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

Q 1PhysicsSection B • Numericallaws of motion

+4 / -1

A body of mass 1 kg rests on a horizontal floor with which it has a coefficient of static friction

{1 \over {\sqrt 3 }}

. It is desired to make the body move by applying the minimum possible force F N. The value of F will be ____________. (Round off to the Nearest Integer) [Take g = 10 ms^{$-$ 2} ]

Answer Format:Enter numerical value rounded to the nearest integer

Q 2PhysicsSection A • MCQcommunication systems

+4 / -1

A carrier signal C(t) = 25 sin(2.512

\times

10¹⁰t) is amplitude modulated by a message signal m(t) = 5 sin(1.57

\times

10⁸t) and transmitted through an antenna. What will be the bandwidth of the modulated signal?

A

50 MHz

B

8 GHz

C

1987.5 MHz

D

2.01 GHz

Q 3PhysicsSection A • MCQmotion

+4 / -1

A rubber ball is released from a height of 5 m above the floor. It bounces back repeatedly, always rising to

{{81} \over {100}}

of the height through which it falls. Find the average speed of the ball. (Take g = 10 ms^{$-$ 2})

A

2.50 ms^{$-$ 1}

B

3.0 ms^{$-$ 1}

C

2.0 ms^{$-$ 1}

D

3.50 ms^{$-$ 1}

Q 4PhysicsSection B • Numericalproperties of matter

+4 / -1

Suppose you have taken a dilute solution of oleic acid in such a way that its concentration becomes 0.01 cm³ of oleic acid per cm³ of the solution. Then you make a thin film of this solution (monomolecular thickness) of area 4 cm² by considering 100 spherical drops of radius

{\left( {{3 \over {40\pi }}} \right)^{{1 \over 3}}} \times {10^{ - 3}}

cm. Then the thickness of oleic acid layer will be x

\times

10^{$-$ 14} m. Where x is ____________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 5PhysicsSection A • MCQmagnetics

+4 / -1

A hairpin like shape as shown in figure is made by bending a long current carrying wire. What is the magnitude of a magnetic field at point P which lies on the centre of the semicircle?

qImage-biot-savarts-law-and-magnetic-field-due-to-current-carrying-wire-magnetics-electricity-Jeemate

qImage-biot-savarts-law-and-magnetic-field-due-to-current-carrying-wire-magnetics-electricity-Jeemate

A

{{{\mu _0}I} \over {4\pi r}}(2 - \pi )

B

{{{\mu _0}I} \over {2\pi r}}(2 - \pi )

C

{{{\mu _0}I} \over {4\pi r}}(2 + \pi )

D

{{{\mu _0}I} \over {2\pi r}}(2 + \pi )

Q 6PhysicsSection B • Numericalelectromagnetic waves

+4 / -1

Seawater at a frequency f = 9

\times

10² Hz, has permittivity

\varepsilon

= 80

\varepsilon

₀ and resistivity

\rho

= 0.25

\Omega

m. Imagine a parallel plate capacitor is immersed in seawater and is driven by an alternating voltage source V(t) = V₀ sin(2

\pi

ft). Then the conduction current density becomes 10^x times the displacement current density after time t =

{1 \over {800}}

s. The value of x is _____________. (Given :

{1 \over {4\pi {\varepsilon _0}}} = 9 \times {10^9}

Nm²C^{$-$ 2})

Answer Format:Enter numerical value rounded to the nearest integer

Q 7PhysicsSection A • MCQdual nature of radiation

+4 / -1

Two identical photocathodes receive the light of frequencies f₁ and f₂ respectively. If the velocities of the photo-electrons coming out are v₁ and v₂ respectively, then

A

{v_1} - {v_2} = {\left[ {{{2h} \over m}({f_1} - {f_2})} \right]^{{1 \over 2}}}

B

v_1^2 + v_2^2 = {{2h} \over m}[{f_1} + {f_2}]

C

{v_1} + {v_2} = {\left[ {{{2h} \over m}({f_1} + {f_2})} \right]^{{1 \over 2}}}

D

v_1^2 - v_2^2 = {{2h} \over m}[{f_1} - {f_2}]

Q 8PhysicsSection A • MCQelectronic devices

+4 / -1

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

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

A

XOR Gate

B

NOR Gate

C

NAND Gate

D

AND Gate

Q 9PhysicsSection A • MCQcurrent electricity

+4 / -1

Two cells of emf 2E and E with internal resistance r₁ and r₂ respectively are connected in series to an external resistor R (see figure). The value of R, at which the potential difference across the terminals of the first cell becomes zero is

qImage-electric-cell-or-battery-current-electricity-electricity-Jeemate

qImage-electric-cell-or-battery-current-electricity-electricity-Jeemate

A

r₁

-

r₂

B

{{{r_1}} \over 2} - {r_2}

C

{{{r_1}} \over 2} + {r_2}

D

r₁ + r₂

Q 10PhysicsSection A • MCQrotational motion

+4 / -1

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 an angle of 30

^\circ

with the horizontal plane, without slipping. How long will the sphere take to return to the starting point A?

