(a)→(ii),(b)→(iii),(c)→(iv),(d)→(i)

a → iii, b → iv, c → i, d → ii

JEE Main 2021 February 24, Shift 1 Question Paper with Solutions

All 90 questions from the JEE Main 2021 (February 24, Shift 1) 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 work done by a gas molecule in an isolated system is given by,

W = α β^{2} e^{- \frac{x ^{2}}{α k T}}

, where x is the displacement, k is the Boltzmann constant and T is the temperature.

α

and

β

are constants. Then the dimensions of

β

will be:

(A)

M^{2} L T^{2}

(B)

M L^{2} T^{- 2}

(C)

MLT^{- 2}

(D)

M^{0} L T^{0}

Q2Single correctKinematics

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

Velocity-time graph shaped AMB: from A (top-left, positive V) a straight line descends to M (vertex below the t-axis) then rises to B (top-right), with a dashed horizontal line joining A and B.

(A)

(B)

(C)

(D)

Q3Single correctRotational Motion

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

I_{1} =

M.I. of thin circular ring about its diameter,

I_{2} =

M.I. of circular disc about an axis perpendicular to disc and going through the centre,

I_{3} =

M.I. of solid cylinder about its axis and

I_{4} =

M.I. of solid sphere about its diameter.
Then:

(A)

I_{1} + I_{2} = I_{3} + \frac{5}{2} I_{4}

(B)

I_{1} + I_{3} < I_{2} + I_{4}

(C)

I_{1} = I_{2} = I_{3} > I_{4}

(D)

I_{1} = I_{2} = I_{3} < I_{4}

Q4Single correctGravitation

Consider two satellites

S_{1}

and

S_{2}

with periods of revolution 1hr and 8hr respectively revolving around a planet in circular orbits. The ratio of angular velocity of satellite

S_{1}

to the angular velocity of satellite

S_{2}

is:

(A)

8 : 1

(B)

2 : 1

(C)

1 : 8

(D)

1 : 4

Q5Single correctGravitation

Four identical particles of equal masses 1 kg made to move along the circumference of a circle of radius 1 m under the action of their own mutual gravitational attraction. The speed of each particle will be:

(A)

G (1 + 22)

(B)

\frac{G}{2} (1 + 22)

(C)

\frac{G}{2} 22 - 1

(D)

\frac{1 + 2 2 G}{2}

Q6Single correctGravitation

Two stars of masses

m

and

2 m

at a distance

d

rotate about their common centre of mass in free space. The period of revolution is:

(A)

2 π \frac{d ^{3}}{3 G m}

(B)

2 π \frac{3 G m}{d ^{3}}

(C)

\frac{1}{2 π} \frac{3 G m}{d ^{3}}

(D)

\frac{1}{2 π} \frac{d ^{3}}{3 G m}

Q7Single correctProperties of Solids and Liquids

If Y, K and

η

are the values of Young's modulus, bulk modulus and modulus of rigidity of any material respectively. The correct relation for these parameters is:

(A)

Y = \frac{9 Kη}{3 K - η} N m^{- 2}

(B)

η = \frac{3 Y K}{9 K + Y} N m^{- 2}

(C)

K = \frac{Y η}{9 η - 3 Y} N m^{- 2}

(D)

Y = \frac{9 Kη}{2 η + 3 K} N m^{- 2}

Q8Single correctProperties of Solids and Liquids

Each side of a box made of metal sheet in cubic shape is a at room temperature T, the coefficient of linear expansion of the metal sheet is

α

. The metal sheet is heated uniformly, by a small temperature

Δ T

, so that its new temperature is

T + Δ T

. Calculate the increase in the volume of the metal box.

(A)

4 a^{3} α Δ T

(B)

3 a^{3} α Δ T

(C)

4 π a^{3} α Δ T

(D)

\frac{4}{3} π a^{3} α Δ T

Q9Single correctThermodynamics

Match List I with List II.

