JEE Main 2022 26th June Morning Shift Question Paper Question Paper with Solutions | JEE Main Mock Test | JeeMate

Q 1PhysicsSection A • MCQlaws of motion

+4 / -1

A person is standing in an elevator. In which situation, he experiences weight loss?

A

When the elevator moves upward with constant acceleration

B

When the elevator moves downward with constant acceleration

C

When the elevator moves upward with uniform velocity

D

When the elevator moves downward with uniform velocity

Q 2PhysicsSection A • MCQcurrent electricity

+4 / -1

An aluminium wire is stretched to make its length, 0.4% larger. The percentage change in resistance is :

A

0.4%

B

0.2%

C

0.8%

D

0.6%

Q 3PhysicsSection A • MCQelectromagnetic waves

+4 / -1

In free space, an electromagnetic wave of 3 GHz frequency strikes over the edge of an object of size ${\lambda \over {100}}$ , where $\lambda$ is the wavelength of the wave in free space. The phenomenon, which happens there will be :

A

Reflection

B

Refraction

C

Diffraction

D

Scattering

Q 4PhysicsSection B • Numericalmotion

+4 / -1

A ball of mass 0.5 kg is dropped from the height of 10 m. The height, at which the magnitude of velocity becomes equal to the magnitude of acceleration due to gravity, is ________ m. [Use g = 10 m/s²]

Answer Format:Enter numerical value rounded to the nearest integer

Q 5PhysicsSection A • MCQgravitation

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The variation of acceleration due to gravity (g) with distance (r) from the center of the earth is correctly represented by :

(Given R = radius of earth)

A

B

C

D

Q 6PhysicsSection A • MCQdual nature of radiation

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An electron with speed v and a photon with speed c have the same de-Broglie wavelength. If the kinetic energy and momentum of electron are E_e and p_e and that of photon are E_ph and p_ph respectively. Which of the following is correct?

A

{{{E_e}} \over {{E_{ph}}}} = {{2c} \over v}

B

{{{E_e}} \over {{E_{ph}}}} = {v \over {2c}}

C

{{{p_e}} \over {{p_{ph}}}} = {{2c} \over v}

D

{{{p_e}} \over {{p_{ph}}}} = {v \over {2c}}

Q 7PhysicsSection B • Numericalmotion

+4 / -1

A fighter jet is flying horizontally at a certain altitude with a speed of 200 ms^{$-$ 1}. When it passes directly overhead an anti-aircraft gun, a bullet is fired from the gun, at an angle $\theta$ with the horizontal, to hit the jet. If the bullet speed is 400 m/s, the value of $\theta$ will be ___________ $^\circ$ .

Answer Format:Enter numerical value rounded to the nearest integer

Q 8PhysicsSection B • Numericalelectromagnetic induction

+4 / -1

A 10 $\Omega$ , 20 mH coil carrying constant current is connected to a battery of 20 V through a switch. Now after switch is opened current becomes zero in 100 $\mu$ s. The average e.m.f. induced in the coil is ____________ V.

Answer Format:Enter numerical value rounded to the nearest integer

Q 9PhysicsSection B • Numericalalternating current

+4 / -1

A 110 V, 50 Hz, AC source is connected in the circuit (as shown in figure). The current through the resistance 55 $\Omega$ , at resonance in the circuit, will be __________ A.

qImage-ac-circuits-and-power-in-ac-circuits-alternating-current-electricity-Jeemate

Answer Format:Enter numerical value rounded to the nearest integer

Q 10PhysicsSection A • MCQmagnetics

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A proton and an alpha particle of the same velocity enter in a uniform magnetic field which is acting perpendicular to their direction of motion. The ratio of the radii of the circular paths described by the alpha particle and proton is :

A

1 : 4

B

4 : 1

C

2 : 1

D

1 : 2

Q 11PhysicsSection A • MCQsimple harmonic motion

+4 / -1

Time period of a simple pendulum in a stationary lift is 'T'. If the lift accelerates with ${g \over 6}$ vertically upwards then the time period will be :

(Where g = acceleration due to gravity)

A

\sqrt {{6 \over 5}} T

B

\sqrt {{5 \over 6}} T

C

\sqrt {{6 \over 7}} T

D

\sqrt {{7 \over 6}} T

Q 12PhysicsSection B • Numericalproperties of matter

+4 / -1

The elongation of a wire on the surface of the earth is 10^{$-$ 4} m. The same wire of same dimensions is elongated by 6 $\times$ 10^{$-$ 5} m on another planet. The acceleration due to gravity on the planet will be ____________ ms^{$-$ 2}. (Take acceleration due to gravity on the surface of earth = 10 ms^{$-$ 2})

Answer Format:Enter numerical value rounded to the nearest integer

Q 13PhysicsSection A • MCQelectrostatics

+4 / -1

Given below two statements : One is labelled as Assertion (A) and other is labelled as Reason (R).

Assertion (A) : Non-polar materials do not have any permanent dipole moment.

Reason (R) : When a non-polar material is placed in an electric field, the centre of the positive charge distribution of it's individual atom or molecule coincides with the centre of the negative charge distribution.

