JEE Main 2022 27th June Evening Shift Question Paper Question Paper with Solutions | JEE Main Mock Test | JeeMate

Q 1PhysicsSection A • MCQwaves

+4 / -1

If a wave gets refracted into a denser medium, then which of the following is true?

A

wavelength, speed and frequency decreases.

B

wavelength increases, sped decreases and frequency remains constant.

C

wavelength and speed decreases but frequency remains constant.

D

wavelength, speed and frequency increases.

Q 2PhysicsSection A • MCQheat and thermodynamics

+4 / -1

For a perfect gas, two pressures P₁ and P₂ are shown in figure. The graph shows :

qImage-kinetic-theory-of-gases-and-gas-laws-heat-and-thermodynamics-mechanics-Jeemate

A

P₁ > P₂

B

P₁ < P₂

C

P₁ = P₂

D

Insufficient data to draw any conclusion

Q 3PhysicsSection A • MCQheat and thermodynamics

+4 / -1

A lead bullet penetrates into a solid object and melts. Assuming that 40% of its kinetic energy is used to heat it, the initial speed of bullet is :

(Given : initial temperature of the bullet = 127 $^\circ$ C, Melting point of the bullet = 327 $^\circ$ C, Latent heat of fusion of lead = 2.5 $\times$ 10⁴ J kg^{$-$ 1}, Specific heat capacity of lead = 125 J/kg K)

A

125 ms^{$-$ 1}

B

500 ms^{$-$ 1}

C

250 ms^{$-$ 1}

D

600 ms^{$-$ 1}

Q 4PhysicsSection B • Numericalelectronic devices

+4 / -1

The cut-off voltage of the diodes (shown in figure) in forward bias is 0.6 V. The current through the resister of 40 $\Omega$ is __________ mA.

qImage-semiconductor-and-p-n-junction-diode-electronic-devices-modern-physics-Jeemate

Answer Format:Enter numerical value rounded to the nearest integer

Q 5PhysicsSection A • MCQalternating current

+4 / -1

If L, C and R are the self inductance, capacitance and resistance respectively, which of the following does not have the dimension of time?

A

RC

B

{L \over R}

C

\sqrt{LC}

D

{L \over C}

Q 6PhysicsSection A • MCQrotational motion

+4 / -1

One end of a massless spring of spring constant k and natural length l₀ is fixed while the other end is connected to a small object of mass m lying on a frictionless table. The spring remains horizontal on the table. If the object is made to rotate at an angular velocity $\omega$ about an axis passing through fixed end, then the elongation of the spring will be :

A

{{k - m{\omega ^2}{l_0}} \over {m{\omega ^2}}}

B

{{m{\omega ^2}{l_0}} \over {k + m{\omega ^2}}}

C

{{m{\omega ^2}{l_0}} \over {k - m{\omega ^2}}}

D

{{k + m{\omega ^2}{l_0}} \over {m{\omega ^2}}}

Q 7PhysicsSection A • MCQunits and measurements

+4 / -1

The SI unit of a physical quantity is pascal-second. The dimensional formula of this quantity will be :

A

[ML^{$-$ 1}T^{$-$ 1}]

B

[ML^{$-$ 1}T^{$-$ 2}]

C

[ML²T^{$-$ 1}]

D

[M^{$-$ 1}L³T⁰]

Q 8PhysicsSection A • MCQmagnetics

+4 / -1

Two long parallel conductors S₁ and S₂ are separated by a distance 10 cm and carrying currents of 4A and 2A respectively. The conductors are placed along x-axis in X-Y plane. There is a point P located between the conductors (as shown in figure).

A charge particle of 3 $\pi$ coulomb is passing through the point P with velocity $\overrightarrow v = (2\widehat i + 3\widehat j)$ m/s; where $\widehat i$ and $\widehat j$ represents unit vector along x & y axis respectively.

The force acting on the charge particle is $4\pi \times {10^{ - 5}}( - x\widehat i + 2\widehat j)$ N. The value of x is :

qImage-motion-of-charged-particle-inside-magnetic-field-magnetics-electricity-Jeemate

A

2

B

1

C

3

D

-

3

Q 9PhysicsSection B • Numericalheat and thermodynamics

+4 / -1

A diatomic gas ( $\gamma$ = 1.4) does 400J of work when it is expanded isobarically. The heat given to the gas in the process is __________ J.

Answer Format:Enter numerical value rounded to the nearest integer

Q 10PhysicsSection B • Numericallaws of motion

+4 / -1

A mass of 10 kg is suspended vertically by a rope of length 5 m from the roof. A force of 30 N is applied at the middle point of rope in horizontal direction. The angle made by upper half of the rope with vertical is $\theta$ = tan^{$-$ 1} (x $\times$ 10^{$-$ 1}). The value of x is ____________.