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

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

A

0.60 s

B

0.52 s

C

0.80 s

D

0.57 s

Q 11PhysicsSection A • MCQproperties of matter

+4 / -1

An object is located at 2 km beneath the surface of the water. If the fractional compression

{{\Delta V} \over V}

is 1.36%, the ratio of hydraulic stress to the corresponding hydraulic strain will be ____________. [Given : density of water is 1000 kgm^{$-$ 3} and g = 9.8 ms^{$-$ 2}]

A

1.44

\times

10⁷ Nm^{$-$ 2}

B

1.44

\times

10⁹ Nm^{$-$ 2}

C

1.96

\times

10⁷ Nm^{$-$ 2}

D

2.26

\times

10⁹ Nm^{$-$ 2}

Q 12PhysicsSection B • Numericalray optics

+4 / -1

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

{{{2^{rd}}} \over 3}

of the distance of the object from the surface. The wavelength of light inside the surface is

{2 \over 3}

times the wavelength in air. The radius of the curved surface is

{x \over {13}}

m. The value of 'x' is ___________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 13PhysicsSection A • MCQgravitation

+4 / -1

A geostationary satellite is orbiting around an arbitrary planet 'P' at a height of 11R above the surface of 'P', R being the radius of 'P'. The time period of another satellite in hours at a height of 2R from the surface of 'P' is _________. 'P' has the time period of 24 hours.

A

3

B

5

C

6\sqrt 2

D

{6 \over {\sqrt 2 }}

Q 14PhysicsSection A • MCQsimple harmonic motion

+4 / -1

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 amplitude decreases to 6 cm. Determine the value of the damping constant for this motion . (take ln 2 = 0.693)

A

0.69

\times

10² kg s^{$-$ 1}

B

3.3

\times

10² kg s^{$-$ 1}

C

1.16

\times

10^{$-$ 2} kg s^{$-$ 1}

D

5.7

\times

10^{$-$ 3} kg s^{$-$ 1}

Q 15PhysicsSection B • Numericallaws of motion

+4 / -1

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 the floor is 0.5, the maximum force that the boy can exert on the rope so that the piece of wood does not move from its place is __________ N. (Round off to the Nearest Integer) [Take g = 10 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 16PhysicsSection A • MCQcenter of mass

+4 / -1

Two identical blocks A and B each of mass m resting on the smooth horizontal floor are connected by a light spring of natural length L and spring constant K. A third block C of mass m moving with a speed v along the line joining A and B collides with A. The maximum compression in the spring is

qImage-collision-center-of-mass-mechanics-Jeemate

qImage-collision-center-of-mass-mechanics-Jeemate

A

\sqrt {{{mv} \over K}}

B

\sqrt {{m \over {2K}}}

C

\sqrt {{{mv} \over {2K}}}

D

v\sqrt {{m \over {2K}}}

Q 17PhysicsSection A • MCQheat and thermodynamics

+4 / -1

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

qImage-thermodynamics-process-heat-and-thermodynamics-mechanics-Jeemate

qImage-thermodynamics-process-heat-and-thermodynamics-mechanics-Jeemate

A

(a) only

B

(c) and (d)

C

(b) and (c)

D

(c) and (a)

Q 18PhysicsSection B • Numericalcapacitor

+4 / -1

A 2

\mu

F capacitor C₁ is first charged to a potential difference of 10V using a battery. Then the battery is removed and the capacitor is connected to an uncharged capacitor C₂ of 8

\mu

F. The charge in C₂ on equilibrium condition is ____________

\mu

C. (Round off to the Nearest Integer)

qImage-capacitor-in-circuit-capacitor-electricity-Jeemate

Answer Format:Enter numerical value rounded to the nearest integer

Q 19PhysicsSection B • Numericalatoms and nuclei

+4 / -1

A particle of mass m moves in a circular orbit in a
central potential field U(r) = U₀r⁴. If Bohr's quantization conditions
are applied, radii of possible
orbitals r_n vary with

{n^{{1 \over \alpha }}}

, where

\alpha

is ____________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 20PhysicsSection A • MCQheat and thermodynamics

+4 / -1

If one mole of the polyatomic gas is having two vibrational modes and

\beta

is the ratio of molar specific heats for polyatomic gas

\left( {\beta = {{{C_P}} \over {{C_V}}}} \right)

then the value of

\beta

is :

A

1.02

B

1.35

C

1.2

D

1.25

Q 21PhysicsSection B • Numericalelectromagnetic waves

+4 / -1

The electric field intensity produced by the radiation coming from a 100 W bulb at a distance of 3 m is E. The electric field intensity produced by the radiation coming from 60W at the same distance is

\sqrt {{x \over 5}}

E. Where the value of x = ____________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 22PhysicsSection A • MCQalternating current

+4 / -1

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

A

Both, inducting reactance and current will be doubled.

