JEE Main 2021 17th March Morning Shift Question Paper Question Paper with Solutions | JEE Main Mock Test | JeeMate

Q 1PhysicsSection A • MCQmotion

+4 / -1

A car accelerates from rest at a constant rate

\alpha

for some time after which it decelerates at a constant rate

\beta

to come to rest. If the total time elapsed is t seconds, the total distance travelled is :

A

{{4\alpha \beta } \over {(\alpha + \beta )}}{t^2}

B

{{2\alpha \beta } \over {(\alpha + \beta )}}{t^2}

C

{{\alpha \beta } \over {2(\alpha + \beta )}}{t^2}

D

{{\alpha \beta } \over {4(\alpha + \beta )}}{t^2}

Q 2PhysicsSection A • MCQmagnetics

+4 / -1

A solenoid of 1000 turns per metre has a core with relative permeability 500. Insulated windings of the solenoid carry an electric current of 5A. The magnetic flux density produced by the solenoid is : (permeability of free space = 4

\pi

\times

10^{$-$ 7} H/m)

A

\pi

T

B

2

\times

10^{$-$ 3}

\pi

T

C

10^{$-$ 4}

\pi

T

D

{\pi \over 5}

T

Q 3PhysicsSection A • MCQray optics

+4 / -1

The thickness at the centre of a plane convex lens is 3 mm and the diameter is 6 cm. If the speed of light in the material of the lens is 2

\times

10⁸ ms^{$-$ 1}. The focal length of the lens is ____________.

A

0.30 cm

B

30 cm

C

15 cm

D

1.5 cm

Q 4PhysicsSection A • MCQheat and thermodynamics

+4 / -1

A polyatomic ideal gas has 24 vibrational modes. What is the value of

\gamma

?

A

1.37

B

1.30

C

1.03

D

10.3

Q 5PhysicsSection A • MCQheat and thermodynamics

+4 / -1

Two identical metal wires of thermal conductivities K₁ and K₂ respectively are connected in series. The effective thermal conductivity of the combination is :

A

{{2{K_1}{K_2}} \over {{K_1} + {K_2}}}

B

{{{K_1} + {K_2}} \over {{K_1}{K_2}}}

C

{{{K_1} + {K_2}} \over {2{K_1}{K_2}}}

D

{{{K_1}{K_2}} \over {{K_1} + {K_2}}}

Q 6PhysicsSection A • MCQcircular motion

+4 / -1

A modern grand - prix racing car of mass m is travelling on a flat track in a circular arc of radius R with a speed v. If the coefficient of static friction between the tyres and the track is

\mu

_s, then the magnitude of negative lift F_L acting downwards on the car is : (Assume forces on the four tyres are identical and g = acceleration due to gravity)

qImage-uniform-circular-motion-circular-motion-mechanics-Jeemate

qImage-uniform-circular-motion-circular-motion-mechanics-Jeemate

A

m\left( {g - {{{v^2}} \over {{\mu _s}R}}} \right)

B

- m\left( {g + {{{v^2}} \over {{\mu _s}R}}} \right)

C

m\left( {{{{v^2}} \over {{\mu _s}R}} - g} \right)

D

m\left( {{{{v^2}} \over {{\mu _s}R}} + g} \right)

Q 7PhysicsSection A • MCQunits and measurements

+4 / -1

The vernier scale used for measurement has a positive zero error of 0.2 mm. If while taking a measurement it was noted that '0' on the vernier scale lies between 8.5 cm and 8.6 cm, vernier coincidence is 6, then the correct value of measurement is ___________ cm. (least count = 0.01 cm)

A

8.58 cm

B

8.54 cm

C

8.56 cm

D

8.36 cm

Q 8PhysicsSection B • Numericalsimple harmonic motion

+4 / -1

Consider two identical springs each of spring constant k and negligible mass compared to the mass M as shown. Fig. 1 shows one of them and Fig. 2 shows their series combination. The ratios of time period of oscillation of the two SHM is T_b/T_a =

\sqrt x

, where value of x is ___________. (Round off to the Nearest Integer)

qImage-some-systems-of-executing-shm-simple-harmonic-motion-mechanics-Jeemate

Answer Format:Enter numerical value rounded to the nearest integer

Q 9PhysicsSection B • Numericalcommunication systems

+4 / -1

For VHF signal broadcasting, ___________ km² of maximum service area will be covered by an antenna tower of height 30 m, if the receiving antenna is placed at ground. Let radius of the earth be 6400 km. (Round off to the Nearest Integer) (Take

\pi

as 3.14)

Answer Format:Enter numerical value rounded to the nearest integer

Q 10PhysicsSection A • MCQatoms and nuclei

+4 / -1

If an electron is moving in the n^th orbit of the hydrogen atom, then its velocity (v_n) for the n^th orbit is given as :

A

{v_n} \propto {1 \over n}

B

v_n

\propto

n²

C

v_n

\propto

n

D

{v_n} \propto {1 \over {{n^2}}}

Q 11PhysicsSection A • MCQwork power and energy

+4 / -1

A boy is rolling a 0.5 kg ball on the frictionless floor with the speed of 20 ms^-1. The ball gets deflected by an obstacle on the way. After deflection it moves with 5% of its initial kinetic energy. What is the speed of the ball now?