In the light of 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 and (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 14PhysicsSection A • MCQheat and thermodynamics

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A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats 1.4. Vessel is moving with speed v and is suddenly brought to rest. Assuming no heat is lost to the surrounding and vessel temperature of the gas increases by :

(R = universal gas constant)

A

{{M{v^2}} \over {7R}}

B

{{M{v^2}} \over {5R}}

C

2

{{M{v^2}} \over {7R}}

D

7

{{M{v^2}} \over {5R}}

Q 15PhysicsSection B • Numericalproperties of matter

+4 / -1

The elastic behaviour of material for linear stress and linear strain, is shown in the figure. The energy density for a linear strain of 5 $\times$ 10^{$-$ 4} is __________ kJ/m³. Assume that material is elastic upto the linear strain of 5 $\times$ 10^{$-$ 4}.

qImage-stress-strain-curve-thermal-stress-and-elastic-pe-properties-of-matter-mechanics-Jeemate

Answer Format:Enter numerical value rounded to the nearest integer

Q 16PhysicsSection A • MCQelectronic devices

+4 / -1

The I-V characteristics of a p-n junction diode in forward bias is shown in the figure. The ratio of dynamic resistance, corresponding to forward bias voltage of 2 V and 4 V respectively, is :

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

A

1 : 2

B

5 : 1

C

1 : 40

D

20 : 1

Q 17PhysicsSection B • Numericalelectronic devices

+4 / -1

As per the given circuit, the value of current through the battery will be ____________ A.

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

Answer Format:Enter numerical value rounded to the nearest integer

Q 18PhysicsSection A • MCQelectromagnetic waves

+4 / -1

If Electric field intensity of a uniform plane electromagnetic wave is given as $E = - 301.6\sin (kz - \omega t){\widehat a_x} + 452.4\sin (kz - \omega t){\widehat a_y}{V \over m}$ . Then magnetic intensity 'H' of this wave in Am^{$-$ 1} will be :

[Given : Speed of light in vacuum $c = 3 \times {10^8}$ ms^{$-$ 1}, Permeability of vacuum ${\mu _0} = 4\pi \times {10^{ - 7}}$ NA^{$-$ 2}]

A

+ 0.8\sin (kz - \omega t){\widehat a_y} + 0.8\sin (kz - \omega t){\widehat a_x}

B

+ 1.0 \times {10^{ - 6}}\sin (kz - \omega t){\widehat a_y} + 1.5 \times {10^{ - 6}}(kz - \omega t){\widehat a_x}

C

- 0.8\sin (kz - \omega t){\widehat a_y} - 1.2\sin (kz - \omega t){\widehat a_x}

D

- 1.0 \times {10^{ - 6}}\sin (kz - \omega t){\widehat a_y} - 1.5 \times {10^{ - 6}}\sin (kz - \omega t){\widehat a_x}

Q 19PhysicsSection B • Numericalray optics

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A light ray is incident, at an incident angle $\theta$ ₁, on the system of tow plane mirrors M₁ and M₂ having an inclination angle 75 $^\circ$ between them (as shown in figure). After reflecting from mirror M₁ it gets reflected back by the mirror M₂ with an angle of reflection 30 $^\circ$ . The total deviation of the ray will be _____________ degree.

qImage-reflection-of-light-geometrical-optics-optics-Jeemate

Answer Format:Enter numerical value rounded to the nearest integer

Q 20PhysicsSection B • Numericalunits and measurements

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In a vernier callipers, each cm on the main scale is divided into 20 equal parts. If tenth vernier scale division coincides with nineth main scale division. Then the value of vernier constant will be _________ $\times$ 10^{$-$ 2} mm.

Answer Format:Enter numerical value rounded to the nearest integer

Q 21PhysicsSection A • MCQelectromagnetic induction

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The magnetic flux through a coil perpendicular to its plane is varying according to the relation $\phi = (5{t^3} + 4{t^2} + 2t - 5)$ Weber. If the resistance of the coil is 5 ohm, then the induced current through the coil at t = 2 s will be,

A

15.6 A

B

16.6 A

C

17.6 A

D

18.6 A

Q 22PhysicsSection A • MCQunits and measurements

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An expression for a dimensionless quantity P is given by $P = {\alpha \over \beta }{\log _e}\left( {{{kt} \over {\beta x}}} \right)$ ; where $\alpha$ and $\beta$ are constants, x is distance; k is Boltzmann constant and t is the temperature. Then the dimensions of $\alpha$ will be :

A

[M⁰ L^{$-$ 1} T⁰]

B

[M L⁰ T^{$-$ 2}]

C

[M L T^{$-$ 2}]

D

[M L² T^{$-$ 2}]

Q 23PhysicsSection A • MCQcircular motion

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A ball is released from rest from point P of a smooth semi-spherical vessel as shown in figure. The ratio of the centripetal force and normal reaction on the ball at point Q is A while angular position of point Q is $\alpha$ with respect to point P. Which of the following graphs represent the correct relation between A and $\alpha$ when ball goes from Q to R?

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

A

B

C

D

Q 24PhysicsSection A • MCQcenter of mass

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An object is thrown vertically upwards. At its maximum height, which of the following quantity becomes zero?

A

Momentum

B

Potential Energy

C

Acceleration

D

Force

Q 25PhysicsSection A • MCQatoms and nuclei

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How many alpha and beta particles are emitted when Uranium ₉₂U²³⁸ decays to lead ₈₂Pb²⁰⁶ ?

A

3 alpha particles and 5 beta particles

B

6 alpha particles and 4 beta particles

C

4 alpha particles and 5 beta particles

D

8 alpha particles and 6 beta particles

Q 26PhysicsSection B • Numericalproperties of matter

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An ideal fluid of density 800 kgm^{$-$ 3}, flows smoothly through a bent pipe (as shown in figure) that tapers in cross-sectional area from a to ${a \over 2}$ . The pressure difference between the wide and narrow sections of pipe is 4100 Pa. At wider section, the velocity of fluid is ${{\sqrt x } \over 6}$ ms^{$-$ 1} for x = ___________. (Given g = 10 ms^{$-$ 2})

qImage-fluid-flow-bernoullis-principle-and-viscosity-properties-of-matter-mechanics-Jeemate

Answer Format:Enter numerical value rounded to the nearest integer

Q 27PhysicsSection A • MCQcommunication systems

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Choose the correct statement for amplitude modulation :

A

Amplitude of modulating signal is varied in accordance with the information signal.