B

Inductive reactance will be doubled and current will be halved.

C

Both, inductive reactance and current will be halved.

D

Inductive reactance will be halved and current will be doubled.

Q 23PhysicsSection A • MCQsimple harmonic motion

+4 / -1

Two particles A and B of equal masses are suspended from two massless springs of spring constants K₁ and K₂ respectively. If the maximum velocities during oscillations are equal, the ratio of the amplitude of A and B is

A

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

B

\sqrt {{{{K_1}} \over {{K_2}}}}

C

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

D

\sqrt {{{{K_2}} \over {{K_1}}}}

Q 24PhysicsSection A • MCQcurrent electricity

+4 / -1

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

\Omega

resistance is connected across BD. Calculate the current through the galvanometer when a potential difference of 10V is maintained across AC.

qImage-wheatstone-bridge-current-electricity-electricity-Jeemate

qImage-wheatstone-bridge-current-electricity-electricity-Jeemate

A

4.87

\mu

A

B

4.87 mA

C

2.44 mA

D

2.44

\mu

A

Q 25PhysicsSection A • MCQatoms and nuclei

+4 / -1

The atomic hydrogen emits a line spectrum consisting of various series. Which series of hydrogen atomic spectra is lying in the visible region?

A

Brackett series

B

Balmer series

C

Paschen series

D

Lyman series

Q 26PhysicsSection B • Numericalelectrostatics

+4 / -1

The electric field in a region is given by

\overrightarrow E = {2 \over 5}{E_0}\widehat i + {3 \over 5}{E_0}\widehat j

with

{E_0} = 4.0 \times {10^3}{N \over C}

. The flux of this field through a rectangular surface area 0.4 m² parallel to the Y-Z plane is __________ Nm²C^{$-$ 1}.

Answer Format:Enter numerical value rounded to the nearest integer

Q 27PhysicsSection A • MCQwaves

+4 / -1

A sound wave of frequency 245 Hz travels with the speed of 300 ms^{$-$ 1} along the positive x-axis. Each point of the wave moves to and from through a total distance of 6 cm. What will be the mathematical expression of this travelling wave?

A

Y(x, t) = 0.03 [ sin 5.1x

-

(0.2

\times

10³)t ]

B

Y(x, t) = 0.03 [ sin 5.1x

-

(1.5

\times

10³)t ]

C

Y(x, t) = 0.06 [ sin 5.1x

-

(1.5

\times

10³)t ]

D

Y(x, t) = 0.06 [ sin 0.8x

-

(0.5

\times

10³)t ]

Q 28PhysicsSection B • Numericalcenter of mass

+4 / -1

The disc of mass M with uniform surface mass density

\sigma

is shown in the figure. The centre of mass of the quarter disc (the shaded area) is at the position

{x \over 3}{a \over \pi },{x \over 3}{a \over \pi }

where x is _____________. (Round off to the Nearest Integer).

[a is an area as shown in the figure]

qImage-center-of-mass-of-continuous-mass-distribution-center-of-mass-mechanics-Jeemate

qImage-center-of-mass-of-continuous-mass-distribution-center-of-mass-mechanics-Jeemate

Answer Format:Enter numerical value rounded to the nearest integer

Q 29PhysicsSection A • MCQmotion

+4 / -1

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) is :

A

v₀ + g + f

B

v₀ +

{g \over 2}

+

{F \over 3}

C

v₀ + 2g + 3F

D

v₀ +

{g \over 2}

+ F

Q 30PhysicsSection A • MCQalternating current

+4 / -1

Match List - I with List - II

	List - I		List - II
(a)	Phase difference between current and voltage in a purely resistive AC circuit	(i)	${\pi \over 2}$ ; current leads voltage
(b)	Phase difference between current and voltage in a pure inductive AC circuit	(ii)	zero
(c)	Phase difference between current and voltage in a pure capacitive AC circuit	(iii)	${\pi \over 2}$ ; current lags voltage
(d)	Phase difference between current and voltage in an LCR series circuit	(iv)	${\tan ^{ - 1}}\left( {{{{X_C} - {X_L}} \over R}} \right)$

Choose the most appropriate answer from the options given below :

A

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

B

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

C

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

D

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

Q 31ChemistrySection A • MCQcompounds containing nitrogen

+4 / -1

Primary, secondary and tertiary amines can be separated using:

A

Chloroform and KOH

B

Acetyl amide

C

Benzene sulphonic acid

D

para-Toluene sulphonyl chloride

Q 32ChemistrySection A • MCQcompounds containing nitrogen

+4 / -1

qImage-diazonium-salts-and-other-nitrogen-containing-compounds-compounds-containing-nitrogen-organic-chemistry-Jeemate

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

A

B

C

D

Q 33ChemistrySection B • Numericalchemical kinetics and nuclear chemistry

+4 / -1

The reaction 2A + B₂

\to

2AB is an elementary reaction.

