JEE Main 2021 25th February Morning Shift Question Paper Question Paper with Solutions | JEE Main Mock Test | JeeMate

Q 1PhysicsSection A • MCQmotion

+4 / -1

An engine of a train, moving with uniform acceleration, passes the signal-post with velocity u and the last compartment with velocity v. The velocity with which middle point of the train passes the signal post is :

A

{{u + v} \over 2}

B

\sqrt {{{{v^2} - {u^2}} \over 2}}

C

{{v - u} \over 2}

D

\sqrt {{{{v^2} + {u^2}} \over 2}}

Q 2PhysicsSection B • Numericalcircular motion

+4 / -1

A small bob tied at one end of a thin string of length 1 m is describing a vertical circle so that the maximum and minimum tension in the string are in the ratio 5 : 1. The velocity of the bob at the highest position is ________ m/s. (Take g = 10 m/s²)

Answer Format:Enter numerical value rounded to the nearest integer

Q 3PhysicsSection A • MCQunits and measurements

+4 / -1

Match List - I with List - II :

	List I		List II
(a)	h (Planck's constant)	(i)	$[ML{T^{ - 1}}]$
(b)	E (kinetic energy)	(ii)	$[M{L^2}{T^{ - 1}}]$
(c)	V (electric potential)	(iii)	$[M{L^2}{T^{ - 2}}]$
(d)	P (linear momentum)	(iv)	$[M{L^2}{I^{ - 1}}{T^{ - 3}}]$

Choose the correct answer from the options given below :

A

(a)

\to

(ii), (b)

\to

(iii), (c)

\to

(iv), (d)

\to

(i)

B

(a)

\to

(i), (b)

\to

(ii), (c)

\to

(iv), (d)

\to

(iii)

C

(a)

\to

(iii), (b)

\to

(ii), (c)

\to

(iv), (d)

\to

(i)

D

(a)

\to

(iii), (b)

\to

(iv), (c)

\to

(ii), (d)

\to

(i)

Q 4PhysicsSection A • MCQsimple harmonic motion

+4 / -1

If the time period of a two meter long simple pendulum is 2s, the acceleration due to gravity at the place where pendulum is executing S.H.M. is :

A

16 m/s²

B

2

\pi

² ms^{$-$ 2}

C

\pi

² ms^{$-$ 2}

D

9.8 ms^{$-$ 2}

Q 5PhysicsSection A • MCQheat and thermodynamics

+4 / -1

A diatomic gas, having

{C_p} = {7 \over 2}R

and

{C_v} = {5 \over 2}R

, is heated at constant pressure. The ratio dU : dQ : dW :

A

5 : 7 : 3

B

3 : 7 : 2

C

5 : 7 : 2

D

3 : 5 : 2

Q 6PhysicsSection B • Numericalray optics

+4 / -1

The same size images are formed by a convex lens when the object is placed at 20 cm or at 10 cm from the lens. The focal length of convex lens is __________ cm.

Answer Format:Enter numerical value rounded to the nearest integer

Q 7PhysicsSection A • MCQalternating current

+4 / -1

The angular frequency of alternating current in a L-C-R circuit is 100 rad/s. The components connected are shown in the figure. Find the value of inductance of the coil and capacity of condenser.

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

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

A

0.8 H and 150

\mu

F

B

0.8 H and 250

\mu

F

C

1.33 H and 150

\mu

F

D

1.33 H and 250

\mu

F

Q 8PhysicsSection B • Numericalcurrent electricity

+4 / -1

In the given circuit of potentiometer, the potential difference E across AB (10 m length) is larger than E₁ and E₂ as well. For key K₁ (closed), the jockey is adjusted to touch the wire at point J₁ so that there is no deflection in the galvanometer. Now the first battery (E₁) is replaced by second battery (E₂) for working by making K₁ open and K₂ closed. The galvanometer gives then null deflection at J₂. The value of

{{{E_1}} \over {{E_2}}}

is

{a \over b}

, where a = _________.

qImage-potentiometer-current-electricity-electricity-Jeemate

Answer Format:Enter numerical value rounded to the nearest integer

Q 9PhysicsSection A • MCQmagnetics

+4 / -1

Magnetic fields at two points on the axis of a circular coil at a distance of 0.05 m and 0.2 m from the centre are in the ratio 8 : 1. The radius of coil is ________.

A

1.0 m

B

0.15 m

C

0.2 m

D

0.1 m

Q 10PhysicsSection A • MCQvector algebra

+4 / -1

In an octagon ABCDEFGH of equal side, what is the sum of

\overrightarrow {AB} + \overrightarrow {AC} + \overrightarrow {AD} + \overrightarrow {AE} + \overrightarrow {AF} + \overrightarrow {AG} + \overrightarrow {AH}

,

if,

\overrightarrow {AO} = 2\widehat i + 3\widehat j - 4\widehat k

qImage-vector-arithmetic-vector-algebra-mechanics-Jeemate

A

- 16\widehat i - 24\widehat j + 32\widehat k

B

16\widehat i + 24\widehat j - 32\widehat k

C

16\widehat i + 24\widehat j + 32\widehat k

D

16\widehat i - 24\widehat j + 32\widehat k

Q 11PhysicsSection B • Numericalelectrostatics

+4 / -1

The electric field in a region is given by

\overrightarrow E = \left( {{3 \over 5}{E_0}\widehat i + {4 \over 5}{E_0}\widehat j} \right){N \over C}

. The ratio of flux of reported field through the rectangular surface of area 0.2 m² (parallel to y

-

z plane) to that of the surface of area 0.3 m² (parallel to x

-

z plane) is a : b, where a = __________ [Here

{\widehat i}

,

{\widehat j}

and

{\widehat k}

are unit vectors along x, y and z-axes respectively.]