A

14.41 ms^{$-$ 1}

B

19.0 ms^{$-$ 1}

C

4.47 ms^{$-$ 1}

D

1.00 ms^{$-$ 1}

Q 12PhysicsSection B • Numericalrotational motion

+4 / -1

The following bodies,

(1) a ring

(2) a disc

(3) a solid cylinder

(4) a solid sphere,

of same mass 'm' and radius 'R' are allowed to roll down without slipping simultaneously from the top of the inclined plane. The body which will reach first at the bottom of the inclined plane is ___________. [Mark the body as per their respective numbering given in the question]

qImage-combined-translational-and-rotational-motion-rotational-motion-mechanics-Jeemate

qImage-combined-translational-and-rotational-motion-rotational-motion-mechanics-Jeemate

Answer Format:Enter numerical value rounded to the nearest integer

Q 13PhysicsSection B • Numericalelectromagnetic waves

+4 / -1

If 2.5

\times

10^{$-$ 6} N average force is exerted by a light wave on a non-reflecting surface of 30 cm² area during 40 minutes of time span, the energy flux of light just before it falls on the surface is ___________ W/cm². (Round off to the Nearest Integer)

(Assume complete absorption and normal incidence conditions are there)

Answer Format:Enter numerical value rounded to the nearest integer

Q 14PhysicsSection B • Numericalcapacitor

+4 / -1

A parallel plate capacitor whose capacitance C is 14 pF is charged by a battery to a potential difference V = 12 V between its plates. The charging battery is now disconnected and a porcelin plate with k = 7 is inserted between the plates, then the plate would oscillate back and forth between the plates with a constant mechanical energy of _____________ pJ. (Assume no friction)

Answer Format:Enter numerical value rounded to the nearest integer

Q 15PhysicsSection A • MCQdual nature of radiation

+4 / -1

An electron of mass m and a photon have same energy E. The ratio of wavelength of electron to that of photon is : (c being the velocity of light)

A

{1 \over c}{\left( {{{2m} \over E}} \right)^{1/2}}

B

{1 \over c}{\left( {{E \over {2m}}} \right)^{1/2}}

C

{\left( {{E \over {2m}}} \right)^{1/2}}

D

c{(2mE)^{1/2}}

Q 16PhysicsSection A • MCQalternating current

+4 / -1

An AC current is given by I = I₁ sin

\omega

t + I₂ cos

\omega

t. A hot wire ammeter will give a reading :

A

{{{I_1} + {I_2}} \over {\sqrt 2 }}

B

\sqrt {{{I_1^2 - I_2^2} \over 2}}

C

\sqrt {{{I_1^2 + I_2^2} \over 2}}

D

{{{I_1} + {I_2}} \over {2\sqrt 2 }}

Q 17PhysicsSection A • MCQproperties of matter

+4 / -1

When two soap bubbles of radii a and b (b > a) coalesce, the radius of curvature of common surface is :

A

{{b - a} \over {ab}}

B

{{a + b} \over {ab}}

C

{{ab} \over {a + b}}

D

{{ab} \over {b - a}}

Q 18PhysicsSection B • Numericalcapacitor

+4 / -1

Four identical rectangular plates with length, l = 2 cm and breadth, b =

{3 \over 2}

cm are arranged as shown in figure. The equivalent capacitance between A and C is

{{x{\varepsilon _0}} \over d}

. The value of x is ______________. (Round off to the Nearest Integer)

qImage-combination-of-capacitors-capacitor-electricity-Jeemate

Answer Format:Enter numerical value rounded to the nearest integer

Q 19PhysicsSection A • MCQcurrent electricity

+4 / -1

A current of 10A exists in a wire of cross-sectional area of 5 mm² with a drift velocity of 2

\times

10^{$-$ 3} ms^{$-$ 1}. The number of free electrons in each cubic meter of the wire is ___________.

A

625

\times

10²⁵

B

1

\times

10²³

C

2

\times

10²⁵

D

2

\times

10⁶

Q 20PhysicsSection A • MCQsimple harmonic motion

+4 / -1

For what value of displacement the kinetic energy and potential energy of a simple harmonic oscillation become equal ?

