JEE Main 2020 4th September Evening Shift Question Paper Question Paper with Solutions | JEE Main Mock Test | JeeMate

Q 1PhysicsSection A • MCQlaws of motion

+4 / -1

A small ball of mass m is thrown upward with velocity u from the ground. The ball experiences a resistive force mkv² where v is its speed. The maximum height attained by the ball is :

A

{1 \over k}{\tan ^{ - 1}}{{k{u^2}} \over {2g}}

B

{1 \over {2k}}{\tan ^{ - 1}}{{k{u^2}} \over g}

C

{1 \over {2k}}\ln \left( {1 + {{k{u^2}} \over g}} \right)

D

{1 \over k}\ln \left( {1 + {{k{u^2}} \over {2g}}} \right)

Q 2PhysicsSection A • MCQheat and thermodynamics

+4 / -1

Match the thermodynamic processes taking place in a system with the correct conditions. In the table :

\Delta

Q is the heat supplied,

\Delta

W is the work done and

\Delta

U is change in internal energy of the system.

Process	Condition
(I) Adiabatic	(1) $\Delta$ W = 0
(II) Isothermal	(2) $\Delta$ Q = 0
(III) Isochoric	(3) $\Delta$ U $\ne$ 0, $\Delta$ W $\ne$ 0, $\Delta$ Q $\ne$ 0
(IV) Isobaric	(4) $\Delta$ U = 0

A

(I) - (1), (II) - (1), (III) - (2), (IV) - (3)

B

(I) - (2), (II) - (4), (III) - (1), (IV) - (3)

C

(I) - (1), (II) - (2), (III) - (4), (IV) - (4)

D

(I) - (2), (II) - (1), (III) - (4), (IV) - (3)

Q 3PhysicsSection A • MCQmagnetic properties of matter

+4 / -1

A paramagnetic sample shows a net magnetisation of 6 A/m when it is placed in an external magnetic field of 0.4 T at a temperature of 4 K. When the sample is placed in an external magnetic field of 0.3 T at a temperature of 24 K, then the magnetisation will be:

A

4 A/m

B

1 A/m

C

0.75 A/m

D

2.25 A/m

Q 4PhysicsSection A • MCQgravitation

+4 / -1

A body is moving in a low circular orbit about a planet of mass M and radius R. The radius of the orbit can be taken to be R itself. Then the ratio of the speed of this body in the orbit to the escape velocity from the planet is:

A

2

B

1

C

\sqrt 2

D

{1 \over {\sqrt 2 }}

Q 5PhysicsSection A • MCQproperties of matter

+4 / -1

Two identical cylindrical vessels are kept on the ground and each contain the same liquid of density d. The area of the base of both vessels is S but the height of liquid in one vessel is x₁ and in the other, x₂ . When both cylinders are connected through a pipe of negligible volume very close to the bottom, the liquid flows from one vessel to the other until it comes to equilibrium at a new height. The change in energy of the system in the process is:

A

gdS(x₂ + x₁)²

B

gdS

\left( {x_2^2 + x_1^2} \right)

C

{1 \over 4}gdS{\left( {{x_2} - {x_1}} \right)^2}

D

{3 \over 4}gdS{\left( {{x_2} - {x_1}} \right)^2}

Q 6PhysicsSection A • MCQwork power and energy

+4 / -1

A person pushes a box on a rough horizontal plateform surface. He applies a force of 200 N over a distance of 15 m. Thereafter, he gets progressively tired and his applied force reduces linearly with distance to 100 N. The total distance through which the box has been moved is 30 m. What is the work done by the person during the total movement of the box?

A

5690 J

B

5250 J

C

2780 J

D

3280 J

Q 7PhysicsSection B • Numericalmotion

+4 / -0

The speed verses time graph for a particle is shown in the figure. The distance travelled (in m) by the particle during the time interval t = 0 to t = 5 s will be________. qImage-graph-based-problem-motion-mechanics-Jeemate

qImage-graph-based-problem-motion-mechanics-Jeemate

Answer Format:Enter numerical value rounded to the nearest integer

Q 8PhysicsSection B • Numericalcurrent electricity

+4 / -0

Four resistances 40

\Omega

, 60

\Omega

, 90

\Omega

and 110

\Omega

make the arms of a quadrilateral ABCD. Across AC is a battery of emf 40 V and internal resistance negligible.The potential difference across BD in V is _______. qImage-kirchhoffs-circuit-laws-current-electricity-electricity-Jeemate

qImage-kirchhoffs-circuit-laws-current-electricity-electricity-Jeemate

Answer Format:Enter numerical value rounded to the nearest integer

Q 9PhysicsSection B • Numericalwave optics

+4 / -0

Orange light of wavelength 6000

\times

10^–10 m illuminates a single
slit of width 0.6

\times

10^–4 m. The maximum possible number of diffraction minima produced on both sides of the central maximum is ___________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 10PhysicsSection B • Numericalheat and thermodynamics