Answer Format:Enter numerical value rounded to the nearest integer

Q 12PhysicsSection B • Numericalwork power and energy

+4 / -1

The potential energy (U) of a diatomic molecule is a function dependent on r (interatomic distance) as

U = {\alpha \over {{r^{10}}}} - {\beta \over {{r^5}}} - 3

where,

\alpha

and

\beta

are positive constants. The equilibrium distance between two atoms will be

{\left( {{{2\alpha } \over \beta }} \right)^{{a \over b}}}

, where a = ___________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 13PhysicsSection A • MCQcommunication systems

+4 / -1

Given below are two statements :

Statement I : A speech signal of 2 kHz is used to modulate a carrier signal of 1 MHz. The bandwidth requirement for the signal is 4 kHz.

Statement II : The side band frequencies are 1002 kHz and 998 kHz.

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

A

Statement I is false but Statement II is true

B

Both Statement I and Statement II are false

C

Statement I is true but Statement II is false

D

Both Statement I and Statement II are true

Q 14PhysicsSection A • MCQalternating current

+4 / -1

The current (i) at time t = 0 and t =

\infty

respectively for the given circuit is :

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

A

{{18E} \over {55}},{{5E} \over {18}}

B

{{5E} \over {18}},{{18E} \over {55}}

C

{{5E} \over {18}},{{10E} \over {33}}

D

{{10E} \over {33}},{{5E} \over {18}}

Q 15PhysicsSection A • MCQelectronic devices

+4 / -1

A 5V battery is connected across the points X and Y. Assume D₁ and D₂ to be normal silicon diodes. Find the current supplied by the battery if the +ve terminal of the battery is connected to point X.

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

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

A

\sim

0.5 A

B

\sim

1.5 A

C

\sim

0.43 A

D

\sim

0.86 A

Q 16PhysicsSection A • MCQgravitation

+4 / -1

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

Assertion A : The escape velocities of planet A and B are same. But A and B are of unequal mass.

Reason R : The product of their mass and radius must be same. M₁R₁ = M₂R₂

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 17PhysicsSection A • MCQatoms and nuclei

+4 / -1

Two radioactive substances X and Y originally have N₁ and N₂ nuclei respectively. Half life of X is half of the half life of Y. After three half lives of Y, number of nuclei of both are equal. The ratio

{{{N_1}} \over {{N_2}}}

will be equal to :

A

{1 \over 8}

B

{3 \over 1}

C

{1 \over 3}

D

{8 \over 1}

Q 18PhysicsSection B • Numericalelectromagnetic induction

+4 / -1

A coil of inductance 2 H having negligible resistance is connected to a source of supply whose voltage is given by V = 3t volt. (where t is in second). If the voltage is applied when t = 0, then the energy stored in the coil after 4 s is _______J.

Answer Format:Enter numerical value rounded to the nearest integer

Q 19PhysicsSection B • Numericalheat and thermodynamics

+4 / -1

In a certain thermodynamical process, the pressure of a gas depends on its volume as kV³. The work done when the temperature changes from 100

^\circ

C to 300

^\circ

C will be ___________ nR, where n denotes number of moles of a gas.

Answer Format:Enter numerical value rounded to the nearest integer

Q 20PhysicsSection A • MCQwave optics

+4 / -1

Two coherent light sources having intensity in the ratio 2x produce an interference pattern. The ratio

{{{I_{\max }} - {I_{\min }}} \over {{I_{\max }} + {I_{\min }}}}

will be :

A

{{2\sqrt {2x} } \over {2x + 1}}

B

{{2\sqrt {2x} } \over {x + 1}}

C

{{\sqrt {2x} } \over {x + 1}}

D

{{\sqrt {2x} } \over {2x + 1}}

Q 21PhysicsSection A • MCQunits and measurements

+4 / -1

The pitch of the screw gauge is 1 mm and there are 100 divisions on the circular scale. When nothing is put in between the jaws, the zero of the circular scale lies 8 divisions below the reference line. When a wire is placed between the jaws, the first linear scale division is clearly visible while 72^nd division on circular scale coincides with the reference line. The radius of the wire is :

A

1.80 mm

B

0.90 mm

C

0.82 mm

D

1.64 mm

Q 22PhysicsSection A • MCQmagnetics

+4 / -1

A proton, a deuteron and an

\alpha

particle are moving with same momentum in a uniform magnetic field. The ratio of magnetic forces acting on them is _________ and their speed is _______, in the ratio.