List I	List II
(a). Isothermal	(i). Pressure constant
(b). Isochoric	(ii). Temperature constant
(c). Adiabatic	(iii). Volume constant
(d). Isobaric	(iv). Heat content is constant

(A)

(a) \to (ii), (b) \to (iii), (c) \to (i v), (d) \to (i)

(B)

(a) \to (iii), (b) \to (ii), (c) \to (i), (d) \to (i v)

(C)

(a) \to (i), (b) \to (iii), (c) \to (ii), (d) \to (i v)

(D)

(a) \to (ii), (b) \to (i v), (c) \to (iii), (d) \to (i)

Q10Single correctThermodynamics

n mole of a perfect gas undergoes a cyclic process ABCA (see figure) consisting of the following processes.

A \to B

: Isothermal expansion at temperature T so that the volume is doubled from

V_{1}

V_{2} = 2 V_{1}

and pressure changes from

P_{1}

P_{2}

B \to C

: Isobaric compression at pressure

P_{2}

to initial volume

V_{1}

C \to A

: Isochoric change leading to change of pressure from

P_{2}

P_{1}

.
Total work done in the complete cycle ABCA is:

P-V diagram of cycle ABCA: A at (V1,P1), curved path A to B down to (V2=2V1,P2), isobaric B to C leftwards at P2 to V1, isochoric C to A upwards at V1.

(A)

nRT ln 2 - \frac{1}{2}

(B)

nRT ln 2

(C)

nRT ln 2 + \frac{1}{2}

(D)

0

Q11Single correctOscillations and Waves

In the given figure, a mass

M

is attached to a horizontal spring which is fixed on one side to a rigid support. The spring constant of the spring is

k

. The mass oscillates on a frictionless surface with time period

T

and amplitude

A

. When the mass is in equilibrium position, as shown in the figure, another mass

m

is gently fixed upon it. The new amplitude of oscillation will be:

Block M on a hatched horizontal floor attached by a horizontal spring of constant k to a hatched wall on the right.

(A)

A \frac{M + m}{M}

(B)

A \frac{M}{M - m}

(C)

A \frac{M - m}{M}

(D)

A \frac{M}{M + m}

Q12Single correctElectrostatics

A cube of side

a

has point charges

+ Q

located at each of its vertices except at the origin where the charge is

- Q

. The electric field at the centre of cube is:

Cube of side a with axes x (up), y (front-left), z (right); +Q at seven vertices and -Q at the origin vertex.

(A)

\frac{- Q}{3 3 π ε _{0} a ^{2}} (\overset{x}{^} + \overset{y}{^} + \overset{z}{^})

(B)

\frac{Q}{3 3 π ε _{0} a ^{2}} (\overset{x}{^} + \overset{y}{^} + \overset{z}{^})

(C)

\frac{- 2 Q}{3 3 π ε _{0} a ^{2}} (\overset{x}{^} + \overset{y}{^} + \overset{z}{^})

(D)

\frac{2 Q}{3 3 π ε _{0} a ^{2}} (\overset{x}{^} + \overset{y}{^} + \overset{z}{^})

Q13Single correctElectrostatics

Two equal capacitors are first connected in series and then in parallel. The ratio of the equivalent capacities in the two cases will be:

(A)

1 : 2

(B)

1 : 4

(C)

4 : 1

(D)

2 : 1

Q14Single correctCurrent Electricity

A current through a wire depends on time as

i = α_{0} t + β t^{2}

, where

α_{0} = 20

s^{- 1}

and

β = 8

s^{- 2}

. Find the charge crossed through a section of the wire in 15 s.

(A)

2250

(B)

11250

(C)

2100

(D)

260

Q15Single correctCurrent Electricity

A cell

E_{1}

of emf 6 V and internal resistance

2Ω

is connected with another cell

E_{2}

of emf 4 V and internal resistance 8

Ω

(as shown in the figure). The potential difference across points X and Y is:

Series loop: from P, cell E1 (6 V, 2 ohm), node X, cell E2 (4 V, 8 ohm), to Y, with a rectangular return wire from P to Y.