(Given, g = 10 m/s²)

Answer Format:Enter numerical value rounded to the nearest integer

Q 11PhysicsSection B • Numericalcurrent electricity

+4 / -1

The current density in a cylindrical wire of radius r = 4.0 mm is 1.0 $\times$ 10⁶ A/m². The current through the outer portion of the wire between radial distances ${r \over 2}$ and r is x $\pi$ A; where x is __________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 12PhysicsSection A • MCQsimple harmonic motion

+4 / -1

The equation of a particle executing simple harmonic motion is given by $x = \sin \pi \left( {t + {1 \over 3}} \right)m$ . At t = 1s, the speed of particle will be

(Given : $\pi$ = 3.14)

A

0 cm s^{$-$ 1}

B

157 cm s^{$-$ 1}

C

272 cm s^{$-$ 1}

D

314 cm s^{$-$ 1}

Q 13PhysicsSection B • Numericalcapacitor

+4 / -1

A parallel plate capacitor is made up of stair like structure with a plate area A of each stair and that is connected with a wire of length b, as shown in the figure. The capacitance of the arrangement is ${x \over {15}}{{{ \in _0}A} \over b}$ . The value of x is ____________.

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

Answer Format:Enter numerical value rounded to the nearest integer

Q 14PhysicsSection A • MCQproperties of matter

+4 / -1

When a ball is dropped into a lake from a height 4.9 m above the water level, it hits the water with a velocity v and then sinks to the bottom with the constant velocity v. It reaches the bottom of the lake 4.0 s after it is dropped. The approximate depth of the lake is :

A

19.6 m

B

29.4 m

C

39.2 m

D

73.5 m

Q 15PhysicsSection A • MCQheat and thermodynamics

+4 / -1

According to kinetic theory of gases,

A. The motion of the gas molecules freezes at 0 $^\circ$ C.

B. The mean free path of gas molecules decreases if the density of molecules is increased.

C. The mean free path of gas molecules increases if temperature is increased keeping pressure constant.

D. Average kinetic energy per molecule per degree of freedom is ${3 \over 2}{k_B}T$ (for monoatomic gases).

Choose the most appropriate answer from the options given below :

A

A and C only

B

B and C only

C

A and B only

D

C and D only

Q 16PhysicsSection B • Numericalmagnetics

+4 / -1

A deuteron and a proton moving with equal kinetic energy enter into a uniform magnetic field at right angle to the field. If r_d and r_p are the radii of their circular paths respectively, then the ratio ${{{r_d}} \over {{r_p}}}$ will be $\sqrt{x}$ : 1 where x is __________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 17PhysicsSection B • Numericalcurrent electricity

+4 / -1

In the given circuit 'a' is an arbitrary constant. The value of m for which the equivalent circuit resistance is minimum, will be $\sqrt {{x \over 2}}$ . The value of x is __________.

qImage-combination-of-resistances-current-electricity-electricity-Jeemate

Answer Format:Enter numerical value rounded to the nearest integer

Q 18PhysicsSection A • MCQgravitation

+4 / -1

The distance of the Sun from earth is 1.5 $\times$ 10¹¹ m and its angular diameter is (2000) s when observed from the earth. The diameter of the Sun will be :

A

2.45

\times

10¹⁰ m

B

1.45

\times

10¹⁰ m

C

1.45

\times

10⁹ m

D

0.14

\times

10⁹ m

Q 19PhysicsSection A • MCQray optics

+4 / -1

A convex lens has power P. It is cut into two halves along its principal axis. Further one piece (out of the two halves) is cut into two halves perpendicular to the principal axis (as shown in figures). Choose the incorrect option for the reported pieces.

qImage-lenses-geometrical-optics-optics-Jeemate

A

Power of

{L_1} = {P \over 2}

B

Power of

{L_2} = {P \over 2}

C

Power of

{L_3} = {P \over 2}

D

Power of L₁ = P

Q 20PhysicsSection A • MCQcommunication systems

+4 / -1

We do not transmit low frequency signal to long distances because-

(a) The size of the antenna should be comparable to signal wavelength which is unreal solution for a signal of longer wavelength.

(b) Effective power radiated by a long wavelength baseband signal would be high.

(c) We want to avoid mixing up signals transmitted by different transmitter simultaneously.

(d) Low frequency signal can be sent to long distances by superimposing with a high frequency wave as well.

Therefore, the most suitable option will be :

A

All statements are true

B

(a), (b) and (c) are true only

C

(a), (c) and (d) are true only

D

(b), (c) and (d) are true only

Q 21PhysicsSection A • MCQelectrostatics

+4 / -1

If a charge q is placed at the centre of a closed hemispherical non-conducting surface, the total flux passing through the flat surface would be :

qImage-electric-flux-and-gauss-law-electrostatics-electricity-Jeemate

A

{q \over {{ \in _0}}}

B

{q \over {{ 2\in _0}}}

C

{q \over {{ 4\in _0}}}

D

{q \over {{ 2\pi\in _0}}}

Q 22PhysicsSection A • MCQcircular motion

+4 / -1

A stone tide to a spring of length L is whirled in a vertical circle with the other end of the spring at the centre. At a certain instant of time, the stone is at its lowest position and has a speed u. The magnitude of change in its velocity, as it reaches a position where the string is horizontal, is $\sqrt {x({u^2} - gL)}$ . The value of x is -

A

3

B

2

C

1

D

5

Q 23PhysicsSection B • Numericalrotational motion

+4 / -1

A rolling wheel of 12 kg is on an inclined plane at position P and connected to a mass of 3 kg through a string of fixed length and pulley as shown in figure. Consider PR as friction free surface. The velocity of centre of mass of the wheel when it reaches at the bottom Q of the inclined plane PQ will be ${1 \over 2}\sqrt {xgh}$ m/s. The value of x is ___________.