B

Amplitude of modulated signal is varied in accordance with the information signal.

C

Amplitude of carrier signal is varied in accordance with the information signal.

D

Amplitude of modulated signal is varied in accordance with the modulating signal.

Q 28PhysicsSection A • MCQcapacitor

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Two capacitors having capacitance C₁ and C₂ respectively are connected as shown in figure. Initially, capacitor C₁ is charged to a potential difference V volt by a battery. The battery is then removed and the charged capacitor C₁ is now connected to uncharged capacitor C₂ by closing the switch S. The amount of charge on the capacitor C₂, after equilibrium, is :

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

A

{{{C_1}{C_2}} \over {({C_1} + {C_2})}}V

B

{{({C_1} + {C_2})} \over {{C_1}{C_2}}}V

C

({C_1} + {C_2})V

D

({C_1} - {C_2})V

Q 29PhysicsSection A • MCQheat and thermodynamics

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The efficiency of a Carnot's engine, working between steam point and ice point, will be :

A

26.81%

B

37.81%

C

47.81%

D

57.81%

Q 30PhysicsSection A • MCQrotational motion

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A thin circular ring of mass M and radius R is rotating with a constant angular velocity 2 rads^{$-$ 1} in a horizontal plane about an axis vertical to its plane and passing through the center of the ring. If two objects each of mass m be attached gently to the opposite ends of a diameter of ring, the ring will then rotate with an angular velocity (in rads^{$-$ 1}).

A

{M \over {(M + m)}}

B

{{(M + 2m)} \over {2M}}

C

{{2M} \over {(M + 2m)}}

D

{{2(M + 2m)} \over M}

Q 31ChemistrySection A • MCQatomic structure

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If the radius of the 3^rd Bohr's orbit of hydrogen atom is r₃ and the radius of 4^th Bohr's orbit is r₄. Then :

A

{r_4} = {9 \over {16}}{r_3}

B

{r_4} = {16 \over {9}}{r_3}

C

{r_4} = {3 \over {4}}{r_3}

D

{r_4} = {4 \over {3}}{r_3}

Q 32ChemistrySection B • Numericalalcohols phenols and ethers

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Compound 'P' on nitration with dil. HNO₃ yields two isomers (A) and (B). These isomers can be separated by steam distillation. Isomers (A) and (B) show the intramolecular and intermolecular hydrogen bonding respectively. Compound (P) on reaction with conc. HNO₃ yields a yellow compound 'C', a strong acid. The number of oxygen atoms is present in compound 'C' _____________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 33ChemistrySection A • MCQcompounds containing nitrogen

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Among the following structures, which will show the most stable enamine formation? (Where Me is $-$ CH₃)

A

B

C

D

Q 34ChemistrySection B • Numericalionic equilibrium

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50 mL of 0.1 M CH₃COOH is being titrated against 0.1 M NaOH. When 25 mL of NaOH has been added, the pH of the solution will be _____________ $\times$ 10^{$-$ 2}. (Nearest integer)

(Given : pK_a (CH₃COOH) = 4.76)

log 2 = 0.30

log 3 = 0.48

log 5 = 0.69

log 7 = 0.84

log 11 = 1.04

Answer Format:Enter numerical value rounded to the nearest integer

Q 35ChemistrySection A • MCQisolation of elements

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Given below are two statements :

Statement I : According to Ellingham diagram, any metal oxide with higher $\Delta$ G $^\circ$ is more stable than the one with lower $\Delta$ G $^\circ$ .

Statement II : The metal involved in the formation of oxide placed lower in the Ellingham diagram can reduce the oxide of a metal placed higher in the diagram.

In the light of the above statements, choose the most appropriate 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 36ChemistrySection A • MCQp block elements

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Consider the following reaction :

A + alkali $\to$ B (Major Product)

If B is an oxoacid of phosphorus with no P-H bond, then A is :

A

White P₄

B

Red P₄

C

P₂O₃

D

H₃PO₃

Q 37ChemistrySection B • Numericalthermodynamics

+4 / -1

For complete combustion of methanol

CH₃OH(I) + ${3 \over 2}$ O₂(g) $\to$ CO₂(g) + 2H₂O(I)

the amount of heat produced as measured by bomb calorimeter is 726 kJ mol^{$-$ 1} at 27 $^\circ$ C. The enthalpy of combustion for the reaction is $-$ x kJ mol^{$-$ 1}, where x is ___________. (Nearest integer)

(Given : R = 8.3 JK^{$-$ 1} mol^{$-$ 1})

Answer Format:Enter numerical value rounded to the nearest integer

Q 38ChemistrySection B • Numericalbiomolecules

+4 / -1

The number of oxygens present in a nucleotide formed from a base, that is present only in RNA is ___________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 39ChemistrySection B • Numericalsolutions

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A 0.5 percent solution of potassium chloride was found to freeze at $-$ 0.24 $^\circ$ C. The percentage dissociation of potassium chloride is ______________. (Nearest integer)

(Molal depression constant for water is 1.80 K kg mol^{$-$ 1} and molar mass of KCl is 74.6 g mol^{$-$ 1})

Answer Format:Enter numerical value rounded to the nearest integer

Q 40ChemistrySection B • Numericalsome basic concepts of chemistry

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On complete combustion 0.30 g of an organic compound gave 0.20 g of carbon dioxide and 0.10 g of water. The percentage of carbon in the given organic compound is _____________. (Nearest integer)

Answer Format:Enter numerical value rounded to the nearest integer

Q 41ChemistrySection A • MCQelectrochemistry

+4 / -1

The ${\left( {{{\partial E} \over {\partial T}}} \right)_P}$ of different types of half cells are as follows:

A	B	C	D
$1 \times {10^{ - 4}}$	$2 \times {10^{ - 4}}$	$0.1 \times {10^{ - 4}}$	$0.2 \times {10^{ - 4}}$

(Where E is the electromotive force)

Which of the above half cells would be preferred to be used as reference electrode?