(A)

10.0

(B)

5.6

(C)

2.0

(D)

3.6

Q16Single correctOptics

The focal length

f

is related to the radius of curvature

r

of the spherical convex mirror by:

(A)

f = - \frac{1}{2} r

(B)

f = + \frac{1}{2} r

(C)

f = r

(D)

f = - r

Q17Single correctOptics

In a Young's double slit experiment, the width of the one of the slit is three times the other slit. The amplitude of the light coming from a slit is proportional to the slit-width. Find the ratio of the maximum to the minimum intensity in the interference pattern.

(A)

1 : 4

(B)

2 : 1

(C)

3 : 1

(D)

4 : 1

Q18Single correctDual Nature of Matter and Radiation

Given below are two statements:
Statement I: Two photons having equal linear momenta have equal wavelengths.
Statement II: If the wavelength of the photon is decreased, then the momentum and energy of a photon will also decrease.
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)

Both Statement I and Statement II are true

(C)

Statement I is true but Statement II is false

(D)

Statement I is false but Statement II is true

Q19Single correctAtoms and Nuclei

In the given figure, the energy levels of hydrogen atom have been shown along with some transitions marked

A, B, C, D

and

E

.
The transitions

A, B

and

C

respectively represent

Hydrogen energy-level diagram (n=1 at -13.6 eV up to 0 eV with a Continuum box), with downward transition arrows A (n2->n1), B (n5->n2), C (0 eV->n3), D (n4->n2), E (0 eV->n1).

(A)

The ionization potential of hydrogen, second member of Balmer series and third member of Paschen series.

(B)

The series limit of Lyman series, second member of Balmer series and second member of Paschen series.

(C)

The series limit of Lyman series, third member of Balmer series and second member of Paschen series.

(D)

The first member of the Lyman series, third member of Balmer series and second member of Paschen series.

Q20Single correctElectronic Devices

If an emitter current is changed by

4

mA, the collector current changes by

3.5

mA. The value of

β

will be:

(A)

3.5

(B)

0.5

(C)

0.875

(D)

7

Q21NumericalLaws of Motion

The coefficient of static friction between a wooden block of mass

0.5

kg and a vertical rough wall is

0.2

. The magnitude of the horizontal force that should be applied on the block to keep it adhere to the wall will be________N.

g = 10

s^{- 2}

Q22NumericalLaws of Motion

An inclined plane is bent in such a way that the vertical cross-section is given by

y = \frac{x ^{2}}{4}

where y is in vertical and x in horizontal direction. If the upper surface of this curved plane is rough with coefficient of friction

μ = 0.5

, the maximum height in cm at which a stationary block will not slip downward is________cm.

Q23NumericalWork, Energy and Power

A ball with a speed of

9

s^{- 1}

collides with another identical ball at rest. After the collision, the direction of each ball makes an angle of

3 0^{\circ}

with the original direction. If the ratio of velocities of the balls after the collision is x:y, then what is the value of x?

Q24NumericalProperties of Solids and Liquids

A hydraulic press can lift

100

kg when a mass m is placed on the smaller piston. It can lift ____ kg when the diameter of the larger piston is increased by

4

times and that of the smaller piston is decreased by

4

times keeping the same mass m on the smaller piston.

Q25NumericalElectromagnetic Induction and Alternating Currents

A common transistor radio set requires

12

V D.C. for its operation. The D.C. source is constructed by using a transformer and a rectifier circuit, which are operated at

220

V A.C. on standard domestic A.C. supply. The number of turns of secondary coil are

24

, then the number of turns of primary are________.

Q26NumericalElectromagnetic Induction and Alternating Currents

A resonance circuit having inductance and resistance

2 \times 1 0^{- 4}

H and

6.28

Ω

respectively oscillates at

10

MHz frequency. The value of quality factor of this resonator is________.