A

2 : 1 : 1 and 4 : 2 : 1

B

4 : 2 : 1 and 2 : 1 : 1

C

1 : 2 : 4 and 2 : 1 : 1

D

1 : 2 : 4 and 1 : 1 : 2

Q 23PhysicsSection B • Numericalheat and thermodynamics

+4 / -1

A monoatomic gas of mass 4.0 u is kept in an insulated container. Container is moving with velocity 30 m/s. If container is suddenly stopped then change in temperature of the gas (R = gas constant) is

{x \over {3R}}

. Value of x is ___________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 24PhysicsSection A • MCQgravitation

+4 / -1

Two satellites A and B of masses 200 kg and 400 kg are revolving round the earth at height of 600 km and 1600 km respectively.

If T_A and T_B are the time periods of A and B respectively then the value of T_B

-

T_A :

qImage-escape-speed-and-motion-of-satellites-gravitation-mechanics-Jeemate

[Given : radius of earth = 6400 km, mass of earth = 6

\times

10²⁴ kg]

A

1.33

\times

10³ s

B

4.24

\times

10² s

C

3.33

\times

10² s

D

4.24

\times

10³ s

Q 25PhysicsSection A • MCQgravitation

+4 / -1

A solid sphere of radius R gravitationally attracts a particle placed at 3R from its centre with a force F₁. Now a spherical cavity of radius

\left( {{R \over 2}} \right)

is made in the sphere (as shown in figure) and the force becomes F₂. The value of F₁ : F₂ is

qImage-keplers-law-and-universal-law-of-gravitation-gravitation-mechanics-Jeemate

qImage-keplers-law-and-universal-law-of-gravitation-gravitation-mechanics-Jeemate

A

36 : 25

B

41 : 50

C

50 : 41

D

25 : 36

Q 26PhysicsSection A • MCQwaves

+4 / -1

A student is performing the experiment of resonance column. The diameter of the column tube is 6 cm. The frequency of the tuning fork is 504 Hz. Speed of the sound at the given temperature is 336 m/s. The zero of the metre scale coincides with the top end of the resonance column tube. The reading of the water level in the column when the first resonance occurs is :

A

13 cm

B

18.4 cm

C

16.6 cm

D

14.8 cm

Q 27PhysicsSection A • MCQdual nature of radiation

+4 / -1

An

\alpha

particle and a proton are accelerated from rest by a potential difference of 200V. After this, their de Broglie wavelengths are

\lambda

_$\alpha$ and

\lambda

_p respectively. The ratio

{{{{\lambda _p}} \over {{\lambda _\alpha }}}}

is :

A

8

B

2.8

C

7.8

D

3.8

Q 28PhysicsSection B • Numericalelectrostatics

+4 / -1

512 identical drops of mercury are charged to a potential of 2V each. The drops are joined to form a single drop. The potential of this drop is ________ V.

Answer Format:Enter numerical value rounded to the nearest integer

Q 29PhysicsSection B • Numericalalternating current

+4 / -1

A transmitting station releases waves of wavelength 960 m. A capacitor of 2.56

\mu

F is used in the resonant circuit. The self inductance of coil necessary for resonance is __________

\times

10^{$-$ 8} H.

Answer Format:Enter numerical value rounded to the nearest integer

Q 30PhysicsSection A • MCQheat and thermodynamics

+4 / -1

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

Assertion A : When a rod lying freely is heated, no thermal stress is developed in it.

Reason R : On heating, the length of the rod increases.

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

A

A is true but R is false

B

A is false but R is true

C

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

D

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

Q 31ChemistrySection B • Numericalredox reactions

+4 / -1

0.4 g mixture of NaOH, Na₂CO₃ and some inert impurities was first titrated with

{N \over {10}}

HCl using phenolphthalein as an indicator, 17.5 mL of HCl was required at the end point. After this methyl orange was added and titrated. 1.5 mL of same HCl was required for the next end point. The weight percentage of Na₂CO₃ in the mixture is ________. (Rounded off to the nearest integer)

Answer Format:Enter numerical value rounded to the nearest integer

Q 32ChemistrySection A • MCQsome basic concepts of chemistry

+4 / -1

Complete combustion of 1.80 g of an oxygen containing compound (C_xH_yO_z) gave 2.64 g of CO₂ and 1.08 g of H₂O. The percentage of oxygen in the organic compound is :

A

51.63

B

50.33

C

63.53

D

53.33

Q 33ChemistrySection A • MCQhaloalkanes and haloarenes

+4 / -1

Identify A and B in the chemical reaction.

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

A

B

C

D

Q 34ChemistrySection B • Numericalchemical kinetics and nuclear chemistry

+4 / -1

For the reaction, aA + bB

\to

cC + dD, the plot of log k vs

{1 \over T}

is given below :

qImage-arrhenius-equation-chemical-kinetics-and-nuclear-chemistry-physical-chemistry-Jeemate

The temperature at which the rate constant of the reaction is 10^-4 s^-1 is _________ K. (Rounded off to the nearest integer)

[Given : The rate constant of the reaction is 10^-5 s^-1 at 500 K.]