+4 / -0

The change in the magnitude of the volume of an ideal gas when a small additional pressure

\Delta

P is applied at a constant temperature, is the same as the change when the temperature is reduced by a small quantity

\Delta

T at constant pressure. The initial temperature and pressure of the gas were 300 K and 2 atm. respectively.
If |

\Delta

T| = C|

\Delta

P| then value of C in (K/atm.) is _________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 11PhysicsSection A • MCQcapacitor

+4 / -1

A capacitor C is fully charged with voltage V₀. After disconnecting the voltage source, it is connected in parallel with another uncharged capacitor of capacitance

{C \over 2}

. The energy loss in the process after the charge is distributed between the two capacitors is :

A

{1 \over 2}CV_0^2

B

{1 \over 4}CV_0^2

C

{1 \over 3}CV_0^2

D

{1 \over 6}CV_0^2

Q 12PhysicsSection A • MCQunits and measurements

+4 / -1

A quantity x is given by

\left( {{{IF{v^2}} \over {W{L^4}}}} \right)

in terms of moment of inertia I, force F, velocity v, work W and Length L. The dimensional formula for x is same as that of :

A

Coefficient of viscosity

B

Force constant

C

Energy density

D

Planck's constant

Q 13PhysicsSection A • MCQalternating current

+4 / -1

A series L-R circuit is connected to a battery of emf V. If the circuit is switched on at t = 0, then the time at which the energy stored in the inductor reaches

\left( {{1 \over n}} \right)

times of its maximum value, is :

A

{L \over R}\ln \left( {{{\sqrt n } \over {\sqrt n + 1}}} \right)

B

{L \over R}\ln \left( {{{\sqrt n } \over {\sqrt n - 1}}} \right)

C

{L \over R}\ln \left( {{{\sqrt n + 1} \over {\sqrt n - 1}}} \right)

D

{L \over R}\ln \left( {{{\sqrt n - 1} \over {\sqrt n }}} \right)

Q 14PhysicsSection A • MCQrotational motion

+4 / -1

For a uniform rectangular sheet shown in the figure, the ratio of moments of inertia about the axes perpendicular to the sheet and passing through O (the centre of mass) and O' (corner point) is : qImage-moment-of-inertia-rotational-motion-mechanics-Jeemate

qImage-moment-of-inertia-rotational-motion-mechanics-Jeemate

A

{1 \over 2}

B

{1 \over 4}

C

{1 \over 8}

D

{2 \over 3}

Q 15PhysicsSection A • MCQelectromagnetic waves

+4 / -1

The electric field of a plane electromagnetic wave is given by

\overrightarrow E = {E_0}\left( {\widehat x + \widehat y} \right)\sin \left( {kz - \omega t} \right)

Its magnetic field will be given by :

A

{{{E_0}} \over c}\left( {\widehat x + \widehat y} \right)\sin \left( {kz - \omega t} \right)

B

{{{E_0}} \over c}\left( {\widehat x - \widehat y} \right)\sin \left( {kz - \omega t} \right)

C

{{{E_0}} \over c}\left( {\widehat x - \widehat y} \right)\cos \left( {kz - \omega t} \right)

D

{{{E_0}} \over c}\left( { - \widehat x + \widehat y} \right)\sin \left( {kz - \omega t} \right)

Q 16PhysicsSection A • MCQrotational motion

+4 / -1

Consider two uniform discs of the same thickness and different radii R₁ = R and
R₂ =

\alpha

R made of the same material. If the ratio of their moments of inertia I₁ and I₂ , respectively, about their axes is I₁ : I₂ = 1 : 16 then the value of

\alpha

is :