For a certain quantity of reactants, if the volume of the reaction vessel is reduced by a factor of 3, the rate of the reaction increases by a factor of ____________. (Round off to the Nearest Integer).

Answer Format:Enter numerical value rounded to the nearest integer

Q 34ChemistrySection B • Numericalelectrochemistry

+4 / -1

A KCl solution of conductivity 0.14 S m^{$-$ 1} shows a resistance of 4.19

\Omega

in a conductivity cell. If the same cell is filled with an HCl solution, the resistance drops to 1.03

\Omega

. The conductivity of the HCl solution is ____________

\times

10^{$-$ 2} S m^{$-$ 1}. (Round off to the Nearest Integer).

Answer Format:Enter numerical value rounded to the nearest integer

Q 35ChemistrySection A • MCQs block elements

+4 / -1

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

A

Li - Na

B

Be - Al

C

B - Si

D

Li - Mg

Q 36ChemistrySection A • MCQs block elements

+4 / -1

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

A

Ca(OH)₂

B

NH₄Cl

C

NaHCO₃

D

CaCl₂

Q 37ChemistrySection A • MCQp block elements

+4 / -1

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

A

NO and N₂O

B

N₂O and NO₂

C

NO and NO₂

D

N₂O and N₂O₃

Q 38ChemistrySection A • MCQhydrocarbons

+4 / -1

Given below are two statements :

Statement I : 2-methylbutane on oxidation with KMnO₄ gives 2-methylbutan-2-ol.

Statement II : n-alkanes can be easily oxidised to corresponding alcohols with KMnO₄.

Choose the correct option :

A

Both statement I and statement II are incorrect

B

Both statement I and statement II are correct

C

Statement I is correct but statement II is incorrect

D

Statement I is incorrect but statement II is correct

Q 39ChemistrySection B • Numericalchemical equilibrium

+4 / -1

Consider the reaction

N_{2}O_{4}\left( g\right) \rightleftharpoons 2NO_{2}\left( g\right)

The temperature at which K_C = 20.4 and K_P = 600.1, is ____________ K. (Round off to the Nearest Integer). [Assume all gases are ideal and R = 0.0831 L bar K^{$-$ 1} mol^{$-$ 1}]

Answer Format:Enter numerical value rounded to the nearest integer

Q 40ChemistrySection B • Numericalsome basic concepts of chemistry

+4 / -1

qImage-quantitative-measures-in-chemical-equations-some-basic-concepts-of-chemistry-physical-chemistry-Jeemate

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

(Given : Atomic mass : C : 12.0 u, H : 1.0 u, N : 14.0 u, O : 16.0 u, Cl : 35.5 u)

Answer Format:Enter numerical value rounded to the nearest integer

Q 41ChemistrySection A • MCQhydrogen

+4 / -1

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

A

-

SO₃H and

-

NH₂

B

-

NH₂ and COOH

C

-

NH₂ and

-

SO₃H

D

-

SO₃H and

-

COOH

Q 42ChemistrySection A • MCQhaloalkanes and haloarenes

+4 / -1

The correct pair(s) of the ambident nucleophiles is(are)

(A) AgCN/KCN

(B) RCOOAg/RCOOK

(C) AgNO₂/KNO₂

(D) AgI/KI

A

(B) and (C) only

B

(B) only

C

(A) and (C) only

D

(A) only

Q 43ChemistrySection B • Numericalsolutions

+4 / -1

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 which contains 18.1 weight percent of a non electrolytic solute A. The molar mass of A is __________ u. (Round off to the Nearest Integer). [Density of water = 1.0 g cm^{$-$ 3} ]

Answer Format:Enter numerical value rounded to the nearest integer

Q 44ChemistrySection A • MCQenvironmental chemistry

+4 / -1

Which of the following statement(s) is (are) incorrect reason for eutrophication?

(A) excess usage of fertilisers

(B) excess usage of detergents

(C) dense plant population in water bodies

(D) lack of nutrients in water bodies that prevent plant growth

Choose the most appropriate answer from the options given below :

A

(A) Only

B

(B) and (D) only

C

(C) only

D

(D) only

Q 45ChemistrySection A • MCQchemistry in everyday life

+4 / -1

Match List - I with List - II.