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

Answer Format:Enter numerical value rounded to the nearest integer

Q 24PhysicsSection B • Numericalsimple harmonic motion

+4 / -1

A particle executes simple harmonic motion. Its amplitude is 8 cm and time period is 6 s. The time it will take to travel from its position of maximum displacement to the point corresponding to half of its amplitude, is ___________ s.

Answer Format:Enter numerical value rounded to the nearest integer

Q 25PhysicsSection A • MCQatoms and nuclei

+4 / -1

Given below are two statements :

Statement I : In hydrogen atom, the frequency of radiation emitted when an electron jumps from lower energy orbit (E₁) to higher energy orbit (E₂), is given as hf = E₁ $-$ E₂

Statement II : The jumping of electron from higher energy orbit (E₂) to lower energy orbit (E₁) is associated with frequency of radiation given as f = (E₂ $-$ E₁)/h

This condition is Bohr's frequency condition.

In the light of the above statements, choose the correct answer from the options given below :

A

Both Statement I and Statement II are true.

B

Both Statement I and Statement II are false.

C

Statement I is correct but Statement II is false.

D

Statement I is incorrect but Statement II is true.

Q 26PhysicsSection A • MCQelectronic devices

+4 / -1

For a transistor to act as a switch, it must be operated in

A

Active region.

B

Saturation state only.

C

Cut-off state only.

D

Saturation and cut-off state.

Q 27PhysicsSection B • Numericalelectromagnetic induction

+4 / -1

A metallic rod of length 20 cm is placed in North-South direction and is moved at a constant speed of 20 m/s towards East. The horizontal component of the Earth's magnetic field at that place is 4 $\times$ 10^{$-$ 3} T and the angle of dip is 45 $^\circ$ . The emf induced in the rod is ___________ mV.

Answer Format:Enter numerical value rounded to the nearest integer

Q 28PhysicsSection A • MCQelectromagnetic waves

+4 / -1

Given below are two statements :

Statement I : A time varying electric field is a source of changing magnetic field and vice-versa. Thus a disturbance in electric or magnetic field creates EM waves.

Statement II : In a material medium, the EM wave travels with speed $v = {1 \over {\sqrt {{\mu _0}{ \in _0}} }}$ . In the light of the above statements, choose the correct answer from the options given below.

A

Both Statement I and Statement II are true

B

Both Statement I and Statement II are false

C

Statement I is correct but Statement II is false

D

Statement I is incorrect but Statement II is true

Q 29PhysicsSection A • MCQelectrostatics

+4 / -1

Three identical charged balls each of charge 2 C are suspended from a common point P by silk threads of 2 m each (as shown in figure). They form an equilateral triangle of side 1m.

The ratio of net force on a charged ball to the force between any two charged balls will be :

qImage-electric-charges-and-coulombs-law-electrostatics-electricity-Jeemate

A

1 : 1

B

1 : 4

C

\sqrt3

: 2

D

\sqrt3

: 1

Q 30PhysicsSection A • MCQgravitation

+4 / -1

Four spheres each of mass m from a square of side d (as shown in figure). A fifth sphere of mass M is situated at the centre of square. The total gravitational potential energy of the system is :

qImage-gravitational-potential-and-gravitational-potential-energy-gravitation-mechanics-Jeemate

A

- {{Gm} \over d}\left[ {(4 + \sqrt 2 )m + 4\sqrt 2 M} \right]

B

- {{Gm} \over d}\left[ {(4 + \sqrt 2 )M + 4\sqrt 2 m} \right]

C

- {{Gm} \over d}\left[ {3{m^2} + 4\sqrt 2 M} \right]

D

- {{Gm} \over d}\left[ {6{m^2} + 4\sqrt 2 M} \right]

Q 31ChemistrySection B • Numericalsome basic concepts of chemistry

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116 g of a substance upon dissociation reaction, yields 7.5 g of hydrogen, 60 g of oxygen and 48.5 g of carbon. Given that the atomic masses of H, O and C are 1, 16 and 12, respectively. The data agrees with how many formulae of the following?

A. CH₃COOH, B. HCHO, C. CH₃OOCH₃, D. CH₃CHO

Answer Format:Enter numerical value rounded to the nearest integer

Q 32ChemistrySection B • Numericalelectrochemistry

+4 / -1

For the reaction taking place in the cell :

Pt (s)| H₂ (g)|H⁺(aq) || Ag⁺(aq) |Ag (s)

E $_{cell}^o$ = + 0.5332 V.

