Notesale: Turn your study into money

Document Preview

Extracts from the notes are below, to see the PDF you'll receive please use the links above

---

JEE Main 2021 – Question Paper
24th Feb'21 (09:00 AM to 12:00 PM)

PHYSICS
SECTION-A
1
...


In a Young's double slit experiment, the width
of the one of the slit is three times the other slit
...
Find the ratio
of the maximum to the minimum intensity in
the interference pattern
...


Two stars of masses m and 2m at a distance d

n mole a perfect gas undergoes a cyclic process
ABCA (see figure) consisting of the following
processes
...


rotate about their common centre of mass in

B ® C : Isobaric compression at pressure P2

free space
...

C ® A : Isochoric change leading to change

(1)

1
d3
2p 3Gm

(2) 2p

d3
3Gm

(3)

1 3Gm
2p d 3

(4) 2p

3Gm
d3

of pressure from P 2 to P 1
...


A

A current through a wire depends on time as
i = a 0 t + bt 2 where a 0 = 20 A/s and
b = 8 As–2
...


B

V 2=2V1

section of the wire in 15 s
...


Moment of inertia (M
...
) of four bodies, having
same mass and radius, are reported as ;
I1 = M
...
of thin circular ring about its diameter
...
I
...
I
...
I
...


curvature r of the spherical convex mirror by:

Then :
(1) I1 + I3 < I2 + I4

1
(1) f = + r
2

(2) f = –r

1
(3) f = - r
2

(4) f = r

5
I
2 4
(3) I1 = I2 = I3 > I4
(4) I1 = I 2 = I 3 < I 4
(2) I1 + I2 = I3 +

1

JEE Main 2021 – Question Paper
7
...


If Y, K and h are the values of Young's
modulus, bulk modulus and modulus of rigidity

Statement-I : Two photons having equal linear
momenta have equal wavelengths
...
Choose the correct
relation for these parameters
...

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

8
...
The
transitions A, B and C respectively represent :

a rigid support
...
The mass oscillates on a frictionless
surface with time period T and amplitude A
...
The new amplitude of oscillation

+ eV

Continuum
n=5
n=4
n=3

B

will be :

C

0 eV
–0
...
85 eV
–1
...
4 eV
A

n=1

m
M

E
–13
...


k

(1) A

M-m
M

(2) A

M
M+m

(3) A

M+m
M

(4) A

M
M-m

(2) The first member of the Lyman series, third
member of Balmer series and second
member of Paschen series
...

(4) The series limit of Lyman series, second
member of Balmer series and second
member of Paschen series
...


Four identical particles of equal masses 1kg

Two equal capacitors are first connected in

made to move along the circumference of a

series and then in parallel
...
The speed
of each particle will be :

(1) 4 : 1

(2) 2 : 1

(3) 1 : 4

(4) 1 : 2

(1)

(3)

12
...


G
(1 + 2 2)
2

(2)

G
(2 2 - 1)
2

(4)

G(1 + 2 2)

14
...
5 mA
...
5

(3) 0
...
5

acceleration-time graph ?
15
...


Each side of a box made of metal sheet in cubic
shape is 'a' at room temperature 'T', the

(3)

t

coefficient of linear expansion of the metal
sheet is 'a'
...
Calculate the increase
t

in the volume of the metal box
...


A cell E1 of emf 6V and internal resistance 2W

20
...
0 V
(3) 5
...
6 V
(4) 2
...


A cube of side 'a' has point charges +Q located
at each of its vertices except at the origin where
the charge is –Q
...

Then the dimension of b will be :
(1) [M L2 T–2]
(2) [M L T–2]
(3) [M2 L T2]
(4) [M0 L T0]

4V, 8W

6V, 2W

19
...


2

internal resistance 8W (as shown in the figure)
...
5 kg and a vertical
rough wall is 0
...
The magnitude of horizontal
force that should be applied on the block to
keep it adhere to the wall will be ______N
...