Answer Format:Enter numerical value rounded to the nearest integer

Q 35ChemistrySection A • MCQaldehydes ketones and carboxylic acids

+4 / -1

The major product of the following chemical reaction is :

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

C{H_3}C{H_2}CHO

B

C{H_3}C{H_2}C{H_3}

C

C{H_3}C{H_2}C{H_2}OH

D

{(C{H_3}C{H_2}CO)_2}O

Q 36ChemistrySection B • Numericalthermodynamics

+4 / -1

The ionization enthalpy of Na⁺ formation from Na_(g) is 495.8 kJ mol^{$-$ 1}, while the electron gain enthalpy of Br is

-

325.0 kJ mol^{$-$ 1}. Given the lattice enthalpy of NaBr is

-

728.4 kJ mol^{$-$ 1}. The energy for the formation of NaBr ionic solid is (

-

) ____________

\times

10^{$-$ 1} kJ mol^{$-$ 1}.

Answer Format:Enter numerical value rounded to the nearest integer

Q 37ChemistrySection A • MCQionic equilibrium

+4 / -1

The solubility of AgCN in a buffer solution of pH = 3 is x. The value of x is : [Assume : No cyano complex is formed; K_sp(AgCN) = 2.2

\times

10^{$-$ 16} and K_a(HCN) = 6.2

\times

10^{$-$ 10}]

A

1.9

\times

10^{$-$ 5}

B

1.6

\times

10^{$-$ 6}

C

2.2

\times

10^{$-$ 16}

D

0.625

\times

10^{$-$ 6}

Q 38ChemistrySection A • MCQp block elements

+4 / -1

The correct statement about B₂H₆ is :

A

Its fragment, BH₃, behaves as a Lewis base.

B

All B

-

H

-

B angles are of 120

^\circ

.

C

The two B

-

H

-

B bonds are not of same length.

D

Terminal B

-

H bonds have less p-character when compared to bridging bonds.

Q 39ChemistrySection A • MCQhydrocarbons

+4 / -1

Identify A in the given chemical reaction.

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

A

B

C

D

Q 40ChemistrySection B • Numericalhydrocarbons

+4 / -1

Consider the following chemical reaction.

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

The number of sp² hybridized carbon atom(s) present in the product is ________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 41ChemistrySection A • MCQd and f block elements

+4 / -1

In which of the following pairs, the outer most electronic configuration will be the same?

A

Cr⁺ and Mn²⁺

B

Ni²⁺ and Cu⁺

C

V²⁺ and Cr⁺

D

Fe²⁺ and Co⁺

Q 42ChemistrySection A • MCQchemical bonding and molecular structure

+4 / -1

According to molecular orbital theory, the species among the following that does not exist is :

A

{O_2}^{2 - }

B

B{e_2}

C

H{e_2}^ -

D

H{e_2}^ +

Q 43ChemistrySection B • Numericalsolutions

+4 / -1

1 molal aqueous solution of an electrolyte A₂B₃ is 60% ionised. The boiling point of the solution at 1 atm is _________ K. (Rounded off to the nearest integer)

[Given K_b for (H₂O) = 0.52 K kg mol^{$-$ 1}]

Answer Format:Enter numerical value rounded to the nearest integer

Q 44ChemistrySection B • Numericalthermodynamics

+4 / -1

The reaction of cyanamide, NH₂CN_(s) with oxygen was run in a bomb calorimeter and

\Delta

U was found to be

-

742.24 kJ mol^{$-$ 1}. The magnitude of

\Delta

H₂₉₈ for the reaction

N{H_2}C{H_{(S)}} + {3 \over 2}{O_{2(g)}} \to {N_{2(g)}} + {O_{2(g)}} + {H_2}{O_{(I)}}

is _________ kJ. (Rounded off to the nearest integer) [Assume ideal gases and R = 8.314 J mol^{$-$ 1} K^{$-$ 1}]

Answer Format:Enter numerical value rounded to the nearest integer

Q 45ChemistrySection A • MCQbiomolecules

+4 / -1

Which of the glycosidic linkage between galactose and glucose is present in lactose?

A

C-1 of galactose and C-6 of glucose

B

C-1 of glucose and C-6 of galactose

C

C-1 of galactose and C-4 of glucose

D

C-1 of glucose and C-4 of galactose

Q 46ChemistrySection A • MCQenvironmental chemistry

+4 / -1

Given below are two statements :

Statement I : An allotrope of oxygen is an important intermediate in the formation of reducing smog.

Statement II : Gases such as oxides of nitrogen and sulphur present in troposphere contribute to the formation of photochemical smog.

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

A

Statement I is false but Statement II is true

B

Both Statement I and Statement II are false

C

Both Statement I and Statement II are true

D

Statement I is true but Statement II is false

Q 47ChemistrySection A • MCQhydrogen

+4 / -1

Which of the following equation depicts the oxidizing nature of H₂O₂?