	List - I Chemical Compound		List - II Used as
(a)	Sucralose	(i)	Synthetic detergent
(b)	Glyceryl ester of stearic acid	(ii)	Artificial sweetener
(c)	Sodium benzoate	(iii)	Antiseptic
(d)	Bithionol	(iv)	Food preservative

Choose the correct match :

A

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

B

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

C

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

D

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

Q 46ChemistrySection A • MCQcoordination compounds

+4 / -1

Match List - I with List - II :

	List - I		List - II
(a)	$[Co{(N{H_3})_6}][Cr{(CN)_6}]$	(i)	Linkage isomerism
(b)	$[Co{(N{H_3})_3}{(N{O_2})_3}]$	(ii)	Solvate isomerism
(c)	$[Cr{({H_2}O)_6}C{l_3}$	(iii)	Co-ordination isomerism
(d)	$cis - {[CrC{l_2}{(ox)_2}]^{3 - }}$	(iv)	Optical isomerism

Choose the correct answer from the options given below :

A

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

B

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

C

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

D

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

Q 47ChemistrySection B • Numericalaldehydes ketones and carboxylic acids

+4 / -1

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

Answer Format:Enter numerical value rounded to the nearest integer

Q 48ChemistrySection A • MCQthermodynamics

+4 / -1

During which of the following processes, does entropy decrease?

(A) Freezing of water to ice at 0

^\circ

C

(B) Freezing of water to ice at

-

10

^\circ

C

(C) N₂(g) + 3H₂(g)

\to

2NH₃(g)

(D) Adsorption of CO(g) on lead surface.

(E) Dissolution of NaCl in water

Choose the correct answer from the options given below :

A

(A), (C) and (E) only

B

(B) and (C) only

C

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

D

(A) and (E) only

Q 49ChemistrySection A • MCQbasics of organic chemistry

+4 / -1

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

A

B

C

D

Q 50ChemistrySection B • Numericalgaseous state

+4 / -1

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

[Assume chlorine is an ideal gas at STP

R = 0.083 L bar mol^{$-$ 1} K^{$-$ 1}, N_A = 6.023

\times

10²³]

Answer Format:Enter numerical value rounded to the nearest integer

Q 51ChemistrySection A • MCQchemical bonding and molecular structure

+4 / -1

Amongst the following, the linear species is :

A

O₃

B

Cl₂O

C

N

_3^ -

D

NO₂

Q 52ChemistrySection A • MCQsurface chemistry

+4 / -1

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

A

Na⁺

B

Ba²⁺

C

PO

_4^{3 - }

D

SO

_4^{2 - }

Q 53ChemistrySection A • MCQhydrocarbons

+4 / -1

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

qImage-reaction-of-alkenes-hydrocarbons-organic-chemistry-Jeemate

A

Carbocation A is more stable and formed relatively at faster rate

B

Carbocation B is more stable and formed relatively at slow rate

C

Carbocation B is more stable and formed relatively at faster rate

D

Carbocation A is more stable and formed relatively at slow rate

Q 54ChemistrySection B • Numericalsolid state

+4 / -1

KBr is doped with 10^{$-$ 5} mole percent of SrBr₂. The number of cationic vacancies in 1g of KBr crystal is ____________ 10¹⁴. (Round off to the Nearest Integer).

[Atomic Mass : K : 39.1 u, Br : 79.9 u N_A = 6.023

\times

10²³]

Answer Format:Enter numerical value rounded to the nearest integer

Q 55ChemistrySection A • MCQisolation of elements

+4 / -1

Match List - I with List - II :

	List - I		List - II
(a)	Haematite	(i)	$A{l_2}{O_3}\,.\,x{H_2}O$
(b)	Bauxite	(ii)	$F{e_2}{O_3}$
(c)	Magnetite	(iii)	$CuC{O_3}\,.\,Cu{(OH)_2}$
(d)	Malachite	(iv)	$F{e_3}{O_4}$

Choose the correct answer from the options given below :

A

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

B

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

C

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

D

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

Q 56ChemistrySection A • MCQbiomolecules

+4 / -1

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

\mathop {{C_6}{H_{12}}{O_6}}\limits_{Glu\cos e} \buildrel {Enzyme\,B} \over \longrightarrow 2{C_2}{H_5}OH + 2C{O_2}

In the above reactions, the enzyme A and enzyme B respectively are :

A

Zymase and Invertase

B

Invertase and Amylase

C

Amylase and Invertase

D

Invertase and Zymase

Q 57ChemistrySection A • MCQd and f block elements

+4 / -1

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

A

+1 and +3

B

+2 to +6

C

+1 to +6

D

+1 and +3 to +6

Q 58ChemistrySection B • Numericalcoordination compounds

+4 / -1

On complete reaction of FeCl₃ with oxalic acid in aqueous solution containing KOH, resulted in the formation of product A. The secondary valency of Fe in the product A is __________. (Round off to the Nearest Integer).

