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

The plots of radial distribution functions for various orbitals of hydrogen atom against ' r ' are given below. The correct plot for the 3s orbital is :

(drawn graph with three maxima and two radial nodes)

Which of the following equation depicts the oxidizing nature of H_2O_2 ?

2I^- + H_2O_2 + 2H^+ → I_2 + 2H_2O

The incorrect statement about B_2H_6 is :

All B - H - B angles are of 120^°

Identify A and B in the chemical reaction. The starting material (drawn structure) reacts with HCl to give [A] (major), which then reacts with NaI in dry acetone to give [B] major.

A and B drawn structures (set 2)

Which statement is correct?

Synthesis of Buna-S needs nascent oxygen.

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

C - 1 of galactose and C - 4 of glucose

JEE Main 2021 February 25, Shift 1 Question Paper with Solutions

Q1Single correctVector Algebra

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

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

, if,

\vec{AO}=2\hat{i}+3\hat{j}-4\hat{k}

Regular octagon ABCDEFGH (A,B top; C,D right; E,F bottom; G,H left) with centre O.

(A)

\displaystyle 16\hat{i}+24\hat{j}-32\hat{k}

(B)

\displaystyle 16\hat{i}-24\hat{j}+32\hat{k}

(C)

\displaystyle 16\hat{i}+24\hat{j}+32\hat{k}

(D)

\displaystyle -16\hat{i}-24\hat{j}+32\hat{k}

Q2Single correctUnits and Measurements

Match List - I with List - II :

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

(A)

(a)

\displaystyle \rightarrow

(ii), (b)

\displaystyle \rightarrow

(iii), (c)

\displaystyle \rightarrow

(iv), (d)

\displaystyle \rightarrow

(i)

(B)

(a)

\displaystyle \rightarrow

(i), (b)

\displaystyle \rightarrow

(ii), (c)

\displaystyle \rightarrow

(iv), (d)

\displaystyle \rightarrow

(iii)

(C)

(a)

\displaystyle \rightarrow

(iii), (b)

\displaystyle \rightarrow

(ii), (c)

\displaystyle \rightarrow

(iv), (d)

\displaystyle \rightarrow

(i)

(D)

(a)

\displaystyle \rightarrow

(iii), (b)

\displaystyle \rightarrow

(iv), (c)

\displaystyle \rightarrow

(ii), (d)

\displaystyle \rightarrow

(i)

Q3Single correctKinematics

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)

\displaystyle \frac{u+v}{2}

(B)

\displaystyle \sqrt{\frac{v^2+u^2}{2}}

(C)

\displaystyle \frac{v-u}{2}

(D)

\displaystyle \sqrt{\frac{v^2-u^2}{2}}

Q4Single correctGravitation

A solid sphere of radius R gravitationally attracts a particle placed at

3R

from its centre with a force

F_1

. Now a spherical cavity of radius

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

is made in the sphere (as shown in figure) and the force becomes

F_2

. The value of

F_1:F_2

is:

Solid sphere centre O radius R (shaded) with a spherical cavity radius R/2 centred at B; particle m at A, distance 2R from O.

(A)

\displaystyle 41:50

(B)

\displaystyle 50:41

(C)

\displaystyle 25:36

(D)

\displaystyle 36:25

Q5Single correctGravitation

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

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

6\times10^{24}

kg ]

Earth E at centre with two concentric circular orbits; satellite A on the inner orbit, B on the outer orbit.

(A)

\displaystyle 4.\,24\times10^3

s

(B)

\displaystyle 3.\,33\times10^2

s

(C)

\displaystyle 1.\,33\times10^3

s

(D)

\displaystyle 4.\,24\times10^2

s

Q6Single correctGravitation

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.