A

\sqrt 2

B

2

C

2\sqrt 2

D

4

Q 17PhysicsSection A • MCQmagnetics

+4 / -1

A circular coil has moment of inertia 0.8 kg m² around any diameter and is carrying current to produce a magnetic moment of 20 Am² . The coil is kept initially in a vertical position and it can rotate freely around a horizontal diameter. When a uniform magnetic field of 4 T is applied along the vertical,it starts rotating around its horizontal diameter. The angular speed the coil acquires after rotating by 60^o will be:

A

10

\pi

rad s^–1

B

20

\pi

rad s^–1

C

10{\left( 3 \right)^{1/4}}

rad s^–1

D

20 rad s^–1

Q 18PhysicsSection A • MCQproperties of matter

+4 / -1

A cube of metal is subjected to a hydrostatic pressure of 4 GPa. The percentage change in the length of the side of the cube is close to :
(Given bulk modulus of metal, B = 8

\times

10¹⁰ Pa)

A

0.6

B

20

C

1.67

D

5

Q 19PhysicsSection B • Numericalray optics

+4 / -0

The distance between an object and a screen is 100 cm. A lens can produce real image of the object on the screen for two different positions between the screen and the object. The distance between these two positions is 40 cm. If the power of the lens is close to

\left( {{N \over {100}}} \right)D

where N is an integer, the value of N is _________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 20PhysicsSection A • MCQcurrent electricity

+4 / -1

The value of current i₁ flowing from A to C in the circuit diagram is : qImage-wheatstone-bridge-current-electricity-electricity-Jeemate

A

1 A

B

4 A

C

5 A

D

2 A

Q 21PhysicsSection A • MCQelectrostatics

+4 / -1

A particle of charge q and mass m is subjected to an electric field
E = E₀ (1 –

a

x²) in the x-direction, where

a

and E₀ are constants. Initially the particle was at rest at x = 0. Other than the initial position the kinetic energy of the particle becomes zero when the distance of the particle from the origin is :

A

a

B

\sqrt {{2 \over a}}

C

\sqrt {{3 \over a}}

D

\sqrt {{1 \over a}}

Q 22PhysicsSection A • MCQelectronic devices

+4 / -1

Identify the operation performed by the circuit given below : qImage-digital-circuits-electronic-devices-modern-physics-Jeemate

A

AND

B

NAND

C

OR

D

NOT

Q 23PhysicsSection A • MCQwaves

+4 / -1

The driver of a bus approaching a big wall notices that the frequency of his bus's horn changes from 420 Hz to 490 Hz when he hears it after it gets reflected from the wall. Find the speed of the bus if speed of the sound is 330 ms^–1.

A

91 kmh^–1

B

81 kmh^–1

C

61 kmh^–1

D

71 kmh^–1

Q 24PhysicsSection A • MCQdual nature of radiation

+4 / -1

In a photoelectric effect experiment, the graph of stopping potential V versus reciprocal of wavelength obtained is shown in the figure. As the intensity of incident radiation is increased : qImage-photoelectric-effect-dual-nature-of-radiation-modern-physics-Jeemate

qImage-photoelectric-effect-dual-nature-of-radiation-modern-physics-Jeemate

A

Slope of the straight line get more steep

B

Graph does not change

C

Straight line shifts to left

D

Straight line shifts to right

Q 25PhysicsSection A • MCQatoms and nuclei

+4 / -1

Find the Binding energy per neucleon for

{}_{50}^{120}Sn

. Mass of proton m_p = 1.00783 U, mass of neutron m_n = 1.00867 U and mass of tin nucleus m_Sn = 119.902199 U. (take 1U = 931 MeV)

A

9.0 MeV

B

8.5 MeV

C

8.0 MeV

D

7.5 MeV

Q 26ChemistrySection A • MCQchemical equilibrium

+4 / -1

If the equilibrium constant for
A ⇌ B + C is

K_{eq}^{(1)}

and that of
B + C ⇌ P is

K_{eq}^{(2)}

, the equilibrium
constant for A ⇌ P is :

A

{{K_{eq}^{(1)}} \over {K_{eq}^{(2)}}}

B

{K_{eq}^{(1)}}

+

{K_{eq}^{(2)}}

C

{K_{eq}^{(2)}}

-

{K_{eq}^{(1)}}

D

{K_{eq}^{(1)}}

{K_{eq}^{(2)}}

Q 27ChemistrySection A • MCQhaloalkanes and haloarenes

+4 / -1

Among the following compounds, which one has the shortest C – Cl bond?

