JEE Mains 27 July 2021 Question Paper Shift 2 | JEE Main & Advanced Previous Year Papers PDF Download

 Page 1


 1 
FINAL JEE –MAIN EXAMINATION – JULY, 2021 
(Held On Tuesday 27
th
 July, 2021)   TIME : 3 : 00 PM  to 6 : 00 PM
PHYSICS TEST PAPER WITH ANSWER 
 
 
SECTION-A 
1. An electron and proton are separated by a large
distance. The electron starts approaching the
proton with energy 3 eV. The proton captures the
electrons and forms a hydrogen atom in second
excited state. The resulting photon is incident on a
photosensitive metal of threshold wavelength
4000 Å. What is the maximum kinetic energy of
the emitted photoelectron?
(1) 7.61 eV
(2) 1.41 eV
(3) 3.3 eV
(4) No photoelectron would be emitted
Official Ans. by NTA (2) 
2. The expected graphical representation of the
variation of angle of deviation '?' with angle of
incidence 'i' in a prism is :
(1) 
?
(2) 
?
(3) 
?
(4) 
?
Official Ans. by NTA (2) 
3. A raindrop with radius R = 0.2 mm falls from a
cloud at a height h = 2000 m above the ground.
Assume that the drop is spherical throughout its
fall and the force of buoyance may be neglected,
then the terminal speed attained by the raindrop is :
[Density of water f
w
 = 1000 kg m
–3
 and Density of
air f
a
 = 1.2 kg m
–3
, g = 10 m/s
2
Coefficient of viscosity of air = 1.8 × 10
–5
 Nsm
–2
]
(1) 250.6 ms
–1
(2) 43.56 ms
–1
(3) 4.94 ms
–1
(4) 14.4 ms
–1
Official Ans. by NTA (3) 
4. One mole of an ideal gas is taken through an
adiabatic process where the temperature rises from
27°C to 37°C. If the ideal gas is composed of
polyatomic molecule that has 4 vibrational modes,
which of the following is true?
[R = 8.314 J mol
–1
 k
–1
]
(1) work done by the gas is close to 332 J
(2) work done on the gas is close to 582 J
(3) work done by the gas is close to 582 J
(4) work done on the gas is close to 332 J
Official Ans. by NTA (2) 
5. An object of mass 0.5 kg is executing simple
harmonic motion. It amplitude is 5 cm and time
period (T) is 0.2 s. What will be the potential
energy of the object at an instant  
T
ts
4
? starting 
from mean position. Assume that the initial phase
of the oscillation is zero.
(1) 0.62 J (2) 6.2 × 10
–3
 J
(3) 1.2 × 10
3
 J (4) 6.2 × 10
3
 J
Official Ans. by NTA (1) 
6. Match List I with List II.
       List-I List-II 
(a) Capacitance, C (i) M
1
L
1
T
–3
A
–1
(b) Permittivity of free space, ?
0
(ii) M
–1
L
–3
T
4
A
2
(c) Permeability of free space, ?
0
(iii) M
–1
L
–2
T
4
A
2
(d) Electric field, E (iv) M
1
L
1
T
–2
A
–2
Choose the correct answer from the options given 
below 
(1) (a) ? (iii), (b) ? (ii), (c) ? (iv), (d) ? (i)
(2) (a) ? (iii), (b) ? (iv), (c) ? (ii), (d) ? (i)
(3) (a) ? (iv), (b) ? (ii), (c) ? (iii), (d) ? (i)
(4) (a) ? (iv), (b) ? (iii), (c) ? (ii), (d) ? (i)
Official Ans. by NTA (1) 
Page 2


 1 
FINAL JEE –MAIN EXAMINATION – JULY, 2021 
(Held On Tuesday 27
th
 July, 2021)   TIME : 3 : 00 PM  to 6 : 00 PM
PHYSICS TEST PAPER WITH ANSWER 
 