A

B

C

D

Q 42ChemistrySection A • MCQaldehydes ketones and carboxylic acids

+4 / -1

(C₇H₅O₂)₂ $\buildrel {hv} \over \longrightarrow$ [X] $\to$ 2C₆H₅ + 2CO₂

Consider the above reaction and identify the intermediate 'X'

A

B

C

D

Q 43ChemistrySection A • MCQhydrogen

+4 / -1

Consider the following reaction:

$2HSO_4^ - (aq)\mathrel{\mathop{\kern0pt\longrightarrow} \limits_{(2)\,Hydrolysis}^{(1)\,Electrolysis}} 2HSO_4^ - + 2{H^ + } + A$

The dihedral angle in product A in its solid phase at 110 K is :

A

104

^\circ

B

111.5

^\circ

C

90.2

^\circ

D

111.0

^\circ

Q 44ChemistrySection A • MCQaldehydes ketones and carboxylic acids

+4 / -1

Which will have the highest enol content?

A

B

C

D

Q 45ChemistrySection A • MCQalcohols phenols and ethers

+4 / -1

qImage-properties-preparation-and-uses-of-phenols-alcohols-phenols-and-ethers-organic-chemistry-Jeemate

Consider the above reaction sequence and identify the product B.

A

B

C

D

Q 46ChemistrySection A • MCQsome basic concepts of chemistry

+4 / -1

A commercially sold conc. HCl is 35% HCl by mass. If the density of this commercial acid is 1.46 g/mL, the molarity of this solution is:

(Atomic mass : Cl = 35.5 amu, H = 1 amu)

A

10.2 M

B

12.5 M

C

14.0 M

D

18.2 M

Q 47ChemistrySection A • MCQchemistry in everyday life

+4 / -1

A chemical which stimulates the secretion of pepsin is :

A

Anti histamine

B

Cimetidine

C

Histamine

D

Zantac

Q 48ChemistrySection A • MCQs block elements

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The correct order of melting point is :

A

Be > Mg > Ca > Sr

B

Sr > Ca > Mg > Be

C

Be > Ca > Mg > Sr

D

Be > Ca > Sr > Mg

Q 49ChemistrySection A • MCQp block elements

+4 / -1

The correct order of melting points of hydrides of group 16 elements is :

A

H₂S < H₂Se < H₂Te < H₂O

B

H₂O < H₂S < H₂Se < H₂Te

C

H₂S < H₂Te < H₂Se < H₂O

D

H₂Se < H₂S < H₂Te < H₂O

Hydride	M.P.
H₂O	273 K
H₂S	188 K
H₂Se	208 K
H₂Te	222 K

Q 50ChemistrySection A • MCQenvironmental chemistry

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Polar stratospheric clouds facilitate the formation of :

A

ClONO₂

B

HOCl

C

ClO

D

CH₄

Q 51ChemistrySection A • MCQcoordination compounds

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Which statement is not true with respect to nitrate ion test?

A

A dark brown ring is formed at the junction of two solutions.

B

Ring is formed due to nitroferrous sulphate complex.

C

The brown complex is [Fe(H₂O)₅ (NO)]SO₄.

D

Heating the nitrate salt with conc. H₂SO₄, light brown fumes are evolved.

Q 52ChemistrySection A • MCQchemical bonding and molecular structure

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Consider the ions/molecule

O $_2^ +$ , O₂, O $_2^ -$ , O $_2^ {2-}$

For increasing bond order the correct option is :

A

O

_2^ {2-}

< O

_2^ -

< O₂ < O

_2^ +

B

O

_2^ -

< O

_2^ {2-}

< O₂ < O

_2^ +

C

O

_2^ -

< O

_2^ {2-}

< O

_2^ +

< O₂

D

O

_2^ -

< O

_2^ +

< O

_2^ {2-}

< O₂

Official Correct Answer:Option (A)

Step-by-Step Solution:

Note :

(1)

\,\,\,\,

Bond strength

\propto

Bond order

(2)

\,\,\,\,

Bond length

\propto

{1 \over {Bond\,\,order}}

(3)

\,

Bond order

= {1 \over 2}

[N_b

-

N_a]

N_b = Number of electrons in bonding molecular orbital

N_a

=

Number of electrons in anti bonding molecular orbital

(4)

\,\,\,\,

upto 14 electrons, molecular orbital configuration is

qImage-molecular-orbital-theory-chemical-bonding-and-molecular-structure-inorganic-chemistry-Jeemate

qImage-molecular-orbital-theory-chemical-bonding-and-molecular-structure-inorganic-chemistry-Jeemate

Here N_a = Anti bonding electron

=

4 and N_b = 10

(5)

\,\,\,\,

After 14 electrons to 20 electrons molecular orbital configuration is - - -

qImage-molecular-orbital-theory-chemical-bonding-and-molecular-structure-inorganic-chemistry-Jeemate

Here N_a = 10

and N_b = 10

In O atom 8 electrons present, so in O₂, 8

\times

2 = 16 electrons present.