A

C{l_2} + {H_2}{O_2} \to 2HCl + {O_2}

B

KI{O_4} + {H_2}{O_2} \to KI{O_3} + {H_2}O + {O_2}

C

2{I^ - } + {H_2}{O_2} + 2{H^ + } \to {I_2} + 2{H_2}O

D

{I_2} + {H_2}{O_2} + 2O{H^ - } \to 2{I^ - } + 2{H_2}O + {O_2}

Q 48ChemistrySection A • MCQatomic structure

+4 / -1

The plots of radial distribution functions for various orbitals of hydrogen atom against 'r' are given below :

qImage-quantum-mechanical-model-of-atom-structure-of-atom-physical-chemistry-Jeemate

qImage-quantum-mechanical-model-of-atom-structure-of-atom-physical-chemistry-Jeemate

The correct plot for 3s orbital is :

A

(B)

B

(A)

C

(C)

D

(D)

Q 49ChemistrySection B • Numericalsome basic concepts of chemistry

+4 / -1

In basic medium

Cr{O_4}^{2 - }

oxidises

{S_2}{O_3}^{2 - }

to form

S{O_4}^{2 - }

and itself changes into

Cr{(OH)_4}^ -

. The volume of 0.154 M

Cr{O_4}^{2 - }

required to react with 40 mL of 0.25 M

{S_2}{O_3}^{2 - }

is __________ mL. (Rounded off to the nearest integer)

Answer Format:Enter numerical value rounded to the nearest integer

Q 50ChemistrySection A • MCQaldehydes ketones and carboxylic acids

+4 / -1

Which one of the following reactions will not form acetaldehyde?

A

C{H_3}C{H_2}OH\mathrel{\mathop{\kern0pt\longrightarrow} \limits_{573K}^{Cu}}

B

C{H_3}C{H_2}OH\buildrel {Cr{O_3} - {H_2}S{O_4}} \over \longrightarrow

C

C{H_2} = C{H_2} + {O_2}\mathrel{\mathop{\kern0pt\longrightarrow} \limits_{{H_2}O}^{Pd(II)/Cu(II)}}

D

C{H_3}CN\mathrel{\mathop{\kern0pt\longrightarrow} \limits_{ii)\,{H_2}O}^{i)\,DIBAL - H}}

Q 51ChemistrySection A • MCQd and f block elements

+4 / -1

Given below are two statements :

Statement I : CeO₂ can be used for oxidation of aldehydes and ketones.

Statement II : Aqueous solution of EuSO₄ is a strong reducing agent.

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

A

Statement I is true but Statement II is false.

B

Statement I is false but Statement II is true

C

Both Statement I and Statement II are false

D

Both Statement I and Statement II are true

Q 52ChemistrySection A • MCQcoordination compounds

+4 / -1

The hybridization and magnetic nature of

{[Mn{(CN)_6}]^{4 - }}

and

{[Fe{(CN)_6}]^{3 - }}

, respectively are :

A

sp³d² and diamagnetic

B

d²sp³ and paramagnetic

C

sp³d² and paramagnetic

D

d²sp³ and diamagnetic

Q 53ChemistrySection A • MCQaldehydes ketones and carboxylic acids

+4 / -1

Compound(s) which will liberate carbon dioxide with sodium bicarbonate solution is/are :

qImage-preparation-properties-and-uses-of-carboxylic-acids-aldehydes-ketones-and-carboxylic-acids-organic-chemistry-Jeemate

qImage-preparation-properties-and-uses-of-carboxylic-acids-aldehydes-ketones-and-carboxylic-acids-organic-chemistry-Jeemate

A

C only

B

B only

C

B and C only

D

A and B only

Q 54ChemistrySection A • MCQcompounds containing nitrogen

+4 / -1

Which of the following reaction/s will not give p-aminoazobenzene?

qImage-aromatic-amines-compounds-containing-nitrogen-organic-chemistry-Jeemate

qImage-aromatic-amines-compounds-containing-nitrogen-organic-chemistry-Jeemate

A

C only

B

A only

C

A and B

D

B only

Q 55ChemistrySection A • MCQsurface chemistry

+4 / -1

In Freundlich adsorption isotherm at moderate pressure, the extent of adsorption

\left( {{x \over m}} \right)

is directly proportional to P^x. The value of x is :

A

\infty

B

zero

C

1

D

{{1 \over n}}

Q 56ChemistrySection B • Numericalgaseous state

+4 / -1

A car tyre is filled with nitrogen gas at 35 psi at 27

^\circ

C. It will burst if pressure exceeds 40 psi. The temperature in

^\circ

C at which the car tyre will burst is _________. (Rounded off to the nearest integer)

Answer Format:Enter numerical value rounded to the nearest integer

Q 57ChemistrySection B • Numericalchemical bonding and molecular structure

+4 / -1

Among the following, the number of halide(s) which is/are inert to hydrolysis is _________.

(A) BF₃

(B) SiCl₄

(C) PCl₅

(D) SF₆

Answer Format:Enter numerical value rounded to the nearest integer

Q 58ChemistrySection A • MCQisolation of elements

+4 / -1

Ellingham diagram is a graphical representation of :

A

\Delta

G vs P

B

\Delta

G vs T

C

(

\Delta

G

-

T

\Delta

S) vs T

D

\Delta

H vs T

Q 59ChemistrySection B • Numericalbasics of organic chemistry

+4 / -1

Using the provided information in the following paper chromatogram :

qImage-purification-of-organic-compounds-basics-of-organic-chemistry-organic-chemistry-Jeemate

qImage-purification-of-organic-compounds-basics-of-organic-chemistry-organic-chemistry-Jeemate

Fig : Paper chromatography for compounds A and B.

the calculated R_f value of A ________

\times

10^-1.

Answer Format:Enter numerical value rounded to the nearest integer

Q 60ChemistrySection A • MCQpolymers

+4 / -1

Which statement is correct?

A

Buna-N is a natural polymer.