The value of $\Delta$ _fG $^\circ$ is ______________ kJ mol^{$-$ 1}. (in nearest integer)

Answer Format:Enter numerical value rounded to the nearest integer

Q 33ChemistrySection A • MCQenvironmental chemistry

+4 / -1

On the surface of polar stratospheric clouds, hydrolysis of chlorine nitrite gives A and B while its reaction with its reaction with HCl produces B and C. A, B and C are, respectively :

A

HOCl, HNO₃, Cl₂

B

Cl₂, HNO₃, HOCl

C

HClO₂, HNO₂, HOCl

D

HOCl, HNO₂, Cl₂O

Q 34ChemistrySection B • Numericalatomic structure

+4 / -1

Consider the following set of quantum numbers.

	n	1	m $_1$
A.	3	3	$-$ 3
B.	3	2	$-$ 2
C.	2	1	+1
D.	2	2	+2

The number of correct sets of quantum numbers is __________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 35ChemistrySection A • MCQgaseous state

+4 / -1

Which amongst the given plots is the correct plot for pressure (p) vs density (d) for an ideal gas?

A

B

C

D

Q 36ChemistrySection A • MCQhydrocarbons

+4 / -1

Product 'A' of following sequence of reactions is

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

A

B

C

D

Q 37ChemistrySection A • MCQpolymers

+4 / -1

Which is true about Buna-N?

A

It is a linear polymer of 1, 3-butadiene.

B

It is obtained by copolymerization of 1, 3-butadiene and styrene.

C

It is obtained by copolymerization of 1, 3-butadiene and acrylonitrile.

D

The suffix N in Buna-N stands for its natural occurrence.

Q 38ChemistrySection A • MCQbiomolecules

+4 / -1

Given below are two statements.

Statement I : Maltose has two $\alpha$ -D-glucose units linked at C₁ and C₄ and is a reducing sugar.

Statement II : Maltose has two monosaccharides : $\alpha$ -D-glucose and $\beta$ -D-glucose linked at C₁ and C₆ and it is a non-reducing sugar.

In the light of the above statements, choose the correct answer from the options given below :

A

Both Statement I and Statement II are true.

B

Both Statement I and Statement II are false.

C

Statement I is true but Statement II is false.

D

Statement I is false but Statement II is true.

Q 39ChemistrySection B • Numericalionic equilibrium

+4 / -1

pH value of 0.001 M NaOH solution is ____________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 40ChemistrySection A • MCQp block elements

+4 / -1

The gas produced by treating an aqueous solution of ammonium chloride with sodium nitrite is :

A

NH₃

B

N₂

C

N₂O

D

Cl₂

Q 41ChemistrySection A • MCQp block elements

+4 / -1

Match List I with List II.

	List-I (Anion)		List-II (gas evolved on reaction with dil.H $_2$ SO $_2$ )
(A)	CO ${_3^{2 - }}$	I.	Colourless gas which turns lead acetate paper black.
(B)	S $^{2 - }$	II.	Colourless gas which turns acidified potassium dichromate solution green.
(C)	SO ${_3^{2 - }}$	III.	Brown fumes which turns acidified KI solution containing starch blue.
(D)	NO ${_2^ - }$	IV.	Colourless gas evolved with brisk effervescence, which turns lime water milky.

Choose the correct answer from the options given below :

A

A-III, B-I, C-II, D-IV

B

A-II, B-I, C-IV, D-III

C

A-IV, B-I, C-III, D-II

D

A-IV, B-I, C-II, D-III

Q 42ChemistrySection A • MCQp block elements

+4 / -1

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A : Fluorine forms one oxoacid.

Reason R : Fluorine has smallest size amongst all halogens and is highly electronegative.

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

A

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

B

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

C

A is correct but R is not correct.

D

A is not correct but R is correct.

Q 43ChemistrySection B • Numericalsolutions

+4 / -1

A solution containing 2.5 $\times$ 10^{$-$ 3} kg of a solute dissolved in 75 $\times$ 10^{$-$ 3} kg of water boils at 373.535 K. The molar mass of the solute is ____________ g mol^{$-$ 1}. [nearest integer] (Given : K_b(H₂O) = 0.52 K kg mol^{$-$ 1} and boiling point of water = 373.15 K)

Answer Format:Enter numerical value rounded to the nearest integer

Q 44ChemistrySection A • MCQalcohols phenols and ethers

+4 / -1

Match List-I with List-II.

		List-II
(A)	I.	$B{r_2}$ in $C{S_2}$
(B)	II.	$N{a_2}C{r_2}{O_7}/{H_2}S{O_4}$
(C)	III.	$Zn$
(D)	IV.	$CHC{l_3}/NaOH$

Choose the correct answer from the options given below :

A

A-IV, B-III, C-II, D-I

B

A-IV, B-III, C-I, D-II

C

A-II, B-III, C-I, D-IV

D

A-IV, B-II, C-III, D-I

Q 45ChemistrySection A • MCQd and f block elements

+4 / -1

The 'f' orbitals are half and completely filled, respectively in lanthanide ions :

[Given : Atomic no. Eu, 63; Sm, 62; Tm, 69; Tb, 65; Yb, 70; Dy, 66]

A

Eu²⁺ and Tm²⁺

B

Sm²⁺ and Tm³⁺

C

Tb⁴⁺ and Yb²⁺

D

Dy³⁺ and Yb³⁺

Q 46ChemistrySection A • MCQchemical bonding and molecular structure

+4 / -1

Identify the incorrect statement for PCl₅ from the following.

