\circ}

(B)

Distorted trigonal planar; 13 5^{\circ} and 9 0^{\circ}

(C)

Trigonal planar; 12 0^{\circ}

(D)

Linear; 18 0^{\circ}

Q34Single correctClassification of Elements and Periodicity in Properties

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: Hydrogen is the most abundant element in the Universe, but it is not the most abundant gas in the troposphere.
Reason R: Hydrogen is the lightest element.
In the light of the above statements, choose the correct answer from the options given below:

(A)

Both A and R are true but R is NOT the correct explanation of A

(B)

Both A and R are true and R is the correct explanation of A

(C)

A is true but R is false

(D)

A is false but R true

Q35Single correctPrinciples Related to Practical Chemistry

Match List - I with List - II.

List-I (Salt)	List-II (Flame colour wavelength)
(a). $LiCl$	(i). $455.5 nm$
(b). $NaCl$	(ii). $670.8 nm$
(c). $RbCl$	(iii). $780.0 nm$
(d). $CsCl$	(iv). $589.2 nm$

(A)

(a)-(iv), (b)-(ii), (c)-(iii), (d)-(i)

(B)

(a)-(i), (b)-(iv), (c)-(ii), (d)-(iii)

(C)

(a)-(ii), (b)-(i), (c)-(iv), (d)-(iii)

(D)

(a)-(ii), (b)-(iv), (c)-(iii), (d)-(i)

Q36Single correctHydrocarbons

Which one of the following compounds is non-aromatic?

(A)

(B)

(C)

(D)

Q37Single correctOrganic Compounds Containing Nitrogen

What is the correct sequence of reagents used for converting nitrobenzene into m-dibromobenzene?

Nitrobenzene converted through four sequential steps into m-dibromobenzene.

(A)

Q37 option 1 reagent sequence over four arrows

(B)

Q37 option 2 reagent sequence over four arrows

(C)

Q37 option 3 reagent sequence over four arrows

(D)

Q37 option 4 reagent sequence over four arrows

Q38Single correctOrganic Compounds Containing Halogens

The correct order of the following compounds showing increasing tendency towards nucleophilic substitution reaction is:

Four benzene structures (i) chlorobenzene, (ii) p-nitrochlorobenzene, (iii) 2,4-dinitrochlorobenzene, (iv) 2,4,6-trinitrochlorobenzene.

(A)

(iv) < (i) < (ii) < (iii)

(B)

(i) < (ii) < (iii) < (iv)

(C)

(iv) < (i) < (iii) < (ii)

(D)

(iv) < (iii) < (ii) < (i)

Q39Single correctPrinciples Related to Practical Chemistry

Given below are two statements:
Statement I: The value of the parameter "Biochemical Oxygen Demand (BOD)" is important for survival of aquatic life.
Statement II: The optimum value of BOD is

6.5 ppm

.
In the light of the above statements, choose the most appropriate answer from the options given below:

(A)

Statement I is true but Statement II is false

(B)

Statement I is false but Statement II is true

(C)

Both Statement I and Statement II are false

(D)

Both Statement I and Statement II are true

Q40Single correctSome Basic Principles of Organic Chemistry

Most suitable salt which can be used for efficient clotting of blood will be?

(A)

FeCl_{3}

(B)

Mg(HCO_{3})_{2}

(C)

FeSO_{4}

(D)

NaHCO_{3}

Q41Single correctd- and f-Block Elements

Match List - I with List - II.

List-I (Metal)	List-II (Ores)
(a). $Aluminium$	(i). $Siderite$
(b). $Iron$	(ii). $Calamine$
(c). $Copper$	(iii). $Kaolinite$
(d). $Zinc$	(iv). $Malachite$

(A)

(a)-(ii), (b)-(iv), (c)-(i), (d)-(iii)

(B)

(a)-(iv), (b)-(iii), (c)-(ii), (d)-(i)

(C)

(a)-(i), (b)-(ii), (c)-(iii), (d)-(iv)

(D)

(a)-(iii), (b)-(i), (c)-(iv), (d)-(ii)

Q42Single correctd- and f-Block Elements

The incorrect statement among the following is:

(A)

Cr_{2} O_{3} is an amphoteric oxide

(B)

VOSO_{4} is a reducing agent

(C)

RuO_{4} is an oxidizing agent

(D)

Red colour of ruby is due to the presence of Co^{3 +}

Q43Single correctd- and f-Block Elements

What is the correct order of the following elements with respect to their density?

(A)

Zn < Cu < Co < Fe < Cr

(B)

Cr < Zn < Co < Cu < Fe

(C)

Zn < Cr < Fe < Co < Cu

(D)

Cr < Fe < Co < Cu < Zn

Q44Single correctCoordination Compounds

The calculated magnetic moments (spin only value) for species

[FeCl_{4}]^{2 -}

[Co(C_{2} O_{4})_{3}]^{3 -}

and

MnO_{4}^{2 -}

respectively are:

(A)

4.90, 0 and 1.73 BM

(B)

4.90, 0 and 2.83 BM

(C)

5.82, 0 and 0 BM

(D)

5.92, 4.90 and 0 BM

Q45Single correctOrganic Compounds Containing Oxygen

Which of the following reagent is suitable for the preparation of the product in the above reaction?

Carvone reacting with a reagent (?) to give limonene (ketone reduced to CH2).

(A)

Red P + Cl_{2}

(B)

NaBH_{4}

(C)

NH_{2} - NH_{2} / C_{2} H_{5} O ⊖ Na \oplus

(D)

Ni / H_{2}

Q46Single correctHydrocarbons

Which one of the following carbonyl compounds cannot be prepared by addition of water on an alkyne in the presence of

HgSO_{4}

and

H_{2} SO_{4}

(A)

(B)

(C)

(D)

Q47Single correctOrganic Compounds Containing Nitrogen

The diazonium salt of which of the following compounds will form a coloured dye on reaction with

β

-Naphthol in NaOH?