A

x =

{A \over 2}

B

x =

\pm

A

C

x =

\pm

{A \over {\sqrt 2 }}

D

x = 0

Q 21PhysicsSection A • MCQheat and thermodynamics

+4 / -1

Two ideal polyatomic gases at temperatures T₁ and T₂ are mixed so that there is no loss of energy. If F₁ and F₂, m₁ and m₂, n₁ and n₂ be the degrees of freedom, masses, number of molecules of the first and second gas respectively, the temperature of mixture of these two gases is :

A

{{{n_1}{F_1}{T_1} + {n_2}{F_2}{T_2}} \over {{F_1} + {F_2}}}

B

{{{n_1}{F_1}{T_1} + {n_2}{F_2}{T_2}} \over {{n_1}{F_1} + {n_2}{F_2}}}

C

{{{n_1}{T_1} + {n_2}{T_2}} \over {{n_1} + {n_2}}}

D

{{{n_1}{F_1}{T_1} + {n_2}{F_2}{T_2}} \over {{n_1} + {n_2}}}

Q 22PhysicsSection A • MCQheat and thermodynamics

+4 / -1

A Carnot's engine working between 400 K and 800 K has a work output of 1200 J per cycle. The amount of heat energy supplied to the engine from the source in each cycle is :

A

2400 J

B

1600 J

C

1800 J

D

3200 J

Q 23PhysicsSection B • Numericalcurrent electricity

+4 / -1

The equivalent resistance of series combination of two resistors is 's'. When they are connected in parallel, the equivalent resistance is 'p'. If s = np, then the minimum value for n is ____________. (Round off to the Nearest Integer)

Answer Format:Enter numerical value rounded to the nearest integer

Q 24PhysicsSection B • Numericalgravitation

+4 / -1

The radius in kilometer to which the present radius of earth (R = 6400 km) to be compressed so that the escape velocity is increased 10 times is ___________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 25PhysicsSection A • MCQrotational motion

+4 / -1

A triangular plate is shown. A force

\overrightarrow F

= 4

\widehat i

-

3

\widehat j

is applied at point P. The torque at point P with respect to point 'O' and 'Q' are :

qImage-torque-rotational-motion-mechanics-Jeemate

A

-

15 + 20

\sqrt 3

, 15 + 20

\sqrt 3

B

15

-

20

\sqrt 3

, 15 + 20

\sqrt 3

C

15 + 20

\sqrt 3

, 15

-

20

\sqrt 3

D

-

15

-

20

\sqrt 3

, 15

-

20

\sqrt 3

Q 26PhysicsSection B • Numericalrotational motion

+4 / -1

The angular speed of truck wheel is increased from 900 rpm to 2460 rpm in 26 seconds. The number of revolutions by the truck engine during this time is _____________. (Assuming the acceleration to be uniform).

Answer Format:Enter numerical value rounded to the nearest integer

Q 27PhysicsSection A • MCQrotational motion

+4 / -1

A mass M hangs on a massless rod of length l which rotates at a constant angular frequency. The mass M moves with steady speed in a circular path of constant radius. Assume that the system is in steady circular motion with constant angular velocity

\omega

. The angular momentum of M about point A is L_A which lies in the positive z direction and the angular momentum of M about point B is L_B. The correct statement for this system is :

qImage-angular-momentum-rotational-motion-mechanics-Jeemate

qImage-angular-momentum-rotational-motion-mechanics-Jeemate

A

L_A is constant, both in magnitude and direction

B

L_B is constant in direction with varying magnitude

C

L_B is constant, both in magnitude and direction

D

L_A and L_B are both constant in magnitude and direction

Q 28PhysicsSection A • MCQatoms and nuclei

+4 / -1

Which level of the single ionized carbon has the same energy as the ground state energy of hydrogen atom?

A

8

B

6

C

1

D

4

Q 29PhysicsSection B • Numericallaws of motion

+4 / -1

Two blocks (m = 0.5 kg and M = 4.5 kg) are arranged on a horizontal frictionless table as shown in figure. The coefficient of static friction between the two blocks is

{3 \over 7}

. Then the maximum horizontal force that can be applied on the larger block so that the blocks move together is ___________ N. (Round off to the Nearest Integer) [Take g as 9.8 ms^{$-$ 2}]

qImage-friction-force-laws-of-motion-mechanics-Jeemate

qImage-friction-force-laws-of-motion-mechanics-Jeemate

Answer Format:Enter numerical value rounded to the nearest integer

Q 30PhysicsSection A • MCQelectronic devices

+4 / -1

The output of the given combination gates represents :

qImage-digital-circuits-electronic-devices-modern-physics-Jeemate

A

AND Gate

B

NOR Gate

C

NAND Gate

D

XOR Gate

Q 31ChemistrySection B • Numericalsome basic concepts of chemistry

+4 / -1

The mole fraction of a solute in a 100 molal aqueous solution is ___________

\times

10^{$-$ 2}. (Round off to the Nearest Integer).