A

In this molecule, orbitals of phosphorous are assumed to undergo sp³d hybridization.

B

The geometry of PCl₅ is trigonal bipyramidal.

C

PCl₅ has two axial bonds stronger than three equatorial bonds.

D

The three equatorial bonds of PCl₅ lie in a plane.

Q 47ChemistrySection A • MCQcompounds containing nitrogen

+4 / -1

Decarboxylation of all six possible forms of diaminobenzoic acids C₆H₃(NH₂)₂COOH yields three products A, B and C. Three acids give a product 'A', two acids gives a product 'B' and one acid give a product 'C'. The melting point of product 'C' is

A

63

^\circ

C

B

90

^\circ

C

104

^\circ

C

D

142

^\circ

C

Q 48ChemistrySection A • MCQcoordination compounds

+4 / -1

Arrange the following coordination compounds in the increasing order of magnetic moments. (Atomic numbers : Mn = 25; Fe = 26)

A. [FeF₆]^{3 $-$}

B. [Fe(CN)₆]^{3 $-$}

C. [MnCl₆]^{3 $-$} (high spin)

D. [Mn(CN)₆]^{3 $-$}

Choose the correct answer from the options given below :

A

A < B < D < C

B

B < D < C < A

C

A < C < D < B

D

B < D < A < C

Official Correct Answer:Option (B)

Step-by-Step Solution:

Coordination Compound	Number of unpaired e^– (n)	Magnetic moment (µ) (B.M)
A. [FeF₆]^{3 $-$} - d⁵	5	5.91
B. [Fe(CN)₆]^{3 $-$} - d⁵	1	1.73
C. [MnCl₆]^{3 $-$} - d⁴	4	4.89
D. [Mn(CN)₆]^{3 $-$} - d⁴	2	2.82

Hence, correct order of magnetic moment is

2 < 4 < 3 < 1

Q 49ChemistrySection A • MCQperiodic classification of elements

+4 / -1

The correct order of increasing ionic radii is

A

Mg²⁺ < Na⁺ < F^$-$ < O^{2 $-$} < N^{3 $-$}

B

N^{3 $-$} < O^{2 $-$} < F^$-$ < Na⁺ < Mg²⁺

C

F^$-$ < Na⁺ < O^{2 $-$} < Mg²⁺ < N^{3 $-$}

D

Na⁺ < F^$-$ < Mg²⁺ < O^{2 $-$} < N^{3 $-$}

Q 50ChemistrySection A • MCQhydrocarbons

+4 / -1

What will be the major product of following sequence of reactions?

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

A

B

C

D

Q 51ChemistrySection A • MCQbasics of organic chemistry

+4 / -1

Which of the following is most stable?

A

B

C

D

Q 52ChemistrySection B • Numericalsurface chemistry

+4 / -1

qImage-adsorption-surface-chemistry-physical-chemistry-Jeemate

If the initial pressure of a gas is 0.03 atm, the mass of the gas adsorbed per gram of the adsorbent is ___________ $\times$ 10^{$-$ 2} g.

Answer Format:Enter numerical value rounded to the nearest integer

Q 53ChemistrySection B • Numericalpractical organic chemistry

+4 / -1

0.25 g of an organic compound containing chlorine gave 0.40 g of silver chloride in Carius estimation. The percentage of chlorine present in the compound is ___________. [in nearest integer]

(Given : Molar mass of Ag is 108 g mol^{$-$ 1} and that of Cl is 35.5 g mol^{$-$ 1})

Answer Format:Enter numerical value rounded to the nearest integer

Q 54ChemistrySection A • MCQisolation of elements

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Statement I : Leaching of gold with cyanide ion in absence of air / O₂ leads to cyano complex of Au(III).

Statement II : Zinc is oxidized during the displacement reaction carried out for gold extraction.

In the light of the above statements, choose the correct answer from the options given below.

A

Both Statement I and Statement II are correct.

B

Both Statement I and Statement II are incorrect.

C

Statement I is correct but Statement II is incorrect.

D

Statement I is incorrect but Statement II is correct.