A

H₃C - Cl

B

C

D

Q 28ChemistrySection A • MCQcompounds containing nitrogen

+4 / -1

In the following reaction sequence, [C] is :

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

A

B

C

D

Q 29ChemistrySection A • MCQchemical bonding and molecular structure

+4 / -1

The reaction in which the hybridisation of the underlined atom is affected is :

A

B

C

D

Official Correct Answer:Option (A)

Step-by-Step Solution:

To determine the option in which the hybridisation of the underlined atom is affected, we need to look at each reaction and predict the changes in hybridisation that might be occuring with the reactants and products.

Option A:

In the reaction $\underline {Xe}F_4 + SbF_5 \to$ , xenon tetrafluoride (XeF₄) reacts with antimony pentafluoride (SbF₅). XeF₄ is a square planar molecule, and the central Xe atom is $sp^3d^2$ hybridised. The reaction with SbF₅ can lead to the formation of a complex where the hybridisation of Xe changes if it coordinates with SbF₅. Thus, the hybridisation of Xe may indeed be affected in this case.

$\underline {Xe}$ F₄	+	SbF₅	$\to$	[XeF₃]⁺[SbF₆]^-
sp³d²				sp³d sp³d²

Option B:

In the reaction $H_2\underline{S}O_4 + NaCl \buildrel {420K} \over \longrightarrow$ , sulfuric acid (H₂SO₄) reacts with sodium chloride (NaCl). The underlined atom here is sulfur (S). In sulfuric acid, sulfur is hybridised as $sp^3$ . Upon heating, there is typically no change in the hybridisation of the sulfur atom within sulfuric acid as part of this reaction. Therefore, the hybridisation of S is likely not affected.

Option C:

In the reaction $H_3\underline{P}O_2 \buildrel {Disproportionation} \over \longrightarrow$ , phosphorous acid (H₃PO₂) is undergoing a disproportionation reaction. The underlined atom is phosphorus (P). In H₃PO₂, the hybridisation of the phosphorus atom is $sp^3$ . A typical disproportionation reaction of phosphorous acid would result in phosphine (PH₃) and orthophosphoric acid (H₃PO₄). The phosphorus atom in PH₃ will have $sp^3$ hybridisation while in H₃PO₄ the phosphorus atom is $sp^3$ hybridised. Given this information, the hybridisation of phosphorus may or may not change, depending on the resulting state of the phosphorus atom in the products. It's not a clear-cut case without knowing the specific products.

Option D:

In the reaction $\underline{N}H_3 \buildrel {{H^+}} \over \longrightarrow$ , ammonia (NH₃) is reacting with a proton (H⁺). The underlined atom is nitrogen (N). In NH₃, the nitrogen is $sp^3$ hybridised. When ammonia accepts a proton, it forms ammonium ion (NH₄⁺), which is also $sp^3$ hybridised. Therefore, there is no change in the hybridisation of nitrogen in this case.

Given this information, the option in which the hybridisation of the underlined atom is most clearly affected is Option A, where the reaction can lead to coordination changes to the Xe atom, potentially affecting its hybridisation.

Q 30ChemistrySection B • Numericalredox reactions

+4 / -0

A 100 mL solution was made by adding 1.43 g of Na₂CO₃.xH₂O. The normality of the solution is 0.1 N. The value of x is _____.

(The atomic mass of Na is 23 g/mol)

Answer Format:Enter numerical value rounded to the nearest integer

Q 31ChemistrySection B • Numericalbiomolecules

+4 / -0

The number of chiral centres present in threonine is ________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 32ChemistrySection A • MCQs block elements

+4 / -1

An alkaline earth metal ‘M’ readily forms water soluble sulphate and water insoluble hydroxide. Its oxide MO is very stable to heat and does not have rock-salt structure. M is :

A

Ca

B

Mg

C

Sr

D

Be

Q 33ChemistrySection B • Numericalsolutions

+4 / -0

The osmotic pressure of a solution of NaCl is 0.10 atm and that of a glucose solution is 0.20 atm. The osmotic pressure of a solution formed by mixing 1 L of the sodium chloride solution with 2 L of
the glucose solution is x

\times

10^–3 atm. x is _____. (nearest integer)