Answer Format:Enter numerical value rounded to the nearest integer

Q 59ChemistrySection B • Numericald and f block elements

+4 / -1

In the ground state of atomic Fe(Z = 26), the spin-only magnetic moment is ____________

\times

10^{$-$ 1} BM. (Round off to the Nearest Integer). [Given :

\sqrt 3

= 1.73,

\sqrt 2

= 1.41 ]

Answer Format:Enter numerical value rounded to the nearest integer

Q 60ChemistrySection A • MCQbiomolecules

+4 / -1

Fructose is an example of :

A

Heptose

B

Pyranose

C

Ketohexose

D

Aldohexose

Q 61MathematicsSection A • MCQmatrices and determinants

+4 / -1

If x, y, z are in arithmetic progression with common difference d, x

\ne

3d, and the determinant of the matrix

\left[ {\matrix{ 3 & {4\sqrt 2 } & x \cr 4 & {5\sqrt 2 } & y \cr 5 & k & z \cr } } \right]

is zero, then the value of k² is :

A

72

B

12

C

36

D

6

Q 62MathematicsSection A • MCQvector algebra

+4 / -1

Let O be the origin. Let

\overrightarrow {OP} = x\widehat i + y\widehat j - \widehat k

and

\overrightarrow {OQ} = - \widehat i + 2\widehat j + 3x\widehat k

, x, y

\in

R, x > 0, be such that

\left| {\overrightarrow {PQ} } \right| = \sqrt {20}

and the vector

\overrightarrow {OP}

is perpendicular

\overrightarrow {OQ}

. If

\overrightarrow {OR}

=

3\widehat i + z\widehat j - 7\widehat k

, z

\in

R, is coplanar with

\overrightarrow {OP}

and

\overrightarrow {OQ}

, then the value of x² + y² + z² is equal to :

A

2

B

9

C

7

D

1

Q 63MathematicsSection A • MCQcircle

+4 / -1

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. If r is the radius of the circle passing through the origin O and having centre at the incentre of the triangle OPQ, then r² is equal to :

A

{{585} \over {66}}

B

{{625} \over {72}}

C

{{529} \over {64}}

D

{{125} \over {72}}

Q 64MathematicsSection B • Numericalstatistics

+4 / -1

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 remaining n numbers is 3. A new set is constructed by adding 1 into each of first 2n numbers, and subtracting 1 from each of the remaining n numbers. If the variance of the new set is k, then 9k is equal to __________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 65MathematicsSection A • MCQcomplex numbers

+4 / -1

Let S₁, S₂ and S₃ be three sets defined as

S₁ = {z

\in

C : |z

-

1|

\le

\sqrt 2

}

S₂ = {z

\in

C : Re((1

-

i)z)

\ge

1}

S₃ = {z

\in

C : Im(z)

\le

1}

Then the set S₁

\cap

S₂

\cap

S₃ :

A

has exactly three elements

B

is a singleton

C

has infinitely many elements

D

has exactly two elements

Q 66MathematicsSection A • MCQcircle

+4 / -1

Two tangents are drawn from a point P to the circle x² + y²

-

2x

-

4y + 4 = 0, such that the angle between these tangents is

{\tan ^{ - 1}}\left( {{{12} \over 5}} \right)

, where

{\tan ^{ - 1}}\left( {{{12} \over 5}} \right)

\in

(0,

\pi

). If the centre of the circle is denoted by C and these tangents touch the circle at points A and B, then the ratio of the areas of

\Delta

PAB and

\Delta

CAB is :

A

3 : 1

B

9 : 4

C

2 : 1

D

11 : 4

Q 67MathematicsSection A • MCQtrigonometric functions and equations

+4 / -1

The number of solutions of the equation x + 2tanx =

{\pi \over 2}

in the interval [0, 2

\pi

] is :

A

4

B

3

C

2

D

5

Q 68MathematicsSection A • MCQdefinite integration

+4 / -1

If the integral

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

, where

\alpha

,

\beta

,

\gamma

are integers and [x] denotes the greatest integer less than or equal to x, then the value of

\alpha

+

\beta

+

\gamma

is equal to :

A

0

B

10

C

20

D

25

Q 69MathematicsSection A • MCQlimits continuity and differentiability

+4 / -1

The value of

\mathop {\lim }\limits_{n \to \infty } {{[r] + [2r] + ... + [nr]} \over {{n^2}}}

, where r is a non-zero real number and [r] denotes the greatest integer less than or equal to r, is equal to :