Q 55ChemistrySection B • Numericalthermodynamics

+4 / -1

When 5 moles of He gas expand isothermally and reversibly at 300 K from 10 litre to 20 litre, the magnitude of the maximum work obtained is __________ J. [nearest integer] (Given : R = 8.3 J K^{$-$ 1} mol^{$-$ 1} and log 2 = 0.3010)

Answer Format:Enter numerical value rounded to the nearest integer

Q 56ChemistrySection B • Numericals block elements

+4 / -1

BeO reacts with HF in presence of ammonia to give [A] which on thermal decomposition produces [B] and ammonium fluoride. Oxidation state of Be in [A] is ____________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 57ChemistrySection A • MCQelectrochemistry

+4 / -1

In 3d series, the metal having the highest M²⁺/M standard electrode potential is :

A

Cr

B

Fe

C

Cu

D

Zn

Q 58ChemistrySection A • MCQchemistry in everyday life

+4 / -1

Match List-I with List-II

	List-I		List-II
(A)	Antipyretic	I.	Reduces pain
(B)	Analgesic	II.	Reduces stress
(C)	Tranquilizer	III.	Reduces fever
(D)	Antacid	IV.	Reduces acidity (stomach)

Choose the correct answer from the options given below :

A

A-III, B-I, C-II, D-IV

B

A-III, B-I, C-IV, D-II

C

A-I, B-IV, C-II, D-III

D

A-I, B-III, C-II, D-IV

Q 59ChemistrySection A • MCQchemical bonding and molecular structure

+4 / -1

The correct order of increasing intermolecular hydrogen bond strength is

A

HCN < H₂O < NH₃

B

HCN < CH₄ < NH₃

C

CH₄ < HCN < NH₃

D

CH₄ < NH₃ < HCN

Q 60ChemistrySection B • Numericalchemical kinetics and nuclear chemistry

+4 / -1

It has been found that for a chemical reaction with rise in temperature by 9 K the rate constant gets doubled. Assuming a reaction to be occurring at 300 K, the value of activation energy is found to be ____________ kJ mol^{$-$ 1}. [nearest integer]

(Given ln10 = 2.3, R = 8.3 J K^{$-$ 1} mol^{$-$ 1}, log 2 = 0.30)

Answer Format:Enter numerical value rounded to the nearest integer

Q 61MathematicsSection A • MCQmatrices and determinants

+4 / -1

Let $f(x) = \left| {\matrix{ a & { - 1} & 0 \cr {ax} & a & { - 1} \cr {a{x^2}} & {ax} & a \cr } } \right|,\,a \in R$ . Then the sum of the squares of all the values of a, for which $2f'(10) - f'(5) + 100 = 0$ , is

A

117

B

106

C

125

D

136

Q 62MathematicsSection B • Numericalprobability

+4 / -1

Let S = {E₁, E₂, ........., E₈} be a sample space of a random experiment such that $P({E_n}) = {n \over {36}}$ for every n = 1, 2, ........, 8. Then the number of elements in the set $\left\{ {A \subseteq S:P(A) \ge {4 \over 5}} \right\}$ is ___________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 63MathematicsSection A • MCQinverse trigonometric functions

+4 / -1

The value of $\cot \left( {\sum\limits_{n = 1}^{50} {{{\tan }^{ - 1}}\left( {{1 \over {1 + n + {n^2}}}} \right)} } \right)$ is :

A

{{26} \over {25}}

B

{{25} \over {26}}

C

{{50} \over {51}}

D

{{52} \over {51}}

Q 64MathematicsSection A • MCQstatistics

+4 / -1

The mean and variance of the data 4, 5, 6, 6, 7, 8, x, y, where x < y, are 6 and ${9 \over 4}$ respectively. Then ${x^4} + {y^2}$ is equal to :

A

162

B

320

C

674

D

420

Q 65MathematicsSection A • MCQmatrices and determinants

+4 / -1

Let A and B be two 3 $\times$ 3 matrices such that $AB = I$ and $|A| = {1 \over 8}$ . Then $|adj\,(B\,adj(2A))|$ is equal to

A

16

B

32

C

64

D

128

Q 66MathematicsSection A • MCQ3d geometry

+4 / -1

The shortest distance between the lines

${{x - 3} \over 2} = {{y - 2} \over 3} = {{z - 1} \over { - 1}}$ and ${{x + 3} \over 2} = {{y - 6} \over 1} = {{z - 5} \over 3}$ , is :

A

{{18} \over {\sqrt 5 }}

B

{{22} \over {3\sqrt 5 }}

C

{{46} \over {3\sqrt 5 }}

D

6\sqrt 3

Q 67MathematicsSection A • MCQmathematical reasoning

+4 / -1

Which of the following statement is a tautology?