[Given : Atomic masses : H : 1.0 u, O : 16.0 u ]

Answer Format:Enter numerical value rounded to the nearest integer

Q 32ChemistrySection B • Numericalchemical equilibrium

+4 / -1

0.01 moles of a weak acid HA (K_a = 2.0

\times

10^{$-$ 6}) is dissolved in 1.0 L of 0.1 M HCl solution. The degree of dissociation of HA is __________

\times

10^{$-$ 5} (Round off to the Nearest Integer).

[Neglect volume change on adding HA. Assume degree of dissociation <<1 ]

Answer Format:Enter numerical value rounded to the nearest integer

Q 33ChemistrySection B • Numericalsolutions

+4 / -1

The oxygen dissolved in water exerts a partial pressure of 20 kPa in the vapour above water. The molar solubility of oxygen in water is __________

\times

10^{$-$ 5} mol dm^{$-$ 3}. (Round off to the Nearest Integer).

[Given : Henry's law constant = K_H = 8.0

\times

10⁴ kPa for O₂. Density of water with dissolved oxygen = 1.0 kg dm^{$-$ 3} ]

Answer Format:Enter numerical value rounded to the nearest integer

Q 34ChemistrySection A • MCQhaloalkanes and haloarenes

+4 / -1

qImage-haloarenes-haloalkanes-and-haloarenes-organic-chemistry-Jeemate

The above reaction requires which of the following reaction conditions?

A

623 K, Cu, 300 atm

B

623 K, 300 atm

C

573 K, 300 atm

D

573 K, Cu, 300 atm

Q 35ChemistrySection A • MCQcompounds containing nitrogen

+4 / -1

Hoffmann bromomide degradation of benzamide gives product A, which upon heating with CHCl₃ and NaOH gives product B.

The structures of A and B are :

A

B

C

D

Q 36ChemistrySection B • Numericalpractical organic chemistry

+4 / -1

qImage-detection-of-extra-elements-and-functional-groups-practical-organic-chemistry-organic-chemistry-Jeemate

In the above reaction, 3.9 g of benzene on nitration gives 4.92 g of nitrobenzene. The percentage yield of nitrobenzene in the above reaction is ________%. (Round off to the Nearest Integer).

(Given atomic mass : C : 12.0 u, H : 1.0 u, O : 16.0 u, N : 14.0 u)

Answer Format:Enter numerical value rounded to the nearest integer

Q 37ChemistrySection A • MCQd and f block elements

+4 / -1

What is the spin-only magnetic moment value (BM) of a divalent metal ion with atomic number 25, in it's aqueous solution?

A

zero

B

5.26

C

5.0

D

5.92

Q 38ChemistrySection A • MCQs block elements

+4 / -1

The correct order of conductivity of ions in water is :

A

K⁺ > Na⁺ > Cs⁺ > Rb⁺

B

Cs⁺ > Rb⁺ > K⁺ > Na⁺

C

Na⁺ > K⁺ > Rb⁺ > Cs⁺

D

Rb⁺ > Na⁺ > K⁺ > Li⁺

Q 39ChemistrySection A • MCQaldehydes ketones and carboxylic acids

+4 / -1

qImage-chemical-reactions-for-aldehydes-and-ketones-aldehydes-ketones-and-carboxylic-acids-organic-chemistry-Jeemate

The product ''A'' in the above reaction is :

A

B

C

D

Q 40ChemistrySection A • MCQhaloalkanes and haloarenes

+4 / -1

Which of the following reaction is an example of ammonolysis?

A

C₆H₅COCl + C₆H₅NH₂

\to

C₆H₅CONHC₆H₅

B

C₆H₅CH₂CN

\buildrel {[H]} \over \longrightarrow

C₆H₅CH₂CH₂NH₂

C

C₆H₅CH₂CN

\buildrel {HCl} \over \longrightarrow

C₆H₅

\mathop N\limits^ +

H₃Cl^$-$

D

C₆H₅CH₂Cl + NH₃

\to

C₆H₅CH₂NH₂

Q 41ChemistrySection B • Numericalatomic structure

+4 / -1

A certain orbital has n = 4 and m_L =

-

3. The number of radial nodes in this orbital is ____________. (Round off to the Nearest Integer).

Answer Format:Enter numerical value rounded to the nearest integer

Q 42ChemistrySection A • MCQchemistry in everyday life

+4 / -1

With respect to drug-enzyme interaction, identify the wrong statement.

