JEE Mains 27 July 2021 Question Paper Shift 1 | JEE Main & Advanced Previous Year Papers PDF Download

 Page 1


JEE-Main-27-07-2021-Shift-1 (Memory Based) 
 
PHYSICS 
 
Question: Energy of an oscillating system is E. At a particular instant kinetic energy of system is 3E/4. 
Find 
displacement of the oscillating particle from its mean position. Its amplitude of oscillation is A. 
Options: 
(A) 
2
A
  
(B) 
3
A
  
(C) 
4
A
  
(D) 
6
A
  
Answer: (A) 
Solution: 
( )
2 2 2 22
1 31
2 42
m A x mA ??
? ?
- =
? ?
? ?
 
22 2
3
4
Ax A ? -= 
2
2
4
A
x ?= 
2
A
x ?=  
 
 
Question: A capacitor of capacitance 100 F µ discharges through a resistor R. At the same time a 
radioactive 
substance decays with mean life 30 ms. If ratio of charge on capacitor to activity of substance does not 
change 
with time, then find R. 
Page 2


JEE-Main-27-07-2021-Shift-1 (Memory Based) 
 
PHYSICS 
 
Question: Energy of an oscillating system is E. At a particular instant kinetic energy of system is 3E/4. 
Find 
displacement of the oscillating particle from its mean position. Its amplitude of oscillation is A. 
Options: 
(A) 
2
A
  
(B) 
3
A
  
(C) 
4
A
  
(D) 
6
A
  
Answer: (A) 
Solution: 
( )
2 2 2 22
1 31
2 42
m A x mA ??
? ?
- =
? ?
? ?
 
22 2
3
4
Ax A ? -= 
2
2
4
A
x ?= 
2
A
x ?=  
 
 
Question: A capacitor of capacitance 100 F µ discharges through a resistor R. At the same time a 
radioactive 
substance decays with mean life 30 ms. If ratio of charge on capacitor to activity of substance does not 
change 
with time, then find R. 
 
Options: 
(A) 300?  
(B) 100 ?  
(C) 200 ?  
(D) 400 ?  
Answer: (A) 
Solution: 
/
0
t RC
t
o
Q e Q
A Ae
?
-
-
= (ratio is time independent) 
mean 
11
, RC T
RC
?
?
= = = (mean life) 
3
mean 
6
30 10
300
100 10
T
R
C
-
-
×
= = = ?
×
  
 
Question: Three balls A, B and C of masses m, 2 m and 2 m respectively are placed on a smooth 
horizontal 
surface. A is initially moving with velocity 9 m / s, collides elastically with B (initially at rest), which 
in turn collides 
inelastically with C (initially at rest). Assuming all collisions to be head on, final velocity of C is 
Options: 
(A) 
9
( /)
2
ms  
(B) 9( / ) ms  
(C) 6( / ) ms  
(D) 3( / ) ms  
Answer: (D) 
Solution: 
For collision between A and B  
, 2 , 9 / , 0, ?
A B A BB
m m m mu m s u v = = = = = 
Page 3


JEE-Main-27-07-2021-Shift-1 (Memory Based) 
 
PHYSICS 
 
Question: Energy of an oscillating system is E. At a particular instant kinetic energy of system is 3E/4. 
Find 
displacement of the oscillating particle from its mean position. Its amplitude of oscillation is A. 
Options: 
(A) 
2
A
  
(B) 
3
A
  
(C) 
4
A
  
(D) 
6
A
  
Answer: (A) 
Solution: 
( )
2 2 2 22
1 31
2 42
m A x mA ??
? ?
- =
? ?
? ?
 
22 2
3
4
Ax A ? -= 
2
2
4
A
x ?= 
2
A
x ?=  
 
 
Question: A capacitor of capacitance 100 F µ discharges through a resistor R. At the same time a 
radioactive 
substance decays with mean life 30 ms. If ratio of charge on capacitor to activity of substance does not 
change 
with time, then find R. 
 