 
SECTION-A 
1. An electron and proton are separated by a large
distance. The electron starts approaching the
proton with energy 3 eV. The proton captures the
electrons and forms a hydrogen atom in second
excited state. The resulting photon is incident on a
photosensitive metal of threshold wavelength
4000 Å. What is the maximum kinetic energy of
the emitted photoelectron?
(1) 7.61 eV
(2) 1.41 eV
(3) 3.3 eV
(4) No photoelectron would be emitted
Official Ans. by NTA (2) 
2. The expected graphical representation of the
variation of angle of deviation '?' with angle of
incidence 'i' in a prism is :
(1) 
?
(2) 
?
(3) 
?
(4) 
?
Official Ans. by NTA (2) 
3. A raindrop with radius R = 0.2 mm falls from a
cloud at a height h = 2000 m above the ground.
Assume that the drop is spherical throughout its
fall and the force of buoyance may be neglected,
then the terminal speed attained by the raindrop is :
[Density of water f
w
 = 1000 kg m
–3
 and Density of
air f
a
 = 1.2 kg m
–3
, g = 10 m/s
2
Coefficient of viscosity of air = 1.8 × 10
–5
 Nsm
–2
]
(1) 250.6 ms
–1
(2) 43.56 ms
–1
(3) 4.94 ms
–1
(4) 14.4 ms
–1
Official Ans. by NTA (3) 
4. One mole of an ideal gas is taken through an
adiabatic process where the temperature rises from
27°C to 37°C. If the ideal gas is composed of
polyatomic molecule that has 4 vibrational modes,
which of the following is true?
[R = 8.314 J mol
–1
 k
–1
]
(1) work done by the gas is close to 332 J
(2) work done on the gas is close to 582 J
(3) work done by the gas is close to 582 J
(4) work done on the gas is close to 332 J
Official Ans. by NTA (2) 
5. An object of mass 0.5 kg is executing simple
harmonic motion. It amplitude is 5 cm and time
period (T) is 0.2 s. What will be the potential
energy of the object at an instant  
T
ts
4
? starting 
from mean position. Assume that the initial phase
of the oscillation is zero.
(1) 0.62 J (2) 6.2 × 10
–3
 J
(3) 1.2 × 10
3
 J (4) 6.2 × 10
3
 J
Official Ans. by NTA (1) 
6. Match List I with List II.
       List-I List-II 
(a) Capacitance, C (i) M
1
L
1
T
–3
A
–1
(b) Permittivity of free space, ?
0
(ii) M
–1
L
–3
T
4
A
2
(c) Permeability of free space, ?
0
(iii) M
–1
L
–2
T
4
A
2
(d) Electric field, E (iv) M
1
L
1
T
–2
A
–2
Choose the correct answer from the options given 
below 
(1) (a) ? (iii), (b) ? (ii), (c) ? (iv), (d) ? (i)
(2) (a) ? (iii), (b) ? (iv), (c) ? (ii), (d) ? (i)
(3) (a) ? (iv), (b) ? (ii), (c) ? (iii), (d) ? (i)
(4) (a) ? (iv), (b) ? (iii), (c) ? (ii), (d) ? (i)
Official Ans. by NTA (1) 
 
2 
 
7. Given below is the plot of a potential energy 
function U(x) for a system, in which a particle is in 
one dimensional motion, while a conservative 
force F(x) acts on it. Suppose that E
mech
 = 8 J, the 
incorrect statement for this system is : 
 
 
 
 
 
 
 
 
 
     
 
 
 
 (1) at x > x
4
, K.E. is constant throughout the region. 
  (2) at x < x
1
, K.E. is smallest and the particle is 
moving at the slowest speed. 
  (3) at x = x
2
, K.E. is greatest and the particle is 
moving at the fastest speed. 
 (4) at x = x
3
, K.E. = 4 J. 
 Official Ans. by NTA (2) 
8. A 100 ? resistance, a 0.1 ?F capacitor and an 
inductor are connected in series across a 250 V 
supply at variable frequency. Calculate the value of 
inductance of inductor at which resonance will 
occur. Given that the resonant frequency is 60 Hz. 
 (1) 0.70 H  (2) 70.3 mH 
  (3) 7.03 × 10
–5
 H (4) 70.3 H 
 Official Ans. by NTA (4) 
9. A simple pendulum of mass 'm', length 'l' and 
charge '+q' suspended in the electric field produced 
by two conducting parallel plates as shown. The 
value of deflection of pendulum in equilibrium 
position will be 
 
 
d 
–V
1
 
l 
m 
+q 
air 
t 
+V
2
 
Medium 
(K) 
 
 (1) 
1 1 2 1
12
C (V V ) q
tan
mg (C C )(d t)
?
?? ?
?
??
??
??
 