(A)

(B)

(C)

(D)

Q48Single correctOrganic Compounds Containing Oxygen

Match List - I with List - II.

List-I (Salt)	List-II (Flame colour wavelength)
a. $R - CO - Cl \to R - CHO$	i. $Br_{2} / NaOH$
b. $R - CH_{2} - COOH \to R - Cl ∣ CH - COOH$	ii. $H_{2} / Pd - BaSO_{4}$
c. $R - CO - NH_{2} \to R - NH_{2}$	iii. $Zn(Hg) / Conc. HCl$
d. $R - CO - CH_{3} \to R - CH_{2} - CH_{3}$	iv. $Cl_{2} / Red P, H_{2} O$

(A)

(a)-(ii), (b)-(iv), (c)-(i), (d)-(iii)

(B)

(a)-(iii), (b)-(i), (c)-(iv), (d)-(ii)

(C)

(a)-(i), (b)-(iii), (c)-(iv), (d)-(ii)

(D)

(a)-(iii), (b)-(iv), (c)-(i), (d)-(ii)

Q49Single correctSome Basic Principles of Organic Chemistry

In polymer Buna-S 'S' stands for:

(A)

Strength

(B)

Sulphur

(C)

Sulphonation

(D)

Styrene

Q50Single correctBiomolecules

Match List - I with List - II.

List-I	List-II
a. Valium	i. Antifertility drug
b. Morphine	ii. Pernicious anaemia
c. Norethindrone	iii. Analgesic
d. Vitamin $B_{12}$	iv. Tranquilizer

(A)

(a)-(iv), (b)-(iii), (c)-(ii), (d)-(i)

(B)

(a)-(ii), (b)-(iv), (c)-(iii), (d)-(i)

(C)

(a)-(i), (b)-(iii), (c)-(iv), (d)-(ii)

(D)

(a)-(iv), (b)-(iii), (c)-(i), (d)-(ii)

Q51NumericalSome Basic Concepts in Chemistry

The formula of a gaseous hydrocarbon which requires 6 times of its own volume of

O_{2}

for complete oxidation and produces 4 times its own volume of

CO_{2}

C_{x} H_{y}

. The value of y is __________.

Q52NumericalPrinciples Related to Practical Chemistry

1.86 g of aniline completely reacts to form acetanilide. 10% of the product is lost during purification. Amount of acetanilide obtained after purification (in g) is __________

\times 1 0^{- 2}

Q53NumericalSome Basic Concepts in Chemistry

The volume occupied by 4.75 g of acetylene gas at

50^{\circ} C

and 740 mm Hg pressure is __________ L.
(Rounded off to the nearest integer)
[Given

R = 0.0826 L atm K^{- 1} mol^{- 1}

]

Q54NumericalChemical Thermodynamics

Assuming ideal behaviour, the magnitude of log K for the following reaction at

25^{\circ} C

x \times 1 0^{- 1}

. The value of x is __________. (Integer answer)
[Given:

Δ_{f} G^{\circ} (HC \equiv CH) = - 2.04 \times 1 0^{5} J mol^{- 1}; Δ_{f} G^{\circ} (C_{6} H_{6}) = - 1.24 \times 1 0^{5} J mol^{- 1}; R = 8.314 J K^{- 1} mol^{- 1}

]

Q55NumericalEquilibrium

The solubility product of

PbI_{2}

8.0 \times 1 0^{- 9}

. The solubility of lead iodide in 0.1 molar solution of lead nitrate is

x \times 1 0^{- 6}

mol /L. The value of x is __________ (Rounded off to the nearest integer)
[Given

2 = 1.41

]

Q56NumericalSolutions

C_{6} H_{6}

freezes at

5.5^{\circ} C

. The temperature at which a solution of 10 g of

C_{4} H_{10}

in 200 g of

C_{6} H_{6}

freeze is __________

^{\circ} C

. (nearest integer value), (The molal freezing point depression constant of

C_{6} H_{6}

5.12^{\circ} C/m

Q57NumericalRedox Reactions and Electrochemistry

The magnitude of the change in oxidising power of the

MnO_{4}^{-} / Mn^{2 +}

couple is

x \times 1 0^{- 4}

V if the

H^{+}

concentration is decreased from 1 M to

1 0^{- 4}

M at

25^{\circ} C

. (Assume concentration of

MnO_{4}^{-}

and

Mn^{2 +}

to be same on change in

H^{+}

concentration). The value of x is __________.
(Rounded off to the nearest integer)
[Given:

\frac{2.303 RT}{F} = 0.059

]

Q58NumericalChemical Kinetics

Sucrose hydrolyses in acid solution into glucose and fructose following first order rate law with a half-life of 3.33 h at

25^{\circ} C

. After 9 h, the fraction of sucrose remaining is f. The value of

lo g_{10} (\frac{1}{f})

is __________

\times 1 0^{- 2}

.
(Rounded off to the nearest integer)
[Assume: ln10 = 2.303, ln 2 = 0.693]

Q59Numericalp-Block Elements

Among the following allotropic forms of sulphur, the number of allotropic forms, which will show paramagnetism is __________.
(A)

α

-sulphur
(B)

β

-sulphur
(C)

S_{2}

-form

Q60NumericalOrganic Compounds Containing Nitrogen

The total number of amines among the following which can be synthesized by Gabriel synthesis is __________.

Four amine structures labelled A, B, C, D.

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