Options: 
(A) 300?  
(B) 100 ?  
(C) 200 ?  
(D) 400 ?  
Answer: (A) 
Solution: 
/
0
t RC
t
o
Q e Q
A Ae
?
-
-
= (ratio is time independent) 
mean 
11
, RC T
RC
?
?
= = = (mean life) 
3
mean 
6
30 10
300
100 10
T
R
C
-
-
×
= = = ?
×
  
 
Question: Three balls A, B and C of masses m, 2 m and 2 m respectively are placed on a smooth 
horizontal 
surface. A is initially moving with velocity 9 m / s, collides elastically with B (initially at rest), which 
in turn collides 
inelastically with C (initially at rest). Assuming all collisions to be head on, final velocity of C is 
Options: 
(A) 
9
( /)
2
ms  
(B) 9( / ) ms  
(C) 6( / ) ms  
(D) 3( / ) ms  
Answer: (D) 
Solution: 
For collision between A and B  
, 2 , 9 / , 0, ?
A B A BB
m m m mu m s u v = = = = = 
2
A A A B
BB
AB AB
mu m m
v u
mm mm
? ? -
= -
? ?
++
? ?
 
29
0 6/
2
m
ms
mm
××
= -=
+
 
For collision between B and C  
2, 2, 6 / , 0, ?
B C B C
m m m mu m s u v = = = = = 
( )
B BC C BC
mu m u m m v += + 
2 60 4 m mv ×+ = 
12
3/
4
v ms ?= =  
Question: A particle of mass 
31
9.1 10 kg
-
× moving with a velocity 
6
10 / ms has de Broglie wavelength
1
? . A  
photon of momentum 
27
10 / kgm s
-
 has wavelength 
2
· ? Find 
2
1
?
?
 
Options: 
(A) 910 
(B) 667 
(C) 
1
310
  
(D) 1 
Answer: (A) 
Solution:
31 6
2
27
1
/ 9.1 10 10
910
/ 10
h p mv
h mv p
?
?
-
-
××
= = = =  
 
Question: Two disks having same surface mass density have radii r  and  R .  
1
I ? Moment of inertia of 1
st
 disk about an axis perpendicular to the plane and passing through 
centre. 
2
I ? Moment of inertia of 2
nd
 disk about one of its diameters. Find 
1
2
I
I
Memory based questions 
Options: 
Page 4


JEE-Main-27-07-2021-Shift-1 (Memory Based) 
 
PHYSICS 
 
Question: Energy of an oscillating system is E. At a particular instant kinetic energy of system is 3E/4. 
Find 
displacement of the oscillating particle from its mean position. Its amplitude of oscillation is A. 
Options: 
(A) 
2
A
  
(B) 
3
A
  
(C) 
4
A
  
(D) 
6
A
  
Answer: (A) 
Solution: 
( )
2 2 2 22
1 31
2 42
m A x mA ??
? ?
- =
? ?
? ?
 
22 2
3
4
Ax A ? -= 
2
2
4
A
x ?= 
2
A
x ?=  
 
 
Question: A capacitor of capacitance 100 F µ discharges through a resistor R. At the same time a 
radioactive 
substance decays with mean life 30 ms. If ratio of charge on capacitor to activity of substance does not 
change 
with time, then find R. 
 
Options: 
(A) 300?  
(B) 100 ?  
(C) 200 ?  
(D) 400 ?  
Answer: (A) 
Solution: 
/
0
t RC
t
o
Q e Q
A Ae
?
-
-
= (ratio is time independent) 
mean 
11
, RC T
RC
?
?
= = = (mean life) 
3
mean 
6
30 10
300
100 10
T
R
C
-
-
×
= = = ?
×
  
 
Question: Three balls A, B and C of masses m, 2 m and 2 m respectively are placed on a smooth 
horizontal 
surface. A is initially moving with velocity 9 m / s, collides elastically with B (initially at rest), which 
in turn collides 
inelastically with C (initially at rest). Assuming all collisions to be head on, final velocity of C is 
Options: 
(A) 
9
( /)
2
ms  
(B) 9( / ) ms  
(C) 6( / ) ms  
(D) 3( / ) ms  
Answer: (D) 
Solution: 
For collision between A and B  
, 2 , 9 / , 0, ?
A B A BB
m m m mu m s u v = = = = = 
2
A A A B
BB
AB AB
mu m m
v u
mm mm
? ? -
= -
? ?
++
? ?
 