Answer Format:Enter numerical value rounded to the nearest integer

Q 34ChemistrySection A • MCQsurface chemistry

+4 / -1

A sample of red ink (a colloidal suspension) is prepared by mixing eosin dye, egg white, HCHO and water. The component which ensures stability of the ink sample is :

A

HCHO

B

Water

C

Eosin dye

D

Egg white

Q 35ChemistrySection A • MCQchemistry in everyday life

+4 / -1

The mechanism of action of ''Terfenadine'' (Seldane) is :

A

Activates the histamine receptor

B

Helps in the secretion of histamine

C

Inhibits the secretion of histamine

D

Inhibits the action of histamine receptor

Q 36ChemistrySection A • MCQaldehydes ketones and carboxylic acids

+4 / -1

The major product [C] of the following reaction sequence will be : qImage-chemical-reactions-for-aldehydes-and-ketones-aldehydes-ketones-and-carboxylic-acids-organic-chemistry-Jeemate

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

A

B

C

D

Q 37ChemistrySection A • MCQatomic structure

+4 / -1

The shortest wavelength of H atom in the Lyman series is

\lambda

₁. The longest wavelength in the Balmar series of He⁺ is :

A

{{5{\lambda _1}} \over 9}

B

{{36{\lambda _1}} \over 5}

C

{{27{\lambda _1}} \over 5}

D

{{9{\lambda _1}} \over 5}

Q 38ChemistrySection A • MCQalcohols phenols and ethers

+4 / -1

The major product [B] in the following reactions is : qImage-properties-preparation-and-uses-of-alcohols-alcohols-phenols-and-ethers-organic-chemistry-Jeemate

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

A

CH₃ – CH₂ – CH = CH – CH₃

B

CH₂ = CH₂

C

D

Q 39ChemistrySection A • MCQcoordination compounds

+4 / -1

The Crystal Field Stabilization Energy
(CFSE) of [CoF₃(H₂O)₃] (

\Delta

₀ < P) is :

A

-0.8

\Delta

₀

B

-0.4

\Delta

₀

C

-0.8

\Delta

₀ + 2P

D

-0.4

\Delta

₀ + P

Q 40ChemistrySection A • MCQcoordination compounds

+4 / -1

The one that can exhibit highest paramagnetic behaviour among the following is :

gly = glycinato; bpy = 2, 2'-bipyridine

A

[Fe(en)(bpy)(NH₃)₂]²⁺

B

[Pd(gly)₂]

C

[Co(OX)₂(OH)₂]^– (

\Delta

₀ > P)

D

[Ti(NH₃)₆]³⁺

Q 41ChemistrySection A • MCQelectrochemistry

+4 / -1

250 mL of a waste solution obtained from the workshop of a goldsmith contains 0.1 M AgNO₃ and 0.1 M AuCl. The solution was electrolyzed at 2V by passing a current of 1A for 15 minutes. The metal/metals electrodeposited will be

[

E_{A{g^ + }/Ag}^0

= 0.80 V,

E_{A{u^ + }/Au}^0

= 1.69 V ]

A

Silver and gold in equal mass proportion

B

Silver and gold in proportion to their atomic weights

C

Only gold

D

Only silver

Q 42ChemistrySection A • MCQd and f block elements

+4 / -1

The incorrect statement(s) among (a) - (c) is (are)

(a) W(VI) is more stable than Cr(VI).

(b) In the presence of HCl, permanganate titrations provide satisfactory results.

(c) Some lanthanoid oxides can be used as phosphors.

A

(a) and (b) only

B

(a) only

C

(b) only

D

(b) and (c) only

Q 43ChemistrySection A • MCQcoordination compounds

+4 / -1

The molecule in which hybrid MOs involve only one d-orbital of the central atom is :

A

XeF₄

B

[Ni(CN)₄]^2–

C

[CrF₆]^3–

D

BrF₅

Q 44ChemistrySection A • MCQthermodynamics

+4 / -1

Five moles of an ideal gas at 1 bar and 298 K is expanded into vacuum to double the volume. The work done is :

A

Zero

B

-RT

\ln {{{V_2}} \over {{V_1}}}

C

C_V (T₂ – T₁)

D

– RT (V₂ – V₁)

Q 45ChemistrySection A • MCQhaloalkanes and haloarenes

+4 / -1

Which of the following compounds will form the precipitate with aq. AgNO₃ solution most readily?