Then in

O_2^ +

no of electrons = 15

in

O_2^ -

no of electrons = 17

in

O_2^{2 - }

no of electrons = 18

\therefore\,\,\,\,

Molecular orbital configuration of O₂ (16 electrons) is

{\sigma _{1{s^2}}}\,\,\sigma _{1{s^2}}^ * \,

{\sigma _{2{s^2}}}\,\,\sigma _{2{s^2}}^ * \,

{\sigma _{2p_z^2}}\,\,{\pi _{2p_x^2}} = {\pi _{2p_y^2}}\,\,\pi _{2p_x^1}^ * \,\, = \pi _{2p_y^1}^ *

\therefore\,\,\,\,

N_a = 6

N_b = 10

\therefore\,\,\,\,

BO =

{1 \over 2}\left[ {10 - 6} \right] = 2

Molecular orbital configuration of O

_2^ +

(15 electrons) is

{\sigma _{1{s^2}}}\,\sigma _{1{s^2}}^ * \,{\sigma _{2{s^2}}}\,\sigma _{2{s^2}}^ * \,{\sigma _{2p_z^2}}\,{\pi _{2p_x^2}}\, = \,{\pi _{2p_y^2}}\,\pi _{2p_x^1}^ * \, = \,\pi _{2p_y^o}^ *

\therefore\,\,\,\,

N_b = 10

N_a = 5

\therefore\,\,\,\,

BO =

{1 \over 2}\left[ {10 - 5} \right]

= 2.5

Molecular orbital configuration of

O_2^ -

(17 electrons) is

{\sigma _{1{s^2}}}\,\sigma _{1{s^2}}^ * \,{\sigma _{2{s^2}}}\,\sigma _{2{s^2}}^ * \,{\sigma _{2p_z^2}}\,{\pi _{2p_x^2}}\, = \,{\pi _{2p_y^2}}\,\pi _{2p_x^2}^ * \, = \,\pi _{2p_y^1}^ *

\therefore\,\,\,\,

N_b = 10

N_a = 7

\therefore\,\,\,\,

BO =

{1 \over 2}\left[ {10 - 7} \right]

= 1.5

Molecular orbital configuration of O

_2^{2 - }

(18 electrons) is

{\sigma _{1{s^2}}}\,\sigma _{1{s^2}}^ * \,{\sigma _{2{s^2}}}\,\sigma _{2{s^2}}^ * \,{\sigma _{2p_z^2}}\,{\pi _{2p_x^2}}\, = \,{\pi _{2p_y^2}}\,\pi _{2p_x^2}^ * \, = \,\pi _{2p_y^2}^ *

\therefore\,\,\,\,

N_b = 10

N_a = 8

\therefore\,\,\,\,

BO =

{1 \over 2}

[ 10

-

8] = 1

So, correct order of Bond order is

O_2^{2 - } < O_2^ - < {O_2} < O_2^ +

Q 53ChemistrySection B • Numericalchemical kinetics and nuclear chemistry

+4 / -1

A flask is filled with equal moles of A and B. The half lives of A and B are 100 s and 50 s respectively and are independent of the initial concentration. The time required for the concentration of A to be four times that of B is ___________ s.

(Given : ln 2 = 0.693)

Answer Format:Enter numerical value rounded to the nearest integer

Q 54ChemistrySection B • Numericalcoordination compounds

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The spin-only magnetic moment value of an octahedral complex among CoCl₃.4NH₃, NiCl₂.6H₂O and PtCl₄.2HCl, which upon reaction with excess of AgNO₃ gives 2 moles of AgCl is ___________ B.M. (Nearest integer)

Answer Format:Enter numerical value rounded to the nearest integer

Official Correct Answer:3

Step-by-Step Solution:

From the given information, we are looking for a complex which, upon reaction with excess of AgNO₃, gives 2 moles of AgCl. This implies that the complex has 2 chloride ions involved.

Considering the complexes :

CoCl₃.4NH₃ : This complex has 3 chloride ions, so it's not the one we are looking for.

NiCl₂.6H₂O : This complex has 2 chloride ions, so it's a potential candidate.

PtCl₄.2HCl : This complex has 4 chloride ions, so it's not the one we are looking for.

Therefore, the complex we are interested in is NiCl₂.6H₂O.

\mathrm{CoCl}_{3} \cdot 4 \mathrm{NH}_{3} \underset{\text { excess }}{\stackrel{\mathrm{AgNO}_{3}}{\longrightarrow}}\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \cdot \mathrm{Cl}_{2}\right]+\mathrm{AgCl}

\left.\left.\mathrm{NiCl}_{2} \cdot 6 \mathrm{H}_{2} \mathrm{O} \underset{\text { excess }}{\stackrel{\mathrm{AgNO}_{3}}{\longrightarrow}}\right[ \mathrm{Ni}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}+2 \mathrm{AgCl}

\mathrm{PtCl}_{4} \cdot 2 \mathrm{HCl} \longrightarrow\left[\mathrm{PtCl}_{6}\right]^{4-}+\mathrm{No} ~\mathrm{AgCl} ~\mathrm{ppt}

The next step is to find the oxidation state of the nickel ion. The nickel ion must have a charge of +2 to balance the -2 charge from the two chloride ions, thus it is Ni²⁺.

In the case of Ni²⁺, the electron configuration is [Ar]3d⁸. For an octahedral complex, the d-orbitals split into two sets under the influence of ligands: the $e_g$ set which includes d(x²-y²) and d(z²) orbitals, and the $t_{2g}$ set which includes the d(xy), d(xz), and d(yz) orbitals. Electrons will occupy the lower energy $t_{2g}$ orbitals first.