A resonance circuit
resistance 2 × 10–4 H
oscillates at 10 MHz
quality factor of this
= 3
...


A hydraulic press can lift 100 kg when a mass
'm' is placed on the smaller piston
...


4
...
28 W respectively
frequency
...
[p

( xˆ + yˆ + zˆ )
( xˆ + yˆ + zˆ )
( xˆ + yˆ + zˆ )
( xˆ + yˆ + zˆ )

Consider two satellites S1 and S2 with periods
of revolution 1 hr
...
respectively
revolving around a planet in circular orbits
...
If
the upper surface of this curved plane is rough
with coefficient of friction µ = 0
...


JEE Main 2021 – Question Paper
5
...


A ball will a speed of 9 m/s collides with

is travelling in a medium whose relative electric

another identical ball at rest
...
Its velocity in this medium is
________× 107 m/s
...
The ratio of
velocities of the balls after collision is x : y,
where x is ________
...


In connection with the circuit drawn below, the
value of current flowing through 2 kW resistor

9
...
C
...
The D
...
source

is ________ × 10 –4 A
...
C
...
C
...
The

1 kW

2 kW

5V

number of turns of secondary coil are 24, then
the number of turns of primary are _______
...


An audio signal n m = 20 sin 2p (1500 t)
amplitude modulates a carrier

nC = 80 sin 2p (100,000 t)
...


10
...
Now, if
the analyzer is rotated around the horizontal
axis (direction of light) by 30° in clockwise
direction, the intensity of emerging light will
be _______ Lumens
...


3
...


MgBr

enthalpy is :
(1) Mg < Al < Si < S < P

Cl
(B) :

Which of the following ore is concentrated using
group 1 cyanide salt ?

Consider the elements Mg
...


(B) :
+
N2Cl–

CH3–CH–CH2–CH–CH2–CH3

(3) CH3 – CH

CHO

5
...
The
solution of X on passing of gas Y, forms Z
...
xH2O

(4) Al < Mg < S < Si < P

(3) X = Al(OH)3, Y = CO2, Z = Al2O3
(4) X = Al(OH)3, Y = SO2, Z = Al2O3
...


Which of the following are isostructural pairs ?

9
...
SO24- and CrO24B
...
NH3 and NO3D
...
1 to 0
...


(4) B and C only

1
(3) log with ( n < 1)
n

What is the final product (major) 'A' in the given
reaction ?

CH3

1
æ1
ö
with ç = 0 to 1 ÷
èn
ø
n

OH
CH

CH3
(1)

CH3

HCl

'A'
(major product)

CH

CH

(2)

CH3

CH2

(4)

10
...

(1) H2O2 acts as reducing and oxidising agent
respectively in equation (A) and (B)

Cl
CH
CH3

(2) H2O2 acts as oxidising agent in equation (A)
and (B)
(3) H2O2 acts as reducing agent in equation (A)

8
...
HNO3
Conc
...


What is the major product formed by HI on

CH

CH3
reaction with

C

CH3

14
...


CH3

(2) CH3

C

CH

List I

CH3

(a) Caprolactum

CH3

(4)

CH3

List II

(Monomer Unit)

CH3 I

(3) CH3

Match List I with List II
...


Which of the following reagent is used for the

(2) (a) ® (ii), (b) ® (i), (c) ® (iv), (d) ® (iii)

following reaction ?

(3) (a) ® (iii), (b) ® (iv), (c) ® (i), (d) ® (ii)

CH 3 CH 2 CH 3 ¾¾
® CH 3 CH 2 CHO
?

(1)
(2)
(3)
(4)

Manganese acetate
Copper at high temperature and pressure
Molybdenum oxide
Potassium permanganate

(4) (a) ® (i), (b) ® (ii), (c) ® (iii), (d) ® (iv)
16
...


Given below are two statements :
Statement I : Colourless cupric metaborate is
reduced to cuprous metaborate in a luminous
flame
...