B

Synthesis of Buna-S needs nascent oxygen.

C

Buna-S is a synthetic and linear thermosetting polymer.

D

Neoprene is an addition copolymer used in plastic bucket manufacturing.

Q 61MathematicsSection B • Numericalapplication of derivatives

+4 / -1

Let f(x) be a polynomial of degree 6 in x, in which the coefficient of x⁶ is unity and it has extrema at x =

-

1 and x = 1. If

\mathop {\lim }\limits_{x \to 0} {{f(x)} \over {{x^3}}} = 1

, then

5.f(2)

is equal to _________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 62MathematicsSection A • MCQdifferential equations

+4 / -1

If a curve passes through the origin and the slope of the tangent to it at any point (x, y) is

{{{x^2} - 4x + y + 8} \over {x - 2}}

, then this curve also passes through the point :

A

(4, 4)

B

(5, 5)

C

(5, 4)

D

(4, 5)

Q 63MathematicsSection B • Numericalmatrices and determinants

+4 / -1

If the system of equations

kx + y + 2z = 1

3x

-

y

-

2z = 2

-

2x

-

2y

-

4z = 3

has infinitely many solutions, then k is equal to __________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 64MathematicsSection B • Numericalvector algebra

+4 / -1

Let

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

,

\overrightarrow b = \widehat i - \widehat j

and

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

be three given vectors. If

\overrightarrow r

is a vector such that

\overrightarrow r \times \overrightarrow a = \overrightarrow c \times \overrightarrow a

and

\overrightarrow r .\,\overrightarrow b = 0

, then

\overrightarrow r .\,\overrightarrow a

is equal to __________.

Answer Format:Enter numerical value rounded to the nearest integer

Official Correct Answer:12

Step-by-Step Solution:

Given, $\overrightarrow a = \widehat i + 2\widehat j - \widehat k$ ,

$\overrightarrow b = \widehat i - \widehat j$ ,

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

$\overrightarrow r \times \overrightarrow a = \overrightarrow c \times \overrightarrow a$

$\Rightarrow \overrightarrow r \times \overrightarrow a - \overrightarrow c \times \overrightarrow a = 0$

$\Rightarrow (\overrightarrow r - \overrightarrow c ) \times \overrightarrow a = 0$

$\therefore$ $\overrightarrow r - \overrightarrow c = \lambda \overrightarrow a$

$\Rightarrow \overrightarrow r = \lambda \overrightarrow a + \overrightarrow c$

$\Rightarrow \overrightarrow r \,.\,\overrightarrow b = \lambda \overrightarrow a \,.\,\overrightarrow b + \overrightarrow c \,.\,\overrightarrow b$ (taking dot with $\overrightarrow b$ )

$\Rightarrow 0 = \lambda \overrightarrow a \,.\,\overrightarrow b + \overrightarrow c \,.\,\overrightarrow b$ [ $\because$ $\overrightarrow r \,.\,\overrightarrow b = 0$ ]

$\Rightarrow \lambda (\widehat i + 2\widehat j - \widehat k)\,.\,(\widehat i - \widehat j) + (\widehat i - \widehat j - \widehat k)\,.\,(\widehat i - \widehat j) = 0$

$\Rightarrow \lambda (1 - 2) + 2 = 0$

$\Rightarrow \lambda = 2$

$\therefore$ $\overrightarrow r = 2\overrightarrow a + \overrightarrow c$

$\Rightarrow \overrightarrow r \,.\,\overrightarrow a = 2\overrightarrow a \,.\,\overrightarrow a + \overrightarrow c \,.\,\overrightarrow a$ [taking dot with ${\overrightarrow a }$ ]

$= 2{\left| {\overrightarrow a } \right|^2} + \overrightarrow a \,.\,\overrightarrow c$

$= 2(1 + 4 + 1) + (1 - 2 + 1)$

$\Rightarrow \overrightarrow r \,.\,\overrightarrow a = 12$

Q 65MathematicsSection A • MCQ3d geometry

+4 / -1

Let

\alpha

be the angle between the lines whose direction cosines satisfy the equations l + m

-

n = 0 and l² + m²

-

n² = 0. Then the value of sin⁴

\alpha

+ cos⁴

\alpha

is :

A

{{3 \over 8}}

B

{{3 \over 4}}

C

{{1 \over 2}}

D

{{5 \over 8}}

Q 66MathematicsSection A • MCQpermutations and combinations

+4 / -1

The total number of positive integral solutions (x, y, z) such that xyz = 24 is :

A

36

B

24

C

45

D

30

Q 67MathematicsSection A • MCQparabola

+4 / -1

A tangent is drawn to the parabola y² = 6x which is perpendicular to the line 2x + y = 1. Which of the following points does NOT lie on it?