A

B

C

D

Q 46ChemistrySection A • MCQthermodynamics

+4 / -1

The process that is NOT endothermic in nature is :

A

Ar(g) + e^-

\to

Ar^-(g)

B

H(g) + e^-

\to

H^-(g)

C

Na(g)

\to

Na⁺(g) + e^-

D

O^-(g) + e^-

\to

O^2-(g)

Q 47ChemistrySection A • MCQenvironmental chemistry

+4 / -1

The processes of calcination and roasting in metallurgical industries, respectively, can Iead to :

A

Global warming and photochemical smog

B

Photochemical smog and ozone layer depletion

C

Photochemical smog and global warming

D

Global warming and acid rain

Q 48ChemistrySection B • Numericalsome basic concepts of chemistry

+4 / -0

Consider the following equations :
2Fe²⁺ + H₂O₂

\to

xA + yB
(in basic medium)
2MnO₄^- + 6H⁺ + 5H₂O₂

\to

x'C + y'D + z'E
(in acidic medium)
The sum of the stoichiometric coefficients x, y, x', y', and z' for products A, B, C, D and E, respectively, is ______.

Answer Format:Enter numerical value rounded to the nearest integer

Q 49ChemistrySection B • Numericalchemical kinetics and nuclear chemistry

+4 / -0

The number of molecules with energy greater than the threshold energy for a reaction increases five fold by a rise of temperature from 27^oC to 42^oC. Its energy of activation in J/mol is _____.
(Take ln 5 = 1.6094; R = 8.314 J mol^–1 K^–1)

Answer Format:Enter numerical value rounded to the nearest integer

Q 50ChemistrySection A • MCQalcohols phenols and ethers

+4 / -1

The major product [R] in the following sequence of reactions as :
qImage-properties-preparation-and-uses-of-alcohols-alcohols-phenols-and-ethers-organic-chemistry-Jeemate

A

B

C

D

Q 51MathematicsSection A • MCQdefinite integration

+4 / -1

The integral

\int\limits_{{\pi \over 6}}^{{\pi \over 3}} {{{\tan }^3}x.{{\sin }^2}3x\left( {2{{\sec }^2}x.{{\sin }^2}3x + 3\tan x.\sin 6x} \right)dx}

is equal to:

A

- {1 \over {9}}

B

- {1 \over {18}}

C

{7 \over {18}}

D

{9 \over 2}

Q 52MathematicsSection A • MCQmatrices and determinants

+4 / -1

If the system of equations
x+y+z=2
2x+4y–z=6
3x+2y+

\lambda

z=

\mu

has infinitely many solutions, then

A

2

\lambda

-

\mu

= 5

B

\lambda

- 2

\mu

= -5

C

2

\lambda

+

\mu

= 14

D

\lambda

+ 2

\mu

= 14

Q 53MathematicsSection A • MCQapplication of derivatives

+4 / -1

The area (in sq. units) of the largest rectangle ABCD whose vertices A and B lie on the x-axis and vertices C and D lie on the parabola, y = x²–1 below the x-axis, is :

A

{1 \over {3\sqrt 3 }}

B

{2 \over {3\sqrt 3 }}

C

{4 \over {3\sqrt 3 }}

D

{4 \over 3}

Q 54MathematicsSection A • MCQmathematical reasoning

+4 / -1

Contrapositive of the statement :
‘If a function f is differentiable at a, then it is also continuous at a’, is:

A

If a function f is continuous at a, then it is not differentiable at a.

B

If a function f is not continuous at a, then it is differentiable at a.

C

If a function f is not continuous at a, then it is not differentiable at a.

D

If a function f is continuous at a, then it is differentiable at a.