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


The major components in "Gun Metal" are :
(1) Cu, Zn and Ni

(2) Cu, Sn and Zn

(3) Al, Cu, Mg and Mn (4) Cu, Ni and Fe
18
...


SECTION-B

Identify products A and B :
CH3

dil
...


of water, its freezing point drops by 0
...
The
dissociation constant of ClCH 2 COOH is

CH3

x × 10 –3
...


B:

(Rounded off to the nearest integer)

O

Kf(H O) = 1
...
45 g of ClCH2COOH is added to 500 mL

é

O
(3) A : OHC—CH 2CH2CH 2—C—CH 3

2
...
The molarity of the

O

solution in M is x × 10 –1
...
(Rounded off to the nearest integer)

CH3
(4)

OH
20
...
5 g of compound A (MW = 90) was used to make

O

3
...
The value KP for the reaction

colour on reaction with phthalic anhydride in
conc
...
The value of x is _______
...


HO

CH3

following is __________

(2)

HO

CH3
CH3

H 3C

Number of amphoteric compound among the
(A) BeO

(B) BaO

(C) Be(OH)2

(D) Sr(OH)2

(3)
HO

OH

5
...
(Integer answer)

JEE Main 2021 – Question Paper
6
...


The stepwise formation of [Cu(NH3)4]2+ is given
below

equilibrium constant at 300 K and 1 atm is equal
to 100
...
The value of DrG for the reaction at 300

K1
2+
ˆˆˆ
†
Cu 2 + + NH 3 ‡ˆˆ
ˆ[Cu(NH 3 )]

K and 1 atm in J mol–1 is – xR, where x is ______

K2
2+
ˆˆˆ
†
[Cu(NH 3 )]2 + + NH 3 ‡ˆˆ
ˆ[Cu(NH 3 )2 ]

(Rounded of to the nearest integer) (R = 8
...
3)

K3
2+
ˆˆˆ
†
[Cu(NH 3 )2 ]2 + + NH 3 ‡ˆˆ
ˆ[Cu(NH 3 )3 ]
2+
4
ˆˆˆ
†
[Cu(NH 3 )3 ]2 + + NH 3 ‡ˆˆ
ˆ[Cu(NH 3 ) 4 ]
K

7
...
If lLi and lP denote the de Broglie

The value of stability constants K1, K2, K3 and K4
are 104, 1
...


wavelengths of Li3+ and proton respectively, then

The overall equilibrium constants for dissociation
of [Cu(NH3)4]2+ is x × 10–12
...
The value of x is
lP

________
...

(Rounded off to the nearest integer)

9
...


(Mass of Li3+ = 8
...
]
10
...
3 ×
10–4s–1 at 153oC
...
(Rounded off to the
nearest integer)

5

JEE Main 2021 – Question Paper
24th Feb'21 (09:00 AM to 12:00 PM)

MATHEMATICS
1
...


The system of linear equations
3x – 2y – kz = 10

tautology is :

2x – 4y – 2z = 6

(1) A Ú (A Ù B)

x + 2y – z = 5m

(2) A Ù (A Ú B)

is inconsistent if :

(3) B ® [A Ù (A ® B)]

(1) k = 3, m =

4
5

(2) k ¹ 3, m Î R

(3) k ¹ 3, m ¹

4
5

(4) k = 3, m ¹

(4) [A Ù (A ® B)] ® B
2
...
by NTA (4)
A man is walking on a straight line
...


points (1,1), (2, 2) and (4, 4) respectively
...

3
...


If

dP
= 0
...
If P(0) = 850, then the time
dt

(4) 2loge18

(2) 19 2

If the tangent to the curve y = x3 at the point
P(t, t3) meets the curve again at Q, then the
ordinate of the point which divides PQ
internally in the ratio 1 : 2 is :
(1) –2t 3
(2) 0
(3) –t3
(4) 2t3

species follows the differential equation

1
loge 18
2

(1) 2 19

8
...