A

(0, 3)

B

(

-

6, 0)

C

(4, 5)

D

(5, 4)

Q 68MathematicsSection A • MCQindefinite integration

+4 / -1

The value of the integral

\int {{{\sin \theta .\sin 2\theta ({{\sin }^6}\theta + {{\sin }^4}\theta + {{\sin }^2}\theta )\sqrt {2{{\sin }^4}\theta + 3{{\sin }^2}\theta + 6} } \over {1 - \cos 2\theta }}} \,d\theta

is :

A

{1 \over {18}}{\left[ {9 - 2{{\cos }^6}\theta - 3{{\cos }^4}\theta - 6{{\cos }^2}\theta } \right]^{{3 \over 2}}} + c

B

{1 \over {18}}{\left[ {11 - 18{{\sin }^2}\theta + 9{{\sin }^4}\theta - 2{{\sin }^6}\theta } \right]^{{3 \over 2}}} + c

C

{1 \over {18}}{\left[ {11 - 18{{\cos }^2}\theta + 9{{\cos }^4}\theta - 2{{\cos }^6}\theta } \right]^{{3 \over 2}}} + c

D

{1 \over {18}}{\left[ {9 - 2{{\sin }^6}\theta - 3{{\sin }^4}\theta - 6{{\sin }^2}\theta } \right]^{{3 \over 2}}} + c

Q 69MathematicsSection A • MCQlimits continuity and differentiability

+4 / -1

\mathop {\lim }\limits_{n \to \infty } {\left( {1 + {{1 + {1 \over 2} + ........ + {1 \over n}} \over {{n^2}}}} \right)^n}

is equal to :

A

{{1 \over 2}}

B

1

C

0

D

{{1 \over e}}

Q 70MathematicsSection A • MCQmathematical reasoning

+4 / -1

The statement A

\to

(B

\to

A) is equivalent to :

A

\to

(A

\mathrel{\mathop{\kern0pt\longleftrightarrow} \limits_{}}

B)

B

A

\to

(A

\vee

B)

C

A

\to

(A

\wedge

B)

D

A

\to

(A

\to

B)

Q 71MathematicsSection A • MCQapplication of derivatives

+4 / -1

If the curves,

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

and

{{{x^2}} \over c} + {{{y^2}} \over d} = 1

intersect each other at an angle of 90

^\circ

, then which of the following relations is TRUE?

A

a

-

c = b + d

B

a + b = c + d

C

ab = {{c + d} \over {a + b}}

D

a

-

b = c

-

d

Q 72MathematicsSection A • MCQstraight lines and pair of straight lines

+4 / -1

The image of the point (3, 5) in the line x

-

y + 1 = 0, lies on :

A

(x

-

4)² + (y

-

4)² = 8

B

(x

-

4)² + (y

+

2)² = 16

C

(x

-

2)² + (y

-

2)² = 12

D

(x

-

2)² + (y

-

4)² = 4

Q 73MathematicsSection B • Numericallimits continuity and differentiability

+4 / -1

The number of points, at which the function
f(x) = | 2x + 1 |

-

3| x + 2 | + | x² + x

-

2 |, x

\in

R is not differentiable, is __________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 74MathematicsSection A • MCQquadratic equation and inequalities

+4 / -1

The integer 'k', for which the inequality x²

-

2(3k

-

1)x + 8k²

-

7 > 0 is valid for every x in R, is :

A

4

B

2

C

3

D

0

Q 75MathematicsSection A • MCQsequences and series

+4 / -1

If

0 < \theta ,\phi < {\pi \over 2},x = \sum\limits_{n = 0}^\infty {{{\cos }^{2n}}\theta } ,y = \sum\limits_{n = 0}^\infty {{{\sin }^{2n}}\phi }

and

z = \sum\limits_{n = 0}^\infty {{{\cos }^{2n}}\theta .{{\sin }^{2n}}\phi }

then :

A

xy

-

z = (x + y)z

B

xyz = 4

C

xy + z = (x + y)z

D

xy + yz + zx = z

Q 76MathematicsSection A • MCQ3d geometry

+4 / -1

The equation of the line through the point (0, 1, 2) and perpendicular to the line

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

is :

A

{x \over 3} = {{y - 1} \over { - 4}} = {{z - 2} \over 3}

B

{x \over 3} = {{y - 1} \over 4} = {{z - 2} \over { - 3}}

C

{x \over { - 3}} = {{y - 1} \over 4} = {{z - 2} \over 3}

D

{x \over 3} = {{y - 1} \over 4} = {{z - 2} \over 3}

Q 77MathematicsSection A • MCQtrigonometric functions and equations

+4 / -1

All possible values of

\theta

\in

[0, 2

\pi

] for which sin 2

\theta

+ tan 2

\theta

> 0 lie in :

A

\left( {0,{\pi \over 4}} \right) \cup \left( {{\pi \over 2},{{3\pi } \over 4}} \right) \cup \left( {{{3\pi } \over 2},{{11\pi } \over 6}} \right)

B

\left( {0,{\pi \over 2}} \right) \cup \left( {\pi ,{{3\pi } \over 2}} \right)

C

\left( {0,{\pi \over 2}} \right) \cup \left( {{\pi \over 2},{{3\pi } \over 4}} \right) \cup \left( {\pi ,{{7\pi } \over 6}} \right)

D

\left( {0,{\pi \over 4}} \right) \cup \left( {{\pi \over 2},{{3\pi } \over 4}} \right) \cup \left( {\pi ,{{5\pi } \over 4}} \right) \cup \left( {{{3\pi } \over 2},{{7\pi } \over 4}} \right)