A

(( \sim q) \wedge p) \wedge q

B

(( \sim q) \wedge p) \wedge (p \wedge ( \sim p))

C

(( \sim q) \wedge p) \vee (p \vee ( \sim p))

D

(p \wedge q) \wedge ( \sim p \wedge q))

Q 68MathematicsSection A • MCQsequences and series

+4 / -1

Let $S = 2 + {6 \over 7} + {{12} \over {{7^2}}} + {{20} \over {{7^3}}} + {{30} \over {{7^4}}} + \,.....$ . Then 4S is equal to

A

{\left( {{7 \over 3}} \right)^2}

B

{{{7^3}} \over {{3^2}}}

C

{\left( {{7 \over 3}} \right)^3}

D

{{{7^2}} \over {{3^3}}}

Q 69MathematicsSection B • Numericaldifferential equations

+4 / -1

Let $y = y(x)$ be the solution of the differential equation $(1 - {x^2})dy = \left( {xy + ({x^3} + 2)\sqrt {1 - {x^2}} } \right)dx, - 1 < x < 1$ , and $y(0) = 0$ . If $\int_{{{ - 1} \over 2}}^{{1 \over 2}} {\sqrt {1 - {x^2}} y(x)dx = k}$ , then k^{$-$ 1} is equal to _____________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 70MathematicsSection A • MCQdefinite integration

+4 / -1

The integral $\int\limits_0^1 {{1 \over {{7^{\left[ {{1 \over x}} \right]}}}}dx}$ , where [ . ] denotes the greatest integer function, is equal to

A

1 + 6{\log _e}\left( {{6 \over 7}} \right)

B

1 - 6{\log _e}\left( {{6 \over 7}} \right)

C

{\log _e}\left( {{7 \over 6}} \right)

D

1 - 7{\log _e}\left( {{6 \over 7}} \right)

Q 71MathematicsSection A • MCQprobability

+4 / -1

If a point A(x, y) lies in the region bounded by the y-axis, straight lines 2y + x = 6 and 5x $-$ 6y = 30, then the probability that y < 1 is :

A

{1 \over 6}

B

{5 \over 6}

C

{2 \over 3}

D

{6 \over 7}

Q 72MathematicsSection A • MCQdefinite integration

+4 / -1

If m and n respectively are the number of local maximum and local minimum points of the function $f(x) = \int\limits_0^{{x^2}} {{{{t^2} - 5t + 4} \over {2 + {e^t}}}dt}$ , then the ordered pair (m, n) is equal to

A

(3, 2)

B

(2, 3)

C

(2, 2)

D

(3, 4)

Q 73MathematicsSection A • MCQcircle

+4 / -1

The set of values of k, for which the circle $C:4{x^2} + 4{y^2} - 12x + 8y + k = 0$ lies inside the fourth quadrant and the point $\left( {1, - {1 \over 3}} \right)$ lies on or inside the circle C, is :

A

an empty set

B

\left( {6,{{65} \over 9}} \right]

C

\left[ {{{80} \over 9},10} \right)

D

\left( {9,{{92} \over 9}} \right]

Q 74MathematicsSection A • MCQdefinite integration

+4 / -1

Let f be a differentiable function in $\left( {0,{\pi \over 2}} \right)$ . If $\int\limits_{\cos x}^1 {{t^2}\,f(t)dt = {{\sin }^3}x + \cos x}$ , then ${1 \over {\sqrt 3 }}f'\left( {{1 \over {\sqrt 3 }}} \right)$ is equal to

A

6 - 9\sqrt 2

B

6 - {9 \over {\sqrt 2 }}

C

{9 \over 2} - 6\sqrt 2

D

{9 \over {\sqrt 2 }} - 6

Q 75MathematicsSection A • MCQsequences and series

+4 / -1

If a₁, a₂, a₃ ...... and b₁, b₂, b₃ ....... are A.P., and a₁ = 2, a₁₀ = 3, a₁b₁ = 1 = a₁₀b₁₀, then a₄ b₄ is equal to -

A

{{35} \over {27}}

B

1

C

{{27} \over {28}}

D

{{28} \over {27}}

Q 76MathematicsSection A • MCQparabola

+4 / -1

If the equation of the parabola, whose vertex is at (5, 4) and the directrix is $3x + y - 29 = 0$ , is ${x^2} + a{y^2} + bxy + cx + dy + k = 0$ , then $a + b + c + d + k$ is equal to :

A

575

B

-

575

C

576

D

-

576

Q 77MathematicsSection B • Numericallimits continuity and differentiability

+4 / -1

Let [t] denote the greatest integer $\le$ t and {t} denote the fractional part of t. The integral value of $\alpha$ for which the left hand limit of the function

$f(x) = [1 + x] + {{{\alpha ^{2[x] + {\{x\}}}} + [x] - 1} \over {2[x] + \{ x\} }}$ at x = 0 is equal to $\alpha - {4 \over 3}$ , is _____________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 78MathematicsSection A • MCQvector algebra

+4 / -1

Let $\overrightarrow a$ and $\overrightarrow b$ be the vectors along the diagonals of a parallelogram having area $2\sqrt 2$ . Let the angle between $\overrightarrow a$ and $\overrightarrow b$ be acute, $|\overrightarrow a | = 1$ , and $|\overrightarrow a \,.\,\overrightarrow b | = |\overrightarrow a \times \overrightarrow b |$ . If $\overrightarrow c = 2\sqrt 2 \left( {\overrightarrow a \times \overrightarrow b } \right) - 2\overrightarrow b$ , then an angle between $\overrightarrow b$ and $\overrightarrow c$ is :