A

Allosteric inhibitor changes the enzyme's active site

B

Allosteric inhibitor competes with the enzyme's active site

C

Competitive inhibitor binds to the enzyme's active site

D

Non-Competitive inhibitor binds to the allosteric site

Q 43ChemistrySection A • MCQchemical bonding and molecular structure

+4 / -1

A central atom in a molecule has two lone pairs of electrons and forms three single bonds. The shape of this molecule is :

A

trigonal pyramidal

B

T-shaped

C

see-saw

D

planar triangular

Q 44ChemistrySection A • MCQperiodic classification of elements

+4 / -1

The absolute value of the electron gain enthalpy of halogens satisfies :

A

Cl > Br > F > I

B

Cl > F > Br > I

C

I > Br > Cl > F

D

F > Cl > Br > I

Q 45ChemistrySection A • MCQenvironmental chemistry

+4 / -1

Reducing smog is a mixture of :

A

Smoke, fog and O₃

B

Smoke, fog and N₂O₃

C

Smoke, fog and CH₂ = CH

-

CHO

D

Smoke, fog and SO₂

Q 46ChemistrySection A • MCQsurface chemistry

+4 / -1

A colloidal system consisting of a gas dispersed in a solid is called a/an :

A

foam

B

aerosol

C

solid sol

D

gel

Q 47ChemistrySection B • Numericalsome basic concepts of chemistry

+4 / -1

15 mL of aqueous solution of Fe²⁺ in acidic medium completely reacted with 20 mL of 0.03 M aqueous Cr₂O

_7^{2 - }

. The molarity of the Fe²⁺ solution is __________

\times

10^-2 M. (Round off to the Nearest Integer).

Answer Format:Enter numerical value rounded to the nearest integer

Q 48ChemistrySection B • Numericalp block elements

+4 / -1

The reaction of white phosphorus on boiling with alkali in inert atmosphere resulted in the formation of product 'A'. The reaction of 1 mol of 'A' with excess of AgNO₃ in aqueous medium gives ___________ mol(s) of Ag. (Round off to the Nearest Integer).

Answer Format:Enter numerical value rounded to the nearest integer

Q 49ChemistrySection A • MCQaldehydes ketones and carboxylic acids

+4 / -1

Mesityl oxide is a common name of :

A

3-Methyl cyclohexane carbaldehyde

B

4-Methyl pent-3-en-2-one

C

2,4-Dimethyl pentan-3-one

D

2-Methyl cyclohexanone

Q 50ChemistrySection A • MCQd and f block elements

+4 / -1

Given below are two statements :

Statement I : Potassium permanganate on heating at 573K forms potassium manganate.

Statement II : Both potassium permanganate and potassium manganate are tetrahedral and paramagnetic in nature.

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

Q 51ChemistrySection B • Numericalchemical kinetics and nuclear chemistry

+4 / -1

For a certain first order reaction 32% of the reactant is left after 570s. The rate constant of this reaction is _________

\times

10^{$-$ 3} s^{$-$ 1}. (Round off to the Nearest Integer). [Given : log₁₀2 = 0.301, ln10 = 2.303]

Answer Format:Enter numerical value rounded to the nearest integer

Q 52ChemistrySection A • MCQhaloalkanes and haloarenes

+4 / -1

qImage-haloalkanes-haloalkanes-and-haloarenes-organic-chemistry-Jeemate

Product ''A'' in the above chemical reaction is :

A

B

C

D

Q 53ChemistrySection A • MCQionic equilibrium

+4 / -1

Which of the following compound CANNOT act as a Lewis base?

A

SF₄

B

NF₃

C

ClF₃

D

PCl₅

Q 54ChemistrySection A • MCQbasics of organic chemistry

+4 / -1

Given below are two statements :

Statement I : Retardation factor (R_f) can be measured in meter/centimeter.

Statement II : R_f value of a compound remains constant in all solvents.

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 true

D

Both statement I and statement II are false

Q 55ChemistrySection A • MCQbasics of organic chemistry

+4 / -1

Which of the following is an aromatic compound?

A

B

C

D

Q 56ChemistrySection B • Numericalthermodynamics

+4 / -1

The standard enthalpies of formation of Al₂O₃ and CaO are

-

1675 kJ mol^-1 and

-

635 kJ mol^{$-$ 1} respectively.

For the reaction

3CaO + 2Al

\to

3Ca + Al₂O₃ the standard reaction enthalpy

\Delta

_rH⁰ = _________ kJ.