Q 78MathematicsSection A • MCQdefinite integration

+4 / -1

The value of

\int\limits_{ - 1}^1 {{x^2}{e^{[{x^3}]}}} dx

, where [ t ] denotes the greatest integer

\le

t, is :

A

{{e + 1} \over 3}

B

{{e - 1} \over {3e}}

C

{1 \over {3e}}

D

{{e + 1} \over {3e}}

Q 79MathematicsSection B • Numericalsequences and series

+4 / -1

Let A₁, A₂, A₃, ....... be squares such that for each n

\ge

1, the length of the side of A_n equals the length of diagonal of A_n+1. If the length of A₁ is 12 cm, then the smallest value of n for which area of A_n is less than one, is __________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 80MathematicsSection B • Numericalhyperbola

+4 / -1

The locus of the point of intersection of the lines

\left( {\sqrt 3 } \right)kx + ky - 4\sqrt 3 = 0

and

\sqrt 3 x - y - 4\left( {\sqrt 3 } \right)k = 0

is a conic, whose eccentricity is _________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 81MathematicsSection A • MCQcomplex numbers

+4 / -1

Let the lines (2

-

i)z = (2 + i)

\overline z

and (2

+

i)z + (i

-

2)

\overline z

-

4i = 0, (here i² =

-

1) be normal to a circle C. If the line iz +

\overline z

+ 1 + i = 0 is tangent to this circle C, then its radius is :

A

{3 \over {2\sqrt 2 }}

B

3\sqrt 2

C

{1 \over {2\sqrt 2 }}

D

{3 \over {\sqrt 2 }}

Q 82MathematicsSection A • MCQprobability

+4 / -1

The coefficients a, b and c of the quadratic equation, ax² + bx + c = 0 are obtained by throwing a dice three times. The probability that this equation has equal roots is :

A

{1 \over {72}}

B

{5 \over {216}}

C

{1 \over {36}}

D

{1 \over {54}}

Q 83MathematicsSection A • MCQheight and distance

+4 / -1

A man is observing, from the top of a tower, a boat speeding towards the lower from a certain point A, with uniform speed. At that point, angle of depression of the boat with the man's eye is 30

^\circ

(Ignore man's height). After sailing for 20 seconds, towards the base of the tower (which is at the level of water), the boat has reached a point B, where the angle of depression is 45

^\circ

. Then the time taken (in seconds) by the boat from B to reach the base of the tower is :

A

10(\sqrt 3 + 1)

B

10(\sqrt 3 - 1)

C

10

D

10\sqrt 3

Q 84MathematicsSection B • Numericalarea under the curves

+4 / -1

The graphs of sine and cosine functions, intersect each other at a number of points and between two consecutive points of intersection, the two graphs enclose the same area A. Then A⁴ is equal to __________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 85MathematicsSection B • Numericalmatrices and determinants

+4 / -1

If

A = \left[ {\matrix{ 0 & { - \tan \left( {{\theta \over 2}} \right)} \cr {\tan \left( {{\theta \over 2}} \right)} & 0 \cr } } \right]

and

({I_2} + A){({I_2} - A)^{ - 1}} = \left[ {\matrix{ a & { - b} \cr b & a \cr } } \right]

, then

13({a^2} + {b^2})

is equal to

Answer Format:Enter numerical value rounded to the nearest integer

Q 86MathematicsSection B • Numericalmatrices and determinants

+4 / -1

Let

A = \left[ {\matrix{ x & y & z \cr y & z & x \cr z & x & y \cr } } \right]

, where x, y and z are real numbers such that x + y + z > 0 and xyz = 2. If

{A^2} = {I_3}

, then the value of

{x^3} + {y^3} + {z^3}

is ____________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 87MathematicsSection A • MCQprobability

+4 / -1

When a missile is fired from a ship, the probability that it is intercepted is

{1 \over 3}

and the probability that the missile hits the target, given that it is not intercepted, is

{3 \over 4}

. If three missiles are fired independently from the ship, then the probability that all three hit the target, is :

A

{3 \over 4}

B

{3 \over 8}

C

{1 \over 27}

D

{1 \over 8}

Q 88MathematicsSection A • MCQfunctions

+4 / -1

Let f, g : N

\to

N such that f(n + 1) = f(n) + f(1)

\forall

n

\in

N and g be any arbitrary function. Which of the following statements is NOT true?

A

If g is onto, then fog is one-one

B

f is one-one

C

If f is onto, then f(n) = n

\forall

n

\in

N

D

If fog is one-one, then g is one-one

Q 89MathematicsSection A • MCQapplication of derivatives

+4 / -1

If Rolle's theorem holds for the function

f(x) = {x^3} - a{x^2} + bx - 4

,

x \in [1,2]

with

f'\left( {{4 \over 3}} \right) = 0

, then ordered pair (a, b) is equal to :

A

(

-

5,

-

8)

B

(5,

-

8)

C

(

-

5, 8)

D

(5, 8)

Q 90MathematicsSection B • Numericalpermutations and combinations

+4 / -1

The total number of numbers, lying between 100 and 1000 that can be formed with the digits 1, 2, 3, 4, 5, if the repetition of digits is not allowed and numbers are divisible by either 3 or 5, is _____________.

Answer Format:Enter numerical value rounded to the nearest integer

JEE Main 2021 25th February Morning Shift Question Paper with Solutions