A

{\pi \over 4}

B

-

{\pi \over 4}

C

{{5\pi } \over 6}

D

{{3\pi } \over 4}

Q 79MathematicsSection B • Numericaldifferentiation

+4 / -1

If $y(x) = {\left( {{x^x}} \right)^x},\,x > 0$ , then ${{{d^2}x} \over {d{y^2}}} + 20$ at x = 1 is equal to ____________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 80MathematicsSection A • MCQtrigonometric functions and equations

+4 / -1

Let for some real numbers $\alpha$ and $\beta$ , $a = \alpha - i\beta$ . If the system of equations $4ix + (1 + i)y = 0$ and $8\left( {\cos {{2\pi } \over 3} + i\sin {{2\pi } \over 3}} \right)x + \overline a y = 0$ has more than one solution, then ${\alpha \over \beta }$ is equal to

A

- 2\sqrt 3

B

2 - \sqrt 3

C

2 + \sqrt 3

D

- 2 - \sqrt 3

Q 81MathematicsSection B • Numericalarea under the curves

+4 / -1

If the area of the region $\left\{ {(x,y):{x^{{2 \over 3}}} + {y^{{2 \over 3}}} \le 1,\,x + y \ge 0,\,y \ge 0} \right\}$ is A, then ${{256A} \over \pi }$ is equal to __________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 82MathematicsSection A • MCQcomplex numbers

+4 / -1

The number of points of intersection of

$|z - (4 + 3i)| = 2$ and $|z| + |z - 4| = 6$ , z $\in$ C, is :

A

0

B

1

C

2

D

3

Q 83MathematicsSection A • MCQtrigonometric ratios and identities

+4 / -1

$\alpha = \sin 36^\circ$ is a root of which of the following equation?

A

16{x^4} - 10{x^2} - 5 = 0

B

16{x^4} + 20{x^2} - 5 = 0

C

4{x^4} - 20{x^2} + 5 = 0

D

4{x^4} - 10{x^2} + 5 = 0

Q 84MathematicsSection B • Numericalfunctions

+4 / -1

Let S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Define f : S $\to$ S as

$f(n) = \left\{ {\matrix{ {2n} & , & {if\,n = 1,2,3,4,5} \cr {2n - 11} & , & {if\,n = 6,7,8,9,10} \cr } } \right.$ .

Let g : S $\to$ S be a function such that $fog(n) = \left\{ {\matrix{ {n + 1} & , & {if\,n\,\,is\,odd} \cr {n - 1} & , & {if\,n\,\,is\,even} \cr } } \right.$ .

Then $g(10)g(1) + g(2) + g(3) + g(4) + g(5))$ is equal to _____________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 85MathematicsSection A • MCQdifferential equations

+4 / -1

If the solution curve of the differential equation

$(({\tan ^{ - 1}}y) - x)dy = (1 + {y^2})dx$ passes through the point (1, 0), then the abscissa of the point on the curve whose ordinate is tan(1), is

A

2e

B

{2 \over e}

C

2

D

{1 \over e}

Q 86MathematicsSection A • MCQ3d geometry

+4 / -1

Let the foot of the perpendicular from the point (1, 2, 4) on the line ${{x + 2} \over 4} = {{y - 1} \over 2} = {{z + 1} \over 3}$ be P. Then the distance of P from the plane $3x + 4y + 12z + 23 = 0$ is :

A

5

B

{{50} \over {13}}

C

4

D

{{63} \over {13}}

Q 87MathematicsSection B • Numericalpermutations and combinations

+4 / -1

Let A be a matrix of order 2 $\times$ 2, whose entries are from the set {0, 1, 2, 3, 4, 5}. If the sum of all the entries of A is a prime number p, 2 < p < 8, then the number of such matrices A is ___________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 88MathematicsSection B • Numericalcircle

+4 / -1

Let a circle C of radius 5 lie below the x-axis. The line L₁ : 4x + 3y + 2 = 0 passes through the centre P of the circle C and intersects the line L₂ = 3x $-$ 4y $-$ 11 = 0 at Q. The line L₂ touches C at the point Q. Then the distance of P from the line 5x $-$ 12y + 51 = 0 is ______________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 89MathematicsSection B • Numericalbinomial theorem

+4 / -1

If the sum of the coefficients of all the positive powers of x, in the Binomial expansion of ${\left( {{x^n} + {2 \over {{x^5}}}} \right)^7}$ is 939, then the sum of all the possible integral values of n is _________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 90MathematicsSection B • Numericalquadratic equation and inequalities

+4 / -1

Let $\alpha$ , $\beta$ be the roots of the equation ${x^2} - 4\lambda x + 5 = 0$ and $\alpha$ , $\gamma$ be the roots of the equation ${x^2} - \left( {3\sqrt 2 + 2\sqrt 3 } \right)x + 7 + 3\lambda \sqrt 3 = 0$ , $\lambda$ > 0. If $\beta + \gamma = 3\sqrt 2$ , then ${(\alpha + 2\beta + \gamma )^2}$ is equal to __________.

Answer Format:Enter numerical value rounded to the nearest integer

JEE Main 2022 27th June Evening Shift Question Paper with Solutions