A

r

B

{r \over 2}

C

0

D

2r

Q 70MathematicsSection B • Numericalapplication of derivatives

+4 / -1

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 such that f(

-

1) = 2, f'(

-

1) = 1 for x

\in

(

-

1, 1) the maximum value of f ''(x) is

{{1 \over 2}}

. If f(x)

\le

\alpha

, x

\in

[

-

1, 1], then the least value of

\alpha

is equal to _________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 71MathematicsSection B • Numericalvector algebra

+4 / -1

Let

\overrightarrow x

be a vector in the plane containing vectors

\overrightarrow a = 2\widehat i - \widehat j + \widehat k

and

\overrightarrow b = \widehat i + 2\widehat j - \widehat k

. If the vector

\overrightarrow x

is perpendicular to

\left( {3\widehat i + 2\widehat j - \widehat k} \right)

and its projection on

\overrightarrow a

is

{{17\sqrt 6 } \over 2}

, then the value of

|\overrightarrow x {|^2}

is equal to __________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 72MathematicsSection A • MCQbinomial theorem

+4 / -1

The value of

\sum\limits_{r = 0}^6 {\left( {{}^6{C_r}\,.\,{}^6{C_{6 - r}}} \right)}

is equal to :

A

924

B

1024

C

1124

D

1324

Q 73MathematicsSection A • MCQprobability

+4 / -1

Let a computer program generate only the digits 0 and 1 to form a string of binary numbers with probability of occurrence of 0 at even places be

{1 \over 2}

and probability of occurrence of 0 at the odd place be

{1 \over 3}

. Then the probability that '10' is followed by '01' is equal to :

A

{1 \over 18}

B

{1 \over 3}

C

{1 \over 9}

D

{1 \over 6}

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

+4 / -1

Let tan

\alpha

, tan

\beta

and tan

\gamma

;

\alpha

,

\beta

,

\gamma

\ne

{{(2n - 1)\pi } \over 2}

, n

\in

N be the slopes of three line segments OA, OB and OC, respectively, where O is origin. If circumcentre of

\Delta

ABC coincides with origin and its orthocentre lies on y-axis, then the value of

{\left( {{{\cos 3\alpha + \cos 3\beta + \cos 3\gamma } \over {\cos \alpha \cos \beta \cos \gamma }}} \right)^2}

is equal to ____________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 75MathematicsSection B • Numericalmatrices and determinants

+4 / -1

If 1, log₁₀(4^x

-

2) and log₁₀

\left( {{4^x} + {{18} \over 5}} \right)

are in arithmetic progression for a real number x, then the value of the determinant

\left| {\matrix{ {2\left( {x - {1 \over 2}} \right)} & {x - 1} & {{x^2}} \cr 1 & 0 & x \cr x & 1 & 0 \cr } } \right|

is equal to :

Answer Format:Enter numerical value rounded to the nearest integer

Q 76MathematicsSection A • MCQparabola

+4 / -1

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}} \over 2} + {{{y^2}} \over b} = 1

, then the value of b is equal to :

A

20

B

14

C

16

D

11

Q 77MathematicsSection A • MCQpermutations and combinations

+4 / -1

If the sides AB, BC and CA of a triangle ABC have 3, 5 and 6 interior points respectively, then the total number of triangles that can be constructed using these points as vertices, is equal to :

A

240

B

360

C

333

D

364

Q 78MathematicsSection A • MCQmathematical reasoning

+4 / -1

If the Boolean expression

(p \wedge q) \odot (p \otimes q)

is a tautology, then

\odot

and

\otimes

are respectively given by :

A

\vee , \to

B

\to

,

\to

C

\wedge

,

\vee

D

\wedge

,

\to

Q 79MathematicsSection A • MCQinverse trigonometric functions

+4 / -1

The number of solutions of the equation

{\sin ^{ - 1}}\left[ {{x^2} + {1 \over 3}} \right] + {\cos ^{ - 1}}\left[ {{x^2} - {2 \over 3}} \right] = {x^2}

, for x

\in

[

-

1, 1], and [x] denotes the greatest integer less than or equal to x, is :

A

0

B

Infinite

C

2

D

4

Q 80MathematicsSection B • Numericalarea under the curves

+4 / -1

Let f : [

-

3, 1]

\to

R be given as

f(x) = \left\{ \matrix{ \min \,\{ (x + 6),{x^2}\}, - 3 \le x \le 0 \hfill \cr \max \,\{ \sqrt x ,{x^2}\} ,\,0 \le x \le 1. \hfill \cr} \right.