The 3d⁸ electron configuration implies there are 8 electrons in the 3d orbitals. The first six electrons pair up in the three $t_{2g}$ orbitals, and the next two electrons will go into the two $e_g$ orbitals, with each one having one unpaired electron.

The spin-only magnetic moment (μ) can be calculated using the formula :

$\mu = \sqrt{n(n+2)} \, \text{B.M.}$

where n is the number of unpaired electrons. In this case, n = 2, so

$\mu = \sqrt{2 \times (2+2)} = \sqrt{8} \, \text{B.M.}$

Rounding to the nearest integer, the spin-only magnetic moment is approximately 3 B.M.

Q 55ChemistrySection A • MCQpractical organic chemistry

+4 / -1

Given below are two statements :

Statement I : In 'Lassaigne's Test', when both nitrogen and sulphur are present in an organic compound, sodium thiocyanate is formed.

Statement II : If both nitrogen and sulphur are present in an organic compound, then the excess of sodium used in sodium fusion will decompose the sodium thiocyanate formed to give NaCN and Na₂S.

In the light of the above statements, choose the most appropriate 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 56ChemistrySection B • Numericald and f block elements

+4 / -1

The spin-only magnetic moment value of the most basic oxide of vanadium among V₂O₃, V₂O₄ and V₂O₅ is _____________ B.M. (Nearest integer)

Answer Format:Enter numerical value rounded to the nearest integer

Q 57ChemistrySection A • MCQgaseous state

+4 / -1

An evacuated glass vessel weighs 40.0 g when empty, 135.0 g when filled with a liquid of density 0.95 g mL^{$-$ 1} and 40.5 g when filled with an ideal gas at 0.82 atm at 250 K. The molar mass of the gas in g mol^{$-$ 1} is :

(Given : R = 0.082 L atm K^{$-$ 1} mol^{$-$ 1})

A

35

B

50

C

75

D

125

Q 58ChemistrySection A • MCQp block elements

+4 / -1

Choose the correct stability order of group 13 elements in their + 1 oxidation state :

A

Al < Ga < In < Tl

B

Tl < In < Ga < Al

C

Al < Ga < Tl < In

D

Al < Tl < Ga < In

Q 59ChemistrySection A • MCQpolymers

+4 / -1

Which of the following sets are correct regarding polymer?

(A) Copolymer : Buna-S

(B) Condensation polymer : Nylon-6,6

(C) Fibres : Nylon-6,6

(D) Thermosetting polymer : Terylene

(E) Homopolymer : Buna-N

Choose the correct answer from given options below :

A

(A), (B) and (C) are correct

B

(B), (C) and (D) are correct

C

(A), (C) and (E) are correct

D

(A), (B) and (D) are correct

Q 60ChemistrySection B • Numericalgaseous state

+4 / -1

2.0 g of H₂ gas is adsorbed on 2.5 g of platinum powder at 300 K and 1 bar pressure. The volume of the gas adsorbed per gram of the adsorbent is __________ mL.

(Given : R = 0.083 L bar K^{$-$ 1} mol^{$-$ 1})

Answer Format:Enter numerical value rounded to the nearest integer

Q 61MathematicsSection A • MCQcomplex numbers

+4 / -1

Let $A = \left\{ {z \in C:\left| {{{z + 1} \over {z - 1}}} \right| < 1} \right\}$ and $B = \left\{ {z \in C:\arg \left( {{{z - 1} \over {z + 1}}} \right) = {{2\pi } \over 3}} \right\}$ . Then A $\cap$ B is :

A

a portion of a circle centred at

\left( {0, - {1 \over {\sqrt 3 }}} \right)

that lies in the second and third quadrants only

B

a portion of a circle centred at

\left( {0, - {1 \over {\sqrt 3 }}} \right)

that lies in the second quadrant only

C

an empty

D

a portion of a circle of radius

{2 \over {\sqrt 3 }}

that lies in the third quadrant only

Q 62MathematicsSection A • MCQ3d geometry

+4 / -1

If the two lines ${l_1}:{{x - 2} \over 3} = {{y + 1} \over {-2}},\,z = 2$ and ${l_2}:{{x - 1} \over 1} = {{2y + 3} \over \alpha } = {{z + 5} \over 2}$ are perpendicular, then an angle between the lines l₂ and ${l_3}:{{1 - x} \over 3} = {{2y - 1} \over { - 4}} = {z \over 4}$ is :

A

{\cos ^{ - 1}}\left( {{{29} \over 4}} \right)

B

{\sec ^{ - 1}}\left( {{{29} \over 4}} \right)

C

{\cos ^{ - 1}}\left( {{2 \over {29}}} \right)

D

{\cos ^{ - 1}}\left( {{2 \over {\sqrt {29} }}} \right)

Q 63MathematicsSection B • Numericalparabola

+4 / -1

Let the common tangents to the curves $4({x^2} + {y^2}) = 9$ and ${y^2} = 4x$ intersect at the point Q. Let an ellipse, centered at the origin O, has lengths of semi-minor and semi-major axes equal to OQ and 6, respectively. If e and l respectively denote the eccentricity and the length of the latus rectum of this ellipse, then ${l \over {{e^2}}}$ is equal to ______________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 64MathematicsSection B • Numericalsets and relations

+4 / -1

Let $A = \sum\limits_{i = 1}^{10} {\sum\limits_{j = 1}^{10} {\min \,\{ i,j\} } }$ and $B = \sum\limits_{i = 1}^{10} {\sum\limits_{j = 1}^{10} {\max \,\{ i,j\} } }$ . Then A + B is equal to _____________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 65MathematicsSection A • MCQmatrices and determinants