Q 55MathematicsSection A • MCQheight and distance

+4 / -1

The angle of elevation of a cloud C from a point P, 200 m above a still lake is 30°. If the angle of depression of the image of C in the lake from the point P is 60°,then PC (in m) is equal to :

A

200\sqrt 3

B

400

C

100

D

400\sqrt 3

Q 56MathematicsSection A • MCQ3d geometry

+4 / -1

The distance of the point (1, –2, 3) from

the plane x – y + z = 5 measured parallel to

the line

{x \over 2} = {y \over 3} = {z \over { - 6}}

is :

A

7

B

1

C

{1 \over 7}

D

{7 \over 5}

Q 57MathematicsSection B • Numericalvector algebra

+4 / -0

If

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

, then the value of

{\left| {\widehat i \times \left( {\overrightarrow a \times \widehat i} \right)} \right|^2} + {\left| {\widehat j \times \left( {\overrightarrow a \times \widehat j} \right)} \right|^2} + {\left| {\widehat k \times \left( {\overrightarrow a \times \widehat k} \right)} \right|^2}

is equal to____

Answer Format:Enter numerical value rounded to the nearest integer

Q 58MathematicsSection B • Numericaldefinite integration

+4 / -0

Let {x} and [x] denote the fractional part of x and
the greatest integer

\le

x respectively of a real
number x. If

\int_0^n {\left\{ x \right\}dx} ,\int_0^n {\left[ x \right]dx}

and 10(n² – n),

\left( {n \in N,n > 1} \right)

are three consecutive terms of a G.P., then n is equal to_____.

Answer Format:Enter numerical value rounded to the nearest integer

Q 59MathematicsSection A • MCQsequences and series

+4 / -1

Let a₁, a₂, ..., an be a given A.P. whose
common difference is an integer and
S_n = a₁ + a₂ + .... + a_n. If a₁ = 1, a_n = 300 and 15

\le

n

\le

50, then
the ordered pair (S_n-4, a_n–4) is equal to:

A

(2480, 249)

B

(2480, 248)

C

(2490, 248)

D

(2490, 249)

Q 60MathematicsSection A • MCQcircle

+4 / -1

The circle passing through the intersection of the circles,
x² + y² – 6x = 0 and x² + y² – 4y = 0, having its centre on
the line, 2x – 3y + 12 = 0, also passes through the point :

A

(–3, 1)

B

(1, –3)

C

(–1, 3)

D

(–3, 6)

Q 61MathematicsSection A • MCQprobability

+4 / -1

In a game two players A and B take turns in throwing a pair of fair dice starting with player A and total of scores on the two dice, in each throw is noted. A wins the game if he throws total a of 6 before B throws a total of 7 and B wins the game if he throws a total of 7 before A throws a total of six. The game stops as soon as either of the players wins. The probability of A winning the game is :

A

{5 \over {6}}

B

{5 \over {31}}

C

{31 \over {61}}

D

{30 \over {61}}

Q 62MathematicsSection A • MCQquadratic equation and inequalities

+4 / -1

Let

\lambda \ne 0

be in R. If

\alpha

and

\beta

are the roots of the
equation, x² - x + 2

\lambda

= 0 and

\alpha

and

\gamma

are the roots of
the equation,

3{x^2} - 10x + 27\lambda = 0

, then

{{\beta \gamma } \over \lambda }

is equal to:

A

36

B

9

C

27

D

18

Q 63MathematicsSection A • MCQmatrices and determinants

+4 / -1

Suppose the vectors x₁, x₂ and x₃ are the
solutions of the system of linear equations,
Ax = b when the vector b on the right side is equal to b₁, b₂ and b₃ respectively. if

{x_1} = \left[ {\matrix{ 1 \cr 1 \cr 1 \cr } } \right]

,

{x_2} = \left[ {\matrix{ 0 \cr 2 \cr 1 \cr } } \right]

,

{x_3} = \left[ {\matrix{ 0 \cr 0 \cr 1 \cr } } \right]

{b_1} = \left[ {\matrix{ 1 \cr 0 \cr 0 \cr } } \right]

,

{b_2} = \left[ {\matrix{ 0 \cr 2 \cr 0 \cr } } \right]

and

{b_3} = \left[ {\matrix{ 0 \cr 0 \cr 2 \cr } } \right]

,
then the determinant of A is equal to :

A

{3 \over 2}

B

4

C

2

D

{1 \over 2}

Q 64MathematicsSection A • MCQbinomial theorem

+4 / -1

If for some positive integer n, the coefficients
of three consecutive terms in the binomial
expansion of (1 + x)^{n + 5} are in the ratio
5 : 10 : 14, then the largest coefficient in this expansion is :

A

330

B

792

C

252

D

462

Q 65MathematicsSection A • MCQcomplex numbers

+4 / -1

If a and b are real numbers such that

{\left( {2 + \alpha } \right)^4} = a + b\alpha

where

\alpha = {{ - 1 + i\sqrt 3 } \over 2}

then a + b is equal to :