(Round off to the Nearest Integer)

Answer Format:Enter numerical value rounded to the nearest integer

Q 57ChemistrySection A • MCQisolation of elements

+4 / -1

The point of intersection and sudden increase in the slope, in the diagram given below, respectively, indicates :

qImage-ellingham-diagram-isolation-of-elements-inorganic-chemistry-Jeemate

qImage-ellingham-diagram-isolation-of-elements-inorganic-chemistry-Jeemate

A

\Delta

G > 0 and decomposition of the metal oxide

B

\Delta

G < 0 and decomposition of the metal oxide

C

\Delta

G = 0 and reduction of the metal oxide

D

\Delta

G = 0 and melting or boiling point of the metal oxide

Q 58ChemistrySection A • MCQhydrogen

+4 / -1

The INCORRECT statement(s) about heavy water is (are)

(A) used as a moderator in nuclear reactor

(B) obtained as a by-product in fertilizer industry

(C) used for the study of reaction mechanism

(D) has a higher dielectric constant than water

Choose the correct answer from the options given below :

A

(D) only

B

(B) and (D) only

C

(B) only

D

(C) only

Q 59ChemistrySection A • MCQbiomolecules

+4 / -1

Which of the following is correct structure of tyrosine?

A

B

C

D

Q 60ChemistrySection B • Numericalgaseous state

+4 / -1

The pressure exerted by a non-reactive gaseous mixture of 6.4g of methane and 8.8 g of carbon dioxide in a 10L vessel at 27

^\circ

C is __________ kPa. (Round off to the Nearest Integer).

[Assume gases are ideal, R = 8.314 J mol^{$-$ 1} K^{$-$ 1}

Atomic masses : C : 12.0 u, H : 1.0 u, O : 16.0 u]

Answer Format:Enter numerical value rounded to the nearest integer

Q 61MathematicsSection A • MCQbinomial theorem

+4 / -1

If the fourth term in the expansion of

{(x + {x^{{{\log }_2}x}})^7}

is 4480, then the value of x where x

\in

N is equal to :

A

3

B

1

C

4

D

2

Q 62MathematicsSection A • MCQsets and relations

+4 / -1

In a school, there are three types of games to be played. Some of the students play two types of games, but none play all the three games. Which Venn diagrams can justify the above statement?

qImage-venn-diagram-sets-and-relations-algebra-Jeemate

qImage-venn-diagram-sets-and-relations-algebra-Jeemate

A

Q and R

B

None of these

C

P and R

D

P and Q

Q 63MathematicsSection B • Numerical3d geometry

+4 / -1

If the equation of the plane passing through the line of intersection of the planes 2x

-

7y + 4z

-

3 = 0, 3x

-

5y + 4z + 11 = 0 and the point (

-

2, 1, 3) is ax + by + cz

-

7 = 0, then the value of 2a + b + c

-

7 is ____________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 64MathematicsSection A • MCQprobability

+4 / -1

Two dies are rolled. If both dices have six faces numbered 1, 2, 3, 5, 7 and 11, then the probability that the sum of the numbers on the top faces is less than or equal to 8 is :

A

{4 \over 9}

B

{1 \over 2}

C

{5 \over {12}}

D

{17 \over {36}}

Q 65MathematicsSection A • MCQ3d geometry

+4 / -1

The equation of the plane which contains the y-axis and passes through the point (1, 2, 3) is :

A

x + 3z = 0

B

3x

-

z = 0

C

x + 3z = 10

D

3x + z = 6

Q 66MathematicsSection A • MCQcircle

+4 / -1

The line 2x

-

y + 1 = 0 is a tangent to the circle at the point (2, 5) and the centre of the circle lies on x

-

2y = 4. Then, the radius of the circle is :

A

5

\sqrt 3

B

4

\sqrt 5

C

3

\sqrt 5

D

5

\sqrt 4

Q 67MathematicsSection A • MCQfunctions

+4 / -1

The inverse of

y = {5^{\log x}}

is :

A

x = {5^{\log y}}

B

x = {y^{{1 \over {\log 5}}}}

C

x = {5^{{1 \over {\log y}}}}

D

x = {y^{\log 5}}

Q 68MathematicsSection B • Numericallimits continuity and differentiability

+4 / -1

If the function

f(x) = {{\cos (\sin x) - \cos x} \over {{x^4}}}

is continuous at each point in its domain and

f(0) = {1 \over k}

, then k is ____________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 69MathematicsSection A • MCQstraight lines and pair of straight lines

+4 / -1

In a triangle PQR, the co-ordinates of the points P and Q are (

-

2, 4) and (4,

-

2) respectively. If the equation of the perpendicular bisector of PR is 2x

-

y + 2 = 0, then the centre of the circumcircle of the

\Delta

PQR is :

A

(

-

1, 0)

B

(1, 4)

C

(0, 2)

D

(

-

2,

-

2)

Q 70MathematicsSection A • MCQdefinite integration

+4 / -1

Which of the following statements is correct for the function g(

\alpha

) for

\alpha

\in

R such that

g(\alpha ) = \int\limits_{{\pi \over 6}}^{{\pi \over 3}} {{{{{\sin }^\alpha }x} \over {{{\cos }^\alpha }x + {{\sin }^\alpha }x}}dx}