π = 3.14

Q27NumericalElectromagnetic Waves

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

2

. Its velocity in this medium is ____

\times 1 0^{7}

s^{- 1}

Q28NumericalOptics

An unpolarized light beam is incident on the polarizer of a polarization experiment and the intensity of light beam emerging from the analyzer is measured as 100 Lumens. Now, if the analyzer is rotated around the horizontal axis (direction of light) by

3 0^{\circ}

in clockwise direction, the intensity of emerging light will be________Lumens.

Q29NumericalCurrent Electricity

In connection with the circuit drawn below, the value of current flowing through

2

Ω

resistor is________

\times 1 0^{- 4}

Zener regulator: 10 V battery, a 2 k-ohm resistor and a 5 V Zener diode in parallel, with a 1 k-ohm series resistor in the top rail.

Q30NumericalElectromagnetic Waves

An audio signal

v_{m} = 20 sin 2 π 1500 t

amplitude modulates a carrier

v_{c} = 80 sin 2 π 100, 000 t

. The value of percent modulation is

Chemistry30 questions

Q31Single correctClassification of Elements and Periodicity in Properties

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

(A)

Al < Mg < Si < S < P

(B)

Al < Mg < S < Si < P

(C)

Mg < Al < Si < P < S

(D)

Mg < Al < Si < S < P

Q32Single correctChemical Bonding and Molecular Structure

Which of the following are isostructural pairs?
A.

SO_{4}^{2 -}

and

CrO_{4}^{2 -}

SiCl_{4}

and

TiCl_{4}

NH_{3}

and

NO_{3}^{-}

BCl_{3}

and

BrCl_{3}

(A)

A and C only

(B)

B and C only

(C)

A and B only

(D)

C and D only

Q33Single correctRedox Reactions and Electrochemistry

(A)

HOCl + H_{2} O_{2} \to H_{3} O^{+} + Cl^{-} + O_{2}

(B)

I_{2} + H_{2} O_{2} + 2 OH^{-} \to 2 I^{-} + 2 H_{2} O + O_{2}

Choose the correct option.

(A)

H_{2} O_{2}

act as oxidizing and reducing agent respectively in equations ( A ) and ( B ).

(B)

H_{2} O_{2}

acts as oxidising agent in equations ( A ) and ( B ).

(C)

H_{2} O_{2}

acts as reducing and oxidising agent respectively in equations ( A ) and ( B ).

(D)

H_{2} O_{2}

acts as reducing agent in equations ( A ) and ( B ).

Q34Single correctp-Block Elements

Al_{2} O_{3}

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

(A)

X = AlOH_{3}

Y = CO_{2}

Z = Al_{2} O_{3}

(B)

X = NaAlOH_{4}

Y = SO_{2}

Z = Al_{2} O_{3}

(C)

X = AlOH_{3}

Y = SO_{2}

Z = Al_{2} O_{3} \cdot x H_{2} O

(D)

X = NaAlOH_{4}

Y = CO_{2}

Z = Al_{2} O_{3}

x H_{2} O

Q35Single correctOrganic Compounds Containing Oxygen

Identify products A and B.

1-methylcyclopentene reacting: dil. KMnO4 / 275 K gives A, then CrO3 gives B.

(A)

(B)

(C)

(D)

Q36Single correctOrganic Compounds Containing Oxygen

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

H_{2} SO_{4}

followed by treatment with NaOH?

(A)

(B)

(C)

(D)

Q37Single correctHydrocarbons

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

Aniline + Conc. HNO3 / Conc. H2SO4, 288 K gives [A] para-nitroaniline 51% + [B] meta-nitroaniline 47% + [C] ortho-nitroaniline 2%.