29
0 6/
2
m
ms
mm
××
= -=
+
 
For collision between B and C  
2, 2, 6 / , 0, ?
B C B C
m m m mu m s u v = = = = = 
( )
B BC C BC
mu m u m m v += + 
2 60 4 m mv ×+ = 
12
3/
4
v ms ?= =  
Question: A particle of mass 
31
9.1 10 kg
-
× moving with a velocity 
6
10 / ms has de Broglie wavelength
1
? . A  
photon of momentum 
27
10 / kgm s
-
 has wavelength 
2
· ? Find 
2
1
?
?
 
Options: 
(A) 910 
(B) 667 
(C) 
1
310
  
(D) 1 
Answer: (A) 
Solution:
31 6
2
27
1
/ 9.1 10 10
910
/ 10
h p mv
h mv p
?
?
-
-
××
= = = =  
 
Question: Two disks having same surface mass density have radii r  and  R .  
1
I ? Moment of inertia of 1
st
 disk about an axis perpendicular to the plane and passing through 
centre. 
2
I ? Moment of inertia of 2
nd
 disk about one of its diameters. Find 
1
2
I
I
Memory based questions 
Options: 
(A) 
4
4
r
R
  
(B) 
4
4
2r
R
  
(C) 
4
4
2
r
R
  
(D) 
2
4
2r
R
  
Answer: (B) 
Solution: 
Moment of inertia of a disc about it's center perpendicular to the plane of the disc is 
2
2
MR
  
& Moment of inertia of a disc about one of its diameter is 
2
4
MR
  
Now both dices have same surface mass density ( ) ( ) say s  
then mass of 1
st
 discs with radius 
( )
2
rr ps =  
?M.I of disc 1 about center, ? to the plane 
( )
22
2
22
mr r
r ps = =  
4
1
2
r
I
ps
= = 
mass of 2nd disc with radius 
( )
2
RR ps =  
?M.I of 2nd disc about one of it's diameters is 
2
4
mR
 
( )
24
2
2
44
RR
RI
ps
ps = = =  
 
4
4
2r
R
= 
 
Question: Two capacitor 
1
C with capacitor  2 C , and 
2
C with capacitance  C  are connected in 
parallel. They are charged and then the battery is removed. If a material of dielectric constant  K  is 
inserted in 
4
1
4
2
2
4
r
I
R I
ps
ps
? ?
? ?
? ?
=
Page 5


JEE-Main-27-07-2021-Shift-1 (Memory Based) 
 
PHYSICS 
 
Question: Energy of an oscillating system is E. At a particular instant kinetic energy of system is 3E/4. 
Find 
displacement of the oscillating particle from its mean position. Its amplitude of oscillation is A. 
Options: 
(A) 
2
A
  
(B) 
3
A
  
(C) 
4
A
  
(D) 
6
A
  
Answer: (A) 
Solution: 
( )
2 2 2 22
1 31
2 42
m A x mA ??
? ?
- =
? ?
? ?
 
22 2
3
4
Ax A ? -= 
2
2
4
A
x ?= 
2
A
x ?=  
 
 
Question: A capacitor of capacitance 100 F µ discharges through a resistor R. At the same time a 
radioactive 
substance decays with mean life 30 ms. If ratio of charge on capacitor to activity of substance does not 
change 
with time, then find R. 
 