M_1R_1=M_2R_2

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

(A)

Both

\displaystyle A

and

\displaystyle R

are correct and

\displaystyle R

is the correct explanation of

\displaystyle A

(B)

Both

\displaystyle A

and

\displaystyle R

are correct but

\displaystyle R

is NOT the correct explanation of

\displaystyle A

(C)

\displaystyle A

is not correct but

\displaystyle R

is correct

(D)

\displaystyle A

is correct but

\displaystyle R

is not correct

Q7Single correctProperties of Solids and Liquids

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)

Both

\displaystyle A

and

\displaystyle R

are true and

\displaystyle R

is the correct explanation of

\displaystyle A

(B)

\displaystyle A

is false but

\displaystyle R

is true

(C)

Both

\displaystyle A

and

\displaystyle R

are true but

\displaystyle R

is NOT the correct explanation of

\displaystyle A

(D)

\displaystyle A

is true but

\displaystyle R

is false

Q8Single correctKinetic Theory of Gases

A diatomic gas, having

C_P=\frac{7}{2}R

and

C_V=\frac{5}{2}R

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

(A)

\displaystyle 3:5:2

(B)

\displaystyle 5:7:3

(C)

\displaystyle 5:7:2

(D)

\displaystyle 3:7:2

Q9Single correctOscillations and Waves

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

(A)

\displaystyle 2\pi^2

m

\displaystyle s^{-2}

(B)

\displaystyle 16

m

\displaystyle s^{-2}

(C)

\displaystyle \pi^2

m

\displaystyle s^{-2}

(D)

\displaystyle 9.\,8

m

\displaystyle s^{-2}

Q10Single correctOscillations and Waves

A student is performing the experiment of the 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^{-1}

. The zero of the meter 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)

\displaystyle 14.\,8

cm

(B)

\displaystyle 18.\,4

cm

(C)

\displaystyle 16.\,6

cm

(D)

\displaystyle 13

cm

Q11Single correctMagnetic Effects of Current and Magnetism

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)

\displaystyle 2:1:1

and

\displaystyle 4:2:1

(B)

\displaystyle 1:2:4

and

\displaystyle 2:1:1

(C)

\displaystyle 4:2:1

and

\displaystyle 2:1:1

(D)

\displaystyle 1:2:4

and

\displaystyle 1:1:2

Q12Single correctMagnetic Effects of Current and Magnetism

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)

\displaystyle 0.\,15

m

(B)

\displaystyle 0.\,2

m

(C)

\displaystyle 0.\,1

m

(D)

\displaystyle 1.\,0

m

Q13Single correctElectromagnetic Induction and Alternating Currents

The current (i) at time

t=0

and

t=\infty

respectively for the given circuit is :

Bridge: top two 5 ohm resistors, middle 1 ohm and 4 ohm with battery E (current i) between, bottom inductor L.

(A)

\displaystyle \frac{5E}{18},\ \frac{18E}{55}

(B)

\displaystyle \frac{5E}{18},\ \frac{10E}{33}

(C)

\displaystyle \frac{10E}{33},\ \frac{5E}{18}

(D)

\displaystyle \frac{18E}{55},\ \frac{5E}{18}

Q14Single correctElectromagnetic Induction and Alternating Currents

The angular frequency of alternating current in a L-C-R circuit is 100 rad

s^{-1}

. The components connected are shown in the figure. Find the value of inductance of the coil and capacity of condenser.

Series AC L-C-R: R=60 ohm (15 V), capacitor C (10 V), R'=40 ohm branch, inductor (20 V), AC source.

(A)

\displaystyle 1.\,33

H and

\displaystyle 150\ \mu

F

(B)

\displaystyle 0.\,8

H and

\displaystyle 150\ \mu

F

(C)

\displaystyle 1.\,33

H and

\displaystyle 250\ \mu

F

(D)

\displaystyle 0.\,8

H and

\displaystyle 250\ \mu

F

Q15Single correctOptics

Two coherent light sources having intensity in the ratio

2x

produce an interference pattern. The ratio

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

will be

(A)

\displaystyle \frac{2\sqrt{2x}}{x+1}

(B)

\displaystyle \frac{\sqrt{2x}}{2x+1}

(C)

\displaystyle \frac{2\sqrt{2x}}{2x+1}

(D)

\displaystyle \frac{\sqrt{2x}}{x+1}

Q16Single correctDual Nature of Matter and Radiation

An

\alpha

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

\lambda_\alpha

and

\lambda_p

respectively. The ratio

\frac{\lambda_p}{\lambda_\alpha}

is :