If ƒ : R ® R is a function defined by

æ 2x - 1 ö
ƒ(x) = [x - 1]cos ç
÷ p, where [
...
Three stones A, B and C are placed at the
4

(1) A only
(3) All the three

4
5

æ sin x + cos x ö
dx = a sin -1 ç
÷+c,
b
8 - sin 2x
è
ø
where c is a constant of integration, then the
ordered pair (a, b) is equal to :
(1) (–1, 3)
(2) (3, 1)
(3) (1, 3)
(4) (1, –3)

ò

cos x - sin x

1

JEE Main 2021 – Question Paper
10
...
15C2 – 3
...

–15
...


+
–1

15

14C

1

+

14C

3

14C

+
5 +
...


ö

17
...
If the probability of getting an odd
number 2 times is equal to the probability of
getting an even number 3 times, then the
probability of getting an odd number for odd
number of times is :

14
...
Then p and q are

Two vertical poles are 150 m apart and the

elevation of their tops to be complementary,
then the height of the shorter pole (in meters)
is :
(1) 20 3
(3) 30

Then the composition function ƒ(g(x)) is :
(1) onto but not one-one
(2) both one-one and onto
(3) one-one but not onto
(4) neither one-one nor onto

5
(2)
16

(3) 24p - 3 3

If from the middle point of the line joining
their feet, an observer finds the angles of

Let ƒ : R ® R be defined as ƒ(x) = 2x – 1 and

1
(1)
32

(2) 12p - 3 3

height of one is three times that of the other
...

g : R – {1} ® R be defined as g(x) =
x -1

13
...
units) of the part of the circle
x2 + y 2 = 36, which is outside the parabola

is :

ƒ(x) =

12
...


1
(4)
2

A scientific committee is to be formed from 6
Indians and 8 foreigners, which includes at
least 2 Indians and double the number of

x2

18
...


ò (sin t ) dt

2
3

(2)

3
2

(3) 0

(cos 2 x + cos 4 x + cos6 x +
...
Then the number of
ways, the committee can be formed, is :
(1) 1625
(2) 575

(2) 25 3
(4) 25

pö
æ
ç 0 < x < ÷ is
2ø
è
3
2
1
(4)
2
(2)

JEE Main 2021 – Question Paper
20
...


= 4ax to a

moving point of the parabola, is another

equation

parabola whose directrix is :
(1) x = -

a
2

(2) x =

(3) x = 0

4
1
+
= a has at least one
sin x 1 - sin x

æ
è

a
2

solution in ç 0,

pö
÷ is _______
...


The minimum value of a for which the

7
...

2 ÷ý
n®¥
è 1 + r + r øþ
î r =1

8
...


Let Bi (i = 1, 2, 3) be three independent events
in a sample space
...
Let p be the probability that none of
the events B i occurs and these 4 probabilities

If the sum of all the elements of the set

satisfy the equations (a – 2b) p = ab and

A Ç (B È C) is 274 × 400, then l is equal

(b – 3g)p = 2bg (All the probabilities are
assumed to lie in the interval (0,1))
...

4
...


ò (x + [x]) dx is equal to _______
...


r r r

r
r r r2
b = 2iˆ + kˆ , then the value of 2 a + b + c

-a

a

r

r
r
perpendicular to c , where a = - ˆi + ˆj + kˆ and

a

If

r

coplanar with a and b, a
...
by NTA (10)
2
...

P(B3 )

Let M be any 3 × 3 matrix with entries from the
set {0, 1, 2}
...
Suppose
ê
ú
êë 3 -5 0 úû

x2 + y 2 – 2x – 6y + 6 = 0 is a chord of another

Q = [qij] is a matrix satisfying PQ = kI3 for some

circle 'C', whose center is at (2, 1), then its
radius is ______
...
If q 23 = -

elements of MT M is seven, is _______
...

5
...

3



---