(A)

Formation of anilinium ion

(B)

-N

H_{2}

group is highly meta-directive

(C)

-N

O_{2}

substitution always takes place at meta-position

(D)

low temperature

Q38Single correctp-Block Elements

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

(A)

Corrosion of metals

(B)

Ozone hole

(C)

Global warming and cancer

(D)

Acid rain

Q39Single correctSome Basic Concepts in Chemistry

In Freundlich adsorption isotherm, slope of AB line is:

Freundlich isotherm: log(x/m) on the vertical axis versus log P, a straight line AB rising left-to-right through points A (lower) and B (upper).

(A)

\frac{1}{n}

with

\frac{1}{n} = 0

1

(B)

n

with

n = 0.1

0.5

(C)

lo g \frac{1}{n}

with

n < 1

(D)

lo g n

with

n > 1

Q40Single correctd- and f-Block Elements

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

(A)

Malachite

(B)

Calamine

(C)

Siderite

(D)

Sphalerite

Q41Single correctd- and f-Block Elements

The major components in "Gun Metal" are:

(A)

Cu, Sn and Zn

(B)

Al, Cu, Mg and Mn

(C)

Cu, Ni and Fe

(D)

Cu, Zn and Ni

Q42Single correctd- and f-Block Elements

The electrode potential of

M^{2 +} / M

of 3 d-series elements shows positive value for?

(A)

(B)

(C)

(D)

Q43Single correctOrganic Compounds Containing Halogens

The product formed in the first step of the reaction of the following compound with excess Mg /

Et_{2} O

(Et

= C_{2} H_{5}

) is:

3,5-dibromohexane: CH3-CH2-CH(Br)-CH2-CH(Br)-CH3 with Br on the third and fifth carbons.

(A)

(B)

(C)

(D)

Q44Single correctHydrocarbons

What is the major product formed by HI on reaction with the following compound?

(A)

(B)

(C)

(D)

Q45Single correctOrganic Compounds Containing Oxygen

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

1-(2-methylcyclohexyl)ethan-1-ol: cyclohexane ring with a CH3 on one carbon and a CH(OH)CH3 group on the adjacent carbon, reacting with HCl.

(A)

(B)

(C)

(D)

Q46Single correctOrganic Compounds Containing Oxygen

Which of the following reagent is used for the following reaction?

CH_{3} CH_{2} CH_{3} \to CH_{3} CH_{2} CHO

(A)

Copper at high temperature and pressure

(B)

Manganese acetate

(C)

Molybdenum oxide

(D)

Potassium permanganate

Q47Single correctOrganic Compounds Containing Nitrogen

A and B in the following reactions are:

Aniline reacts with NaNO2/HCl then KCN to give (A); (A) reacts with SnCl2/HCl/H3O+ to give (B).

(A)

(B)

(C)

(D)

Q48Single correctSome Basic Principles of Organic Chemistry

Match List I with List II.

List I (Monomer Unit)	List II (Polymer)
(a). Caprolactum	(i). Natural rubber
(b). $2$ - Chloro- $1, 3$ - butadiene	(ii). Buna-N
(c). Isoprene	(iii). Nylon 6
(d). Acrylonitrile	(iv). Neoprene

(A)

\to

iii, b

\to

iv, c

\to

i, d

\to

(B)

\to

i, b

\to

ii, c

\to

iii, d

\to

(C)

\to

ii, b

\to

i, c

\to

iv, d

\to

iii

(D)

\to

iv, b

\to

iii, c

\to

ii, d

\to

Q49Single correctd- and f-Block Elements

Given below are two statements:
Statement I: Colourless cupric metaborate is reduced to cuprous metaborate in a luminous flame.
Statement II: Cuprous metaborate is obtained by heating boric anhydride and copper sulphate in a non-luminous flame.
In the light of the above statements, choose the most appropriate answer from the options given below.

(A)

Statement I is false but Statement II is true

(B)

Both Statement I and Statement II are false

(C)

Both Statement I and Statement II are true

(D)

Statement I is true but Statement II is false

Q50Single correctBiomolecules

Out of the following, which type of interaction is responsible for the stabilisation of

α

- helix structure of proteins?