(A)

\displaystyle 8

(B)

\displaystyle 3.8

(C)

\displaystyle 2.8

(D)

\displaystyle 7.8

Q17Single correctAtoms and Nuclei

Two radioactive substances X and Y originally have

N_1

and

N_2

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

\frac{N_1}{N_2}

will be equal to :

(A)

\displaystyle \frac{1}{3}

(B)

\displaystyle \frac{8}{1}

(C)

\displaystyle \frac{3}{1}

(D)

\displaystyle \frac{1}{8}

Q18Single correctElectronic Devices

A 5 V battery is connected across the points X and Y. Assume

D_1

and

D_2

to be normal silicon diodes. Find the current supplied by the battery if the

+ve

terminal of the battery is connected to point X.

Two parallel branches between X and Y: D1 (forward) + 10 ohm; D2 (reverse) + 5 ohm; 5 V across X-Y.

(A)

\displaystyle \sim 0.86

A

(B)

\displaystyle \sim 0.5

A

(C)

\displaystyle \sim 1.5

A

(D)

\displaystyle \sim 0.43

A

Q19Single correctElectromagnetic Waves

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 true

(C)

Statement I is true but Statement II is false

(D)

Both Statement I and Statement II are false

Q20Single correctExperimental Skills

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)

\displaystyle 1.64

mm

(B)

\displaystyle 0.82

mm

(C)

\displaystyle 0.90

mm

(D)

\displaystyle 1.80

mm

Q21NumericalLaws of Motion

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^{-1}

. (Take

g=10

m

s^{-2}

)

Q22NumericalWork, Energy and Power

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

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

where

\alpha

and

\beta

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

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

, where

a=

_____ .

Q23NumericalThermodynamics

In a certain thermodynamical process, the pressure of a gas depends on its volume as

kV^{3}

. The work done when the temperature changes from 100

^{\circ}

C to 300

^{\circ}

C will be xnR where n denotes number of moles of a gas find x :

Q24NumericalKinetic Theory of Gases

A monoatomic gas of mass

4.0\ u

is kept in an insulated container. The container is moving with velocity 30 m

s^{-1}

. If the container is suddenly stopped then a change in temperature of the gas (

R=

gas constant) is

\frac{x}{3R}

. Value of x is,

Q25NumericalElectrostatics

The electric field in a region is given by

\vec{E}=\left(\frac{3}{5}E_0\hat{i}+\frac{4}{5}E_0\hat{j}\right)

N

C^{-1}

. The ratio of flux of reported field through the rectangular surface of area

0.2

m^2

(parallel to

y-z

plane) to that of the surface of area

0.3

m^2

(parallel to

x-z

plane) is

a:b=a:2

, where

a=

? [Here

\hat{i}

,

\hat{j}

and

\hat{k}

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

Q26NumericalElectrostatics

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

V

in Volt.

Q27NumericalCurrent Electricity

In the given circuit of potentiometer, the potential difference E across AB(10 m length) is larger than

E_1

and

E_2

as well. For key

K_1

(closed), the jockey is adjusted to touch the wire at point

J_1

so that there is no deflection in the galvanometer. Now the first battery (

E_1

) is replaced by second battery (

E_2

) for working by making

K_1

open and

K_2

closed. The galvanometer gives then null deflection at

J_2

. The value of

\frac{E_1}{E_2}

is

\frac{a}{2}

, where

a=

_____ .

Potentiometer with boustrophedon wire AB (10 m), driver cell E + key K + rheostat Rh, cells E1/K1 and E2/K2 into galvanometer G, jockey J1 at 20 cm and J2 at 60 cm.

Q28NumericalElectromagnetic Induction and Alternating Currents

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 in J,

Q29NumericalElectromagnetic Induction and Alternating Currents

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

x\times 10^{-8}

H. find x

Q30NumericalOptics

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 _____ .

JEE Main 2021 February 25, Shift 1 Question Paper with Solutions

Physics30 questions

Chemistry30 questions

Mathematics30 questions

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