A

33

B

9

C

24

D

57

Q 66MathematicsSection A • MCQlimits continuity and differentiability

+4 / -1

The function

f(x) = \left\{ {\matrix{ {{\pi \over 4} + {{\tan }^{ - 1}}x,} & {\left| x \right| \le 1} \cr {{1 \over 2}\left( {\left| x \right| - 1} \right),} & {\left| x \right| > 1} \cr } } \right.

is :

A

continuous on R–{–1} and differentiable on R–{–1, 1}

B

both continuous and differentiable on R–{1}

C

both continuous and differentiable on R–{–1}

D

continuous on R–{1} and differentiable on R–{–1, 1}

Q 67MathematicsSection A • MCQdifferential equations

+4 / -1

The solution of the differential equation

{{dy} \over {dx}} - {{y + 3x} \over {{{\log }_e}\left( {y + 3x} \right)}} + 3 = 0

is:

(where c is a constant of integration)

A

x - {1 \over 2}{\left( {{{\log }_e}\left( {y + 3x} \right)} \right)^2} = C

B

y + 3x - {1 \over 2}{\left( {{{\log }_e}x} \right)^2} = C

C

x – log_e(y+3x) = C

D

x – 2log_e(y+3x) = C

Q 68MathematicsSection A • MCQellipse

+4 / -1

Let x = 4 be a directrix to an ellipse whose centre is at the origin and its eccentricity is

{1 \over 2}

. If P(1,

\beta

),

\beta

> 0 is a point on this ellipse, then the equation of the normal to it at P is :

A

4x – 3y = 2

B

8x – 2y = 5

C

7x – 4y = 1

D

4x – 2y = 1

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

+4 / -1

If the perpendicular bisector of the line segment joining the points P(1 ,4) and Q(k, 3) has y-intercept equal to –4, then a value of k is :

A

\sqrt {14}

B

-4

C

–2

D

\sqrt {15}

Q 70MathematicsSection A • MCQsets and relations

+4 / -1

Let

\mathop \cup \limits_{i = 1}^{50} {X_i} = \mathop \cup \limits_{i = 1}^n {Y_i} = T

where each X_i contains 10 elements and each Y_i contains 5 elements. If each element of the set T is an element of exactly 20 of sets X_i’s and exactly 6 of sets Y_i’s, then n is equal to :

A

30

B

50

C

15

D

45

Q 71MathematicsSection A • MCQsequences and series

+4 / -1

The minimum value of 2^sinx + 2^cosx is :

A

{2^{-1 + \sqrt 2 }}

B

{2^{1 - {1 \over {\sqrt 2 }}}}

C

{2^{1 - \sqrt 2 }}

D

{2^{-1 + {1 \over {\sqrt 2 }}}}

Q 72MathematicsSection A • MCQlimits continuity and differentiability

+4 / -1

Let

f:\left( {0,\infty } \right) \to \left( {0,\infty } \right)

be a differentiable function such that f(1) = e and

\mathop {\lim }\limits_{t \to x} {{{t^2}{f^2}(x) - {x^2}{f^2}(t)} \over {t - x}} = 0

. If f(x) = 1, then x is equal to :

A

{1 \over e}

B

e

C

{1 \over 2e}

D

2e

Q 73MathematicsSection B • Numericalpermutations and combinations

+4 / -0

A test consists of 6 multiple choice questions, each having 4 alternative answers of which only one is correct. The number of ways, in which a candidate answers all six questions such that exactly four of the answers are correct, is __________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 74MathematicsSection B • Numericalstatistics

+4 / -0

If the variance of the following frequency distribution :

Class : 10–20 20–30 30–40

Frequency : 2 x 2

is 50, then x is equal to____

Answer Format:Enter numerical value rounded to the nearest integer

Q 75MathematicsSection B • Numericalcircle

+4 / -0

Let PQ be a diameter of the circle x² + y² = 9. If

\alpha

and

\beta

are the lengths of the perpendiculars from P and Q on the straight line,
x + y = 2 respectively, then the maximum value of

\alpha\beta

is _____.

Answer Format:Enter numerical value rounded to the nearest integer

JEE Main 2020 4th September Evening Shift Question Paper with Solutions