+4 / -1

A

6⁶

B

2¹²

C

2⁶

D

1

Q 66MathematicsSection A • MCQ3d geometry

+4 / -1

Let the plane 2x + 3y + z + 20 = 0 be rotated through a right angle about its line of intersection with the plane x $-$ 3y + 5z = 8. If the mirror image of the point $\left( {2, - {1 \over 2},2} \right)$ in the rotated plane is B(a, b, c), then :

A

{a \over 8} = {b \over 5} = {c \over { - 4}}

B

{a \over 4} = {b \over 5} = {c \over { - 2}}

C

{a \over 8} = {b \over { - 5}} = {c \over 4}

D

{a \over 4} = {b \over 5} = {c \over 2}

Q 67MathematicsSection B • Numericaltrigonometric ratios and identities

+4 / -1

If ${\sin ^2}(10^\circ )\sin (20^\circ )\sin (40^\circ )\sin (50^\circ )\sin (70^\circ ) = \alpha - {1 \over {16}}\sin (10^\circ )$ , then $16 + {\alpha ^{ - 1}}$ is equal to __________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 68MathematicsSection A • MCQapplication of derivatives

+4 / -1

Let $f(x) = 2{\cos ^{ - 1}}x + 4{\cot ^{ - 1}}x - 3{x^2} - 2x + 10$ , $x \in [ - 1,1]$ . If [a, b] is the range of the function f, then 4a $-$ b is equal to :

A

11

B

11

-

\pi

C

11 +

\pi

D

15

-

\pi

Q 69MathematicsSection A • MCQprobability

+4 / -1

Let a biased coin be tossed 5 times. If the probability of getting 4 heads is equal to the probability of getting 5 heads, then the probability of getting atmost two heads is :

A

{{275} \over {{6^5}}}

B

{{36} \over {{5^4}}}

C

{{181} \over {{5^5}}}

D

{{46} \over {{6^4}}}

Q 70MathematicsSection A • MCQarea under the curves

+4 / -1

The area bounded by the curve y = |x² $-$ 9| and the line y = 3 is :

A

4(2\sqrt 3 + \sqrt 6 - 4)

B

4(4\sqrt 3 + \sqrt 6 - 4)

C

8(4\sqrt 3 + 3\sqrt 6 - 9)

D

8(4\sqrt 3 + \sqrt 6 - 9)

Q 71MathematicsSection A • MCQlimits continuity and differentiability

+4 / -1

$\mathop {\lim }\limits_{x \to {1 \over {\sqrt 2 }}} {{\sin ({{\cos }^{ - 1}}x) - x} \over {1 - \tan ({{\cos }^{ - 1}}x)}}$ is equal to :

A

\sqrt 2

B

- \sqrt 2

C

{1 \over {\sqrt 2 }}

D

- {1 \over {\sqrt 2 }}

Q 72MathematicsSection B • Numericalpermutations and combinations

+4 / -1

There are ten boys B₁, B₂, ......., B₁₀ and five girls G₁, G₂, ........, G₅ in a class. Then the number of ways of forming a group consisting of three boys and three girls, if both B₁ and B₂ together should not be the members of a group, is ___________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 73MathematicsSection A • MCQstraight lines and pair of straight lines

+4 / -1

Let R be the point (3, 7) and let P and Q be two points on the line x + y = 5 such that PQR is an equilateral triangle. Then the area of $\Delta$ PQR is :

A

{{25} \over {4\sqrt 3 }}

B

{{25\sqrt 3 } \over 2}

C

{{25} \over {\sqrt 3 }}

D

{{25} \over {2\sqrt 3 }}

Q 74MathematicsSection B • Numericaldefinite integration

+4 / -1

The value of the integral

${{48} \over {{\pi ^4}}}\int\limits_0^\pi {\left( {{{3\pi {x^2}} \over 2} - {x^3}} \right){{\sin x} \over {1 + {{\cos }^2}x}}dx}$ is equal to __________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 75MathematicsSection A • MCQapplication of derivatives

+4 / -1

The sum of the absolute minimum and the absolute maximum values of the

function f(x) = |3x $-$ x² + 2| $-$ x in the interval [ $-$ 1, 2] is :

A

{{\sqrt {17} + 3} \over 2}

B

{{\sqrt {17} + 5} \over 2}

C

5

D

{{9 - \sqrt {17} } \over 2}

Q 76MathematicsSection B • Numericaldifferential equations

+4 / -1

Let the solution curve y = y(x) of the differential equation

$(4 + {x^2})dy - 2x({x^2} + 3y + 4)dx = 0$ pass through the origin. Then y(2) is equal to _____________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 77MathematicsSection A • MCQmatrices and determinants

+4 / -1

The ordered pair (a, b), for which the system of linear equations

3x $-$ 2y + z = b

5x $-$ 8y + 9z = 3

2x + y + az = $-$ 1

has no solution, is :

A

\left( {3,{1 \over 3}} \right)

B

\left( { - 3,{1 \over 3}} \right)

C

\left( { - 3, - {1 \over 3}} \right)

D

\left( {3, - {1 \over 3}} \right)

Q 78MathematicsSection A • MCQfunctions

+4 / -1

Let $f(x) = {{x - 1} \over {x + 1}},\,x \in R - \{ 0, - 1,1\}$ . If ${f^{n + 1}}(x) = f({f^n}(x))$ for all n $\in$ N, then ${f^6}(6) + {f^7}(7)$ is equal to :