Options: 
(A) 300?  
(B) 100 ?  
(C) 200 ?  
(D) 400 ?  
Answer: (A) 
Solution: 
/
0
t RC
t
o
Q e Q
A Ae
?
-
-
= (ratio is time independent) 
mean 
11
, RC T
RC
?
?
= = = (mean life) 
3
mean 
6
30 10
300
100 10
T
R
C
-
-
×
= = = ?
×
  
 
Question: Three balls A, B and C of masses m, 2 m and 2 m respectively are placed on a smooth 
horizontal 
surface. A is initially moving with velocity 9 m / s, collides elastically with B (initially at rest), which 
in turn collides 
inelastically with C (initially at rest). Assuming all collisions to be head on, final velocity of C is 
Options: 
(A) 
9
( /)
2
ms  
(B) 9( / ) ms  
(C) 6( / ) ms  
(D) 3( / ) ms  
Answer: (D) 
Solution: 
For collision between A and B  
, 2 , 9 / , 0, ?
A B A BB
m m m mu m s u v = = = = = 
2
A A A B
BB
AB AB
mu m m
v u
mm mm
? ? -
= -
? ?
++
? ?
 
29
0 6/
2
m
ms
mm
××
= -=
+
 
For collision between B and C  
2, 2, 6 / , 0, ?
B C B C
m m m mu m s u v = = = = = 
( )
B BC C BC
mu m u m m v += + 
2 60 4 m mv ×+ = 
12
3/
4
v ms ?= =  
Question: A particle of mass 
31
9.1 10 kg
-
× moving with a velocity 
6
10 / ms has de Broglie wavelength
1
? . A  
photon of momentum 
27
10 / kgm s
-
 has wavelength 
2
· ? Find 
2
1
?
?
 
Options: 
(A) 910 
(B) 667 
(C) 
1
310
  
(D) 1 
Answer: (A) 
Solution:
31 6
2
27
1
/ 9.1 10 10
910
/ 10
h p mv
h mv p
?
?
-
-
××
= = = =  
 
Question: Two disks having same surface mass density have radii r  and  R .  
1
I ? Moment of inertia of 1
st
 disk about an axis perpendicular to the plane and passing through 
centre. 
2
I ? Moment of inertia of 2
nd
 disk about one of its diameters. Find 
1
2
I
I
Memory based questions 
Options: 
(A) 
4
4
r
R
  
(B) 
4
4
2r
R
  
(C) 
4
4
2
r
R
  
(D) 
2
4
2r
R
  
Answer: (B) 
Solution: 
Moment of inertia of a disc about it's center perpendicular to the plane of the disc is 
2
2
MR
  
& Moment of inertia of a disc about one of its diameter is 
2
4
MR
  
Now both dices have same surface mass density ( ) ( ) say s  
then mass of 1
st
 discs with radius 
( )
2
rr ps =  
?M.I of disc 1 about center, ? to the plane 
( )
22
2
22
mr r
r ps = =  
4
1
2
r
I
ps
= = 
mass of 2nd disc with radius 
( )
2
RR ps =  
?M.I of 2nd disc about one of it's diameters is 
2
4
mR
 
( )
24
2
2
44
RR
RI
ps
ps = = =  
 
4
4
2r
R
= 
 
Question: Two capacitor 
1
C with capacitor  2 C , and 
2
C with capacitance  C  are connected in 
parallel. They are charged and then the battery is removed. If a material of dielectric constant  K  is 
inserted in 
4
1
4
2
2
4
r
I
R I
ps
ps
? ?
? ?
? ?
=
2
C
'
, find final potential across them 
 
Options: 
(A) KV 
(B) 
3
2
V
K +
  
(C) 
V
K
  
(D) 
3
KV
  
Answer: (B) 
Solution: 
Both are in parallel, so p.d across them will be same. 
11
(2 ) 2 Q CV C V CV = = = 
2 2
Q CV CV = = 
Total charge = 3CV 
When dielectric is inserted in it's capacitance becomes KC. 
If V' is final common potential, then since total charge remains unchanged  
1 2 12
3
ff
Q Q Q Q CV + = += 
( ) 2 () 3 C V KC V CV + ' = ' 
3
2
V
V
k
? ?
=
? ?
+
? ?
' 
 
Question: Pressure of a monatomic gas in a container is 2 atm. Average kinetic energy per molecule is 
9
2 10 . J
-
× 
Volume of gas is 1 litre. Find number of molecules of gas present in the container. 
Options: 
(A) 
11
3
10
2
×  
(B) 
10
3
10
2
×