A

g(\alpha )

is a strictly increasing function

B

g(\alpha )

is an even function

C

g(\alpha )

has an inflection point at

\alpha

=

-

{1 \over 2}

D

g(\alpha )

is a strictly decreasing function

Q 71MathematicsSection A • MCQmatrices and determinants

+4 / -1

The system of equations kx + y + z = 1, x + ky + z = k and x + y + zk = k² has no solution if k is equal to :

A

0

B

-

1

C

-

2

D

1

Q 72MathematicsSection B • Numericalmatrices and determinants

+4 / -1

If

A = \left[ {\matrix{ 2 & 3 \cr 0 & { - 1} \cr } } \right]

, then the value of det(A⁴) + det(A¹⁰

-

(Adj(2A))¹⁰) is equal to _____________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 73MathematicsSection A • MCQdifferential equations

+4 / -1

Which of the following is true for y(x) that satisfies the differential equation

{{dy} \over {dx}}

= xy

-

1 + x

-

y; y(0) = 0 :

A

y(1) = 1

B

y(1) = e^{$-$ ${1 \over 2}$}

-

1

C

y(1) = e^{${1 \over 2}$}

-

e^{$-$ ${1 \over 2}$}

D

y(1) = e^{${1 \over 2}$}

-

1

Q 74MathematicsSection B • Numericalstraight lines and pair of straight lines

+4 / -1

The maximum value of z in the following equation z = 6xy + y², where 3x + 4y

\le

100 and 4x + 3y

\le

75 for x

\ge

0 and y

\ge

0 is __________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 75MathematicsSection A • MCQcircle

+4 / -1

Choose the incorrect statement about the two circles whose equations are given below :

x² + y²

-

10x

-

10y + 41 = 0 and

x² + y²

-

16x

-

10y + 80 = 0

A

Distance between two centres is the average of radii of both the circles.

B

Both circles pass through the centre of each other.

C

Circles have two intersection points.

D

Both circle's centers lie inside region of one another.

Q 76MathematicsSection A • MCQcomplex numbers

+4 / -1

The area of the triangle with vertices A(z), B(iz) and C(z + iz) is :

A

1

B

{1 \over 2}

| z |²

C

{1 \over 2}

| z + iz |²

D

{1 \over 2}

Q 77MathematicsSection B • Numericalcircle

+4 / -1

The minimum distance between any two points P₁ and P₂ while considering point P₁ on one circle and point P₂ on the other circle for the given circles' equations

x² + y²

-

10x

-

10y + 41 = 0

x² + y²

-

24x

-

10y + 160 = 0 is ___________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 78MathematicsSection B • Numericalprobability

+4 / -1

Let there be three independent events E₁, E₂ and E₃. The probability that only E₁ occurs is

\alpha

, only E₂ occurs is

\beta

and only E₃ occurs is

\gamma

. Let 'p' denote the probability of none of events occurs that satisfies the equations
(

\alpha

-

2

\beta

)p =

\alpha

\beta

and (

\beta

-

3

\gamma

)p = 2

\beta

\gamma

. All the given probabilities are assumed to lie in the interval (0, 1).

Then,

\frac{Probability\ of\ occurrence\ of\ E_{1}}{Probability\ of\ occurrence\ of\ E_{3}}

is equal to _____________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 79MathematicsSection A • MCQquadratic equation and inequalities

+4 / -1

The value of

4 + {1 \over {5 + {1 \over {4 + {1 \over {5 + {1 \over {4 + ......\infty }}}}}}}}

is :

A

2 +

{2 \over 5}\sqrt {30}

B

2 +

{4 \over {\sqrt 5 }}\sqrt {30}

C

5 +

{2 \over 5}\sqrt {30}

D

4 +

{4 \over {\sqrt 5 }}\sqrt {30}

Q 80MathematicsSection A • MCQmatrices and determinants

+4 / -1

If

A = \left( {\matrix{ 0 & {\sin \alpha } \cr {\sin \alpha } & 0 \cr } } \right)

and

\det \left( {{A^2} - {1 \over 2}I} \right) = 0

, then a possible value of

\alpha

is :

A

{\pi \over 4}

B

{\pi \over 6}

C

{\pi \over 2}

D

{\pi \over 3}

Q 81MathematicsSection B • Numericaldifferentiation

+4 / -1

If

f(x) = \sin \left( {{{\cos }^{ - 1}}\left( {{{1 - {2^{2x}}} \over {1 + {2^{2x}}}}} \right)} \right)

and its first derivative with respect to x is

- {b \over a}{\log _e}2

when x = 1, where a and b are integers, then the minimum value of | a²

-

b² | is ____________ .