A

{7 \over 6}

B

- {3 \over 2}

C

{7 \over {12}}

D

- {{11} \over {12}}

Q 79MathematicsSection A • MCQvector algebra

+4 / -1

If $\overrightarrow a \,.\,\overrightarrow b = 1,\,\overrightarrow b \,.\,\overrightarrow c = 2$ and $\overrightarrow c \,.\,\overrightarrow a = 3$ , then the value of $\left[ {\overrightarrow a \times \left( {\overrightarrow b \times \overrightarrow c } \right),\,\overrightarrow b \times \left( {\overrightarrow c \times \overrightarrow a } \right),\,\overrightarrow c \times \left( {\overrightarrow b \times \overrightarrow a } \right)} \right]$ is :

A

0

B

- 6\overrightarrow a \,.\,\left( {\overrightarrow b \times \overrightarrow c } \right)

C

- 12\overrightarrow c \,.\,\left( {\overrightarrow a \times \overrightarrow b } \right)

D

- 12\overrightarrow b \,.\,\left( {\overrightarrow c \times \overrightarrow a } \right)

Q 80MathematicsSection B • Numericalsets and relations

+4 / -1

Let A = {n $\in$ N : H.C.F. (n, 45) = 1} and

Let B = {2k : k $\in$ {1, 2, ......., 100}}. Then the sum of all the elements of A $\cap$ B is ____________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 81MathematicsSection A • MCQapplication of derivatives

+4 / -1

Let S be the set of all the natural numbers, for which the line ${x \over a} + {y \over b} = 2$ is a tangent to the curve ${\left( {{x \over a}} \right)^n} + {\left( {{y \over b}} \right)^n} = 2$ at the point (a, b), ab $\ne$ 0. Then :

A

S =

\phi

B

n(S) = 1

C

S = {2k : k

\in

N}

D

S = N

Q 82MathematicsSection A • MCQparabola

+4 / -1

Let the normal at the point on the parabola y² = 6x pass through the point (5, $-$ 8). If the tangent at P to the parabola intersects its directrix at the point Q, then the ordinate of the point Q is :

A

-

3

B

-

{{9} \over 4}

C

-

{{5} \over 2}

D

-

2

Q 83MathematicsSection A • MCQlimits continuity and differentiability

+4 / -1

Let f, g : R $\to$ R be two real valued functions defined as $f(x) = \left\{ {\matrix{ { - |x + 3|} & , & {x < 0} \cr {{e^x}} & , & {x \ge 0} \cr } } \right.$ and $g(x) = \left\{ {\matrix{ {{x^2} + {k_1}x} & , & {x < 0} \cr {4x + {k_2}} & , & {x \ge 0} \cr } } \right.$ , where k₁ and k₂ are real constants. If (gof) is differentiable at x = 0, then (gof) ( $-$ 4) + (gof) (4) is equal to :

A

4({e^4} + 1)

B

2(2{e^4} + 1)

C

4{e^4}

D

2(2{e^4} - 1)

Q 84MathematicsSection B • Numericaldefinite integration

+4 / -1

Let f(x) = max {|x + 1|, |x + 2|, ....., |x + 5|}. Then $\int\limits_{ - 6}^0 {f(x)dx}$ is equal to __________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 85MathematicsSection A • MCQbinomial theorem

+4 / -1

The remainder when (2021)²⁰²³ is divided by 7 is :

A

1

B

2

C

5

D

6

Q 86MathematicsSection A • MCQstatistics

+4 / -1

The mean of the numbers a, b, 8, 5, 10 is 6 and their variance is 6.8. If M is the mean deviation of the numbers about the mean, then 25 M is equal to :

A

60

B

55

C

50

D

45

Q 87MathematicsSection A • MCQmathematical reasoning

+4 / -1

Let $\Delta$ , $\nabla$ $\in$ { $\wedge$ , $\vee$ } be such that p $\nabla$ q $\Rightarrow$ ((p $\Delta$ q) $\nabla$ r) is a tautology. Then (p $\nabla$ q) $\Delta$ r is logically equivalent to :

A

(p

\Delta

r)

\vee

q

B

(p

\Delta

r)

\wedge

q

C

(p

\wedge

r)

\Delta

q

D

(p

\nabla

r)

\wedge

q

Q 88MathematicsSection B • Numericaldifferential equations

+4 / -1

Let $S = (0,2\pi ) - \left\{ {{\pi \over 2},{{3\pi } \over 4},{{3\pi } \over 2},{{7\pi } \over 4}} \right\}$ . Let $y = y(x)$ , x $\in$ S, be the solution curve of the differential equation ${{dy} \over {dx}} = {1 \over {1 + \sin 2x}},\,y\left( {{\pi \over 4}} \right) = {1 \over 2}$ . If the sum of abscissas of all the points of intersection of the curve y = y(x) with the curve $y = \sqrt 2 \sin x$ is ${{k\pi } \over {12}}$ , then k is equal to _____________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 89MathematicsSection B • Numericalquadratic equation and inequalities

+4 / -1

The sum of the cubes of all the roots of the equation

${x^4} - 3{x^3} - 2{x^2} + 3x + 1 = 0$ is _________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 90MathematicsSection A • MCQcircle

+4 / -1

Let C be a circle passing through the points A(2, $-$ 1) and B(3, 4). The line segment AB s not a diameter of C. If r is the radius of C and its centre lies on the circle ${(x - 5)^2} + {(y - 1)^2} = {{13} \over 2}$ , then r² is equal to :

A

32

B

{{65} \over 2}

C

{{61} \over 2}

D

30

JEE Main 2022 26th June Morning Shift Question Paper with Solutions