(A)

Covalent bonding

(B)

Ionic bonding

(C)

Hydrogen bonding

(D)

vander Waals forces

Q51NumericalSome Basic Concepts in Chemistry

4.5

g of compound AM .W .

= 90

was used to make

250

mL of its aqueous solution. The molarity of the solution in M is

x \times 1 0^{- 1}

. The value of x is_____ (Rounded off to the nearest integer)

Q52NumericalAtomic Structure

A proton and a

Li^{3 +}

nucleus are accelerated by the same potential. If

λ_{Li}

and

λ_{p}

denote the de Broglie wavelengths of

Li^{3 +}

and proton respectively, then the value of

\frac{λ _{Li}}{λ _{p}}

x \times 1 0^{- 1}

. The value of x is _____ (Rounded off to the nearest integer) [Mass of

Li^{3 +} = 8.3

mass of proton]

Q53NumericalEquilibrium

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 value of

Δ G^{\circ}

for the reaction at

300

K and

1

atm in

Jmol^{- 1}

- x R

, where x is (Rounded off to the nearest integer)

R = 8.31 J mol^{- 1} K^{- 1}

and

ln 10 = 2.3

Q54NumericalCoordination Compounds

The stepwise formation of

CuNH_{34}^{2 +}

is given below:

Cu^{2 +} + NH_{3} K_{1} CuNH_{3}^{2 +}

CuNH_{3}^{2 +} + NH_{3} K_{2} CuNH_{32}^{2 +}

CuNH_{32}^{2 +} + NH_{3} K_{3} CuNH_{33}^{2 +}

CuNH_{33}^{2 +} + NH_{3} K_{4} CuNH_{34}^{2 +}

The value of stability constants

K_{1}, K_{2}, K_{3}

and

K_{4}

are

1 0^{4}, 1.58 \times 1 0^{3}, 5 \times 1 0^{2}

and

1 0^{2}

respectively. The overall equilibrium constants for dissociation of

CuNH_{34}^{2 +}

x \times 1 0^{- 12}

. The value of x is _____ (Rounded off to the nearest integer)

Q55NumericalEquilibrium

1990

K and

1

atm pressure, there are equal number of

Cl_{2}

molecules and Cl atoms in the reaction mixture. The value of

K_{p}

for the reaction

Cl_{2} (g) ⇌ 2 Cl (g)

under the above conditions is

x \times 1 0^{- 1}

. The value of x is _____ (Rounded off to the nearest integer)

Q56NumericalRedox Reactions and Electrochemistry

The reaction of sulphur in alkaline medium is given below:

S_{8 s} + a OH_{a q}^{-} \to b S_{a q}^{2 -} + c S_{2} O_{3 a q}^{2 -} + d H_{2} O_{l}

The values of 'a' is _____ (Integer answer)

Q57Numericalp-Block Elements

Number of amphoteric compounds among the following is
(A) BeO
(B) BaO
(C) BeO

H_{2}

(D) Sr O

H_{2}

Q58NumericalSome Basic Concepts in Chemistry

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

Q59NumericalSolutions

When

9.45

g of

ClCH_{2} COOH

is added to

500

mL of water, its freezing point drops by

0. 5^{\circ}

C. The dissociation constant of

ClCH_{2} COOH

x \times 1 0^{- 3}

. The value of x is off to the nearest integer)

K_{f H_{2} O} = 1.86 K kg mol^{- 1}

Q60NumericalChemical Kinetics

Gaseous cyclobutene isomerizes to butadiene in a first order process which has a 'K' value of

3.3 \times 1 0^{- 4}

s^{- 1}

15 3^{\circ}

C. The time in minutes it takes for the isomerization to proceed

40%

to completion at this temperature is_____. (Rounded off to the nearest integer)

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