If the area bounded by y = f(x) and x-axis is A, then the value of 6A is equal to ___________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 81MathematicsSection B • Numerical3d geometry

+4 / -1

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

-

nz = 0 and x

-

2y + z = 0, equal to 9. If the locus of the point P is x² + y² + z² = 9, then the value of l

-

n is equal to _________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 82MathematicsSection B • Numericalmatrices and determinants

+4 / -1

Let

A = \left[ {\matrix{ a & b \cr c & d \cr } } \right]

and

B = \left[ {\matrix{ \alpha \cr \beta \cr } } \right] \ne \left[ {\matrix{ 0 \cr 0 \cr } } \right]

such that AB = B and a + d = 2021, then the value of ad

-

bc is equal to ___________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 83MathematicsSection A • MCQapplication of derivatives

+4 / -1

Consider the function f : R

\to

R defined by

f(x) = \left\{ \matrix{ \left( {2 - \sin \left( {{1 \over x}} \right)} \right)|x|,x \ne 0 \hfill \cr 0,\,\,x = 0 \hfill \cr} \right.

. Then f is :

A

not monotonic on (

-

\infty

, 0) and (0,

\infty

)

B

monotonic on (0,

\infty

) only

C

monotonic on (

-

\infty

, 0) only

D

monotonic on (

-

\infty

, 0)

\cup

(0,

\infty

)

Q 84MathematicsSection A • MCQ3d geometry

+4 / -1

If the equation of plane passing through the mirror image of a point (2, 3, 1) with respect to line

{{x + 1} \over 2} = {{y - 3} \over 1} = {{z + 2} \over { - 1}}

and containing the line

{{x - 2} \over 3} = {{1 - y} \over 2} = {{z + 1} \over 1}

is

\alpha

x +

\beta

y +

\gamma

z = 24, then

\alpha

+

\beta

+

\gamma

is equal to :

A

21

B

19

C

18

D

20

Q 85MathematicsSection A • MCQdefinite integration

+4 / -1

Let f : R

\to

R be defined as f(x) = e^{$-$ x}sinx. If F : [0, 1]

\to

R is a differentiable function with that F(x) =

\int_0^x {f(t)dt}

, then the value of

\int_0^1 {(F'(x) + f(x)){e^x}dx}

lies in the interval

A

\left[ {{{331} \over {360}},{{334} \over {360}}} \right]

B

\left[ {{{330} \over {360}},{{331} \over {360}}} \right]

C

\left[ {{{335} \over {360}},{{336} \over {360}}} \right]

D

\left[ {{{327} \over {360}},{{329} \over {360}}} \right]

Q 86MathematicsSection A • MCQdifferential equations

+4 / -1

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 x + 3))dx,0 \le x \le {\pi \over 2},y(0) = 0

. Then,

y\left( {{\pi \over 3}} \right)

is equal to :

A

2{\log _e}\left( {{{\sqrt 3 + 7} \over 2}} \right)

B

2{\log _e}\left( {{{3\sqrt 3 - 8} \over 4}} \right)

C

2{\log _e}\left( {{{2\sqrt 3 + 10} \over {11}}} \right)

D

2{\log _e}\left( {{{2\sqrt 3 + 9} \over 6}} \right)

Q 87MathematicsSection B • Numericalbinomial theorem

+4 / -1

Let the coefficients of third, fourth and fifth terms in the expansion of

{\left( {x + {a \over {{x^2}}}} \right)^n},x \ne 0

, be in the ratio 12 : 8 : 3. Then the term independent of x in the expansion, is equal to ___________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 88MathematicsSection A • MCQdifferential equations

+4 / -1

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^{9/4}}dx

, x > 0 which

passes through the point

\left( {1,1 - {4 \over 3}{{\log }_e}2} \right)

, then the value of y(16) is equal to :

A

4\left( {{{31} \over 3} - {8 \over 3}{{\log }_e}3} \right)

B

\left( {{{31} \over 3} - {8 \over 3}{{\log }_e}3} \right)

C

\left( {{{31} \over 3} + {8 \over 3}{{\log }_e}3} \right)

D

4\left( {{{31} \over 3} + {8 \over 3}{{\log }_e}3} \right)

Q 89MathematicsSection B • Numericaldefinite integration

+4 / -1

Let

{I_n} = \int_1^e {{x^{19}}{{(\log |x|)}^n}} dx

, where n

\in

N. If (20)I₁₀ =

\alpha

I₉ +

\beta

I₈, for natural numbers

\alpha

and

\beta

, then

\alpha

-

\beta

equals to ___________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 90MathematicsSection A • MCQlimits continuity and differentiability

+4 / -1

The value of the limit

\mathop {\lim }\limits_{\theta \to 0} {{\tan (\pi {{\cos }^2}\theta )} \over {\sin (2\pi {{\sin }^2}\theta )}}

is equal to :

A

0

B

-

{1 \over 2}

C

{1 \over 4}

D

-

{1 \over 4}

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