Answer Format:Enter numerical value rounded to the nearest integer

Q 82MathematicsSection A • MCQpermutations and combinations

+4 / -1

Team 'A' consists of 7 boys and n girls and Team 'B' has 4 boys and 6 girls. If a total of 52 single matches can be arranged between these two teams when a boy plays against a boy and a girl plays against a girl, then n is equal to :

A

5

B

2

C

4

D

6

Q 83MathematicsSection A • MCQmathematical reasoning

+4 / -1

If the Boolean expression (p

\Rightarrow

q)

\Leftrightarrow

(q * (

\sim

p) is a tautology, then the boolean expression (p * (

\sim

q)) is equivalent to :

A

q

\Rightarrow

p

B

p

\Rightarrow

q

C

p

\Rightarrow

\sim

q

D

\sim

q

\Rightarrow

p

Official Correct Answer:Option (A)

Step-by-Step Solution:

The Boolean expression

$(p \Rightarrow q) \Leftrightarrow\left(q^*(\sim p)\right)$ is a tautology.

Making the truth table for this

p	q	$p \rightarrow q$	$q^* \sim p$	$\sim q$	$-q \wedge p$	$\sim(\sim {q} \wedge p)$
$\mathrm{T}$	$\mathrm{T}$	$\mathrm{T}$	$\mathrm{T}$	$\mathrm{F}$	$\mathrm{F}$	$\mathrm{T}$
T	F	F	F	T	T	F
F	T	T	T	F	F	T
F	F	T	T	T	F	T

$\therefore \quad \sim(\sim q \wedge p)=q \vee \sim p=\sim p \vee q$

$\therefore{ }^*$ is equivalent to $v$ .

So, $\quad p^* \sim q=p \vee \sim q=\sim q \vee p$

$=q \Rightarrow p$

Q 84MathematicsSection B • Numericalbinomial theorem

+4 / -1

If (2021)³⁷⁶² is divided by 17, then the remainder is __________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 85MathematicsSection A • MCQlimits continuity and differentiability

+4 / -1

The value of

\mathop {\lim }\limits_{x \to {0^ + }} {{{{\cos }^{ - 1}}(x - {{[x]}^2}).{{\sin }^{ - 1}}(x - {{[x]}^2})} \over {x - {x^3}}}

, where [ x ] denotes the greatest integer

\le

x is :

A

\pi

B

{\pi \over 4}

C

{\pi \over 2}

D

0

Q 86MathematicsSection A • MCQinverse trigonometric functions

+4 / -1

If cot^{$-$ 1}(

\alpha

) = cot^{$-$ 1} 2 + cot^{$-$ 1} 8 + cot^{$-$ 1} 18 + cot^{$-$ 1} 32 + ...... upto 100 terms, then

\alpha

is :

A

1.02

B

1.03

C

1.01

D

1.00

Q 87MathematicsSection B • Numericalvector algebra

+4 / -1

If

\overrightarrow a = \alpha \widehat i + \beta \widehat j + 3\widehat k

,

\overrightarrow b = - \beta \widehat i - \alpha \widehat j - \widehat k

and

\overrightarrow c = \widehat i - 2\widehat j - \widehat k

such that

\overrightarrow a \,.\,\overrightarrow b = 1

and

\overrightarrow b \,.\,\overrightarrow c = - 3

, then

{1 \over 3}\left( {\left( {\overrightarrow a \times \overrightarrow b } \right)\,.\,\overrightarrow c } \right)

is equal to _____________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 88MathematicsSection A • MCQvector algebra

+4 / -1

Let

\overrightarrow a

= 2

\widehat i

-

3

\widehat j

+ 4

\widehat k

and

\overrightarrow b

= 7

\widehat i

+

\widehat j

-

6

\widehat k

.

If

\overrightarrow r

\times

\overrightarrow a

=

\overrightarrow r

\times

\overrightarrow b

,

\overrightarrow r

. (

\widehat i

+ 2

\widehat j

+

\widehat k

) =

-

3, then

\overrightarrow r

. (2

\widehat i

-

3

\widehat j

+

\widehat k

) is equal to :

A

10

B

8

C

13

D

12

Q 89MathematicsSection A • MCQinverse trigonometric functions

+4 / -1

The sum of possible values of x for

tan^{$-$ 1}(x + 1) + cot^{$-$ 1}

\left( {{1 \over {x - 1}}} \right)

= tan^{$-$ 1}

\left( {{8 \over {31}}} \right)

is :

A

-

{{{32} \over 4}}

B

-

{{{33} \over 4}}

C

-

{{{31} \over 4}}

D

-

{{{30} \over 4}}

Q 90MathematicsSection B • Numericaldefinite integration

+4 / -1

If [ . ] represents the greatest integer function, then the value of

\left| {\int\limits_0^{\sqrt {{\pi \over 2}} } {\left[ {[{x^2}] - \cos x} \right]dx} } \right|

is ____________.

Answer Format:Enter numerical value rounded to the nearest integer

JEE Main 2021 17th March Morning Shift Question Paper with Solutions