 (2) 
1 2 2 1
12
C (V V ) q
tan
mg (C C )(d t)
?
?? ?
?
??
??
??
 
  (3) 
1 2 1 2
12
C (V V ) q
tan
mg (C C )(d t)
?
?? ?
?
??
??
??
  
 (4) 
1 1 1 2
12
C (V V ) q
tan
mg (C C )(d t)
?
?? ?
?
??
??
??
 
 Official Ans. by NTA (3) 
10. Two Carnot engines A and B operate in series such 
that engine A absorbs heat at T
1
 and rejects heat to 
a sink at temperature T. Engine B absorbs half of 
the heat rejected by Engine A and rejects heat to 
the sink at T
3
. When workdone in both the cases is 
equal, to value of T is : 
 (1) 
13
23
TT
32
? (2) 
13
12
TT
33
? 
  (3) 
13
31
TT
23
? (4) 
13
21
TT
33
? 
 Official Ans. by NTA (4) 
11. Find the truth table for the function Y of A and B 
represented in the following figure. 
 
  
  
A 
B 
Y 
 
 (1) 
A B Y
000
0 1 1
1 0 0
1 1 0
  (2) 
A B Y
0 0 1
0 1 0
1 0 1
111
 
  (3) 
A B Y
000
0 1 0
1 0 0
111
 (4) 
A B Y
000
0 1 1
1 0 1
111
 
 Official Ans. by NTA (2) 
Page 3


 1 
FINAL JEE –MAIN EXAMINATION – JULY, 2021 
(Held On Tuesday 27
th
 July, 2021)   TIME : 3 : 00 PM  to 6 : 00 PM
PHYSICS TEST PAPER WITH ANSWER 
 
 
SECTION-A 
1. An electron and proton are separated by a large
distance. The electron starts approaching the
proton with energy 3 eV. The proton captures the
electrons and forms a hydrogen atom in second
excited state. The resulting photon is incident on a
photosensitive metal of threshold wavelength
4000 Å. What is the maximum kinetic energy of
the emitted photoelectron?
(1) 7.61 eV
(2) 1.41 eV
(3) 3.3 eV
(4) No photoelectron would be emitted
Official Ans. by NTA (2) 
2. The expected graphical representation of the
variation of angle of deviation '?' with angle of
incidence 'i' in a prism is :
(1) 
?
(2) 
?
(3) 
?
(4) 
?
Official Ans. by NTA (2) 
3. A raindrop with radius R = 0.2 mm falls from a
cloud at a height h = 2000 m above the ground.
Assume that the drop is spherical throughout its
fall and the force of buoyance may be neglected,
then the terminal speed attained by the raindrop is :
[Density of water f
w
 = 1000 kg m
–3
 and Density of
air f
a
 = 1.2 kg m
–3
, g = 10 m/s
2
Coefficient of viscosity of air = 1.8 × 10
–5
 Nsm
–2
]
(1) 250.6 ms
–1
(2) 43.56 ms
–1
(3) 4.94 ms
–1
(4) 14.4 ms
–1
Official Ans. by NTA (3) 
4. One mole of an ideal gas is taken through an
adiabatic process where the temperature rises from
27°C to 37°C. If the ideal gas is composed of
polyatomic molecule that has 4 vibrational modes,
which of the following is true?
[R = 8.314 J mol
–1
 k
–1
]
(1) work done by the gas is close to 332 J
(2) work done on the gas is close to 582 J
(3) work done by the gas is close to 582 J
(4) work done on the gas is close to 332 J
Official Ans. by NTA (2) 
5. An object of mass 0.5 kg is executing simple
harmonic motion. It amplitude is 5 cm and time
period (T) is 0.2 s. What will be the potential
energy of the object at an instant  
T
ts
4
? starting 
from mean position. Assume that the initial phase
of the oscillation is zero.
(1) 0.62 J (2) 6.2 × 10
–3
 J
(3) 1.2 × 10
3
 J (4) 6.2 × 10
3
 J
Official Ans. by NTA (1) 
6. Match List I with List II.
       List-I List-II 
(a) Capacitance, C (i) M
1
L
1
T
–3
A
–1
(b) Permittivity of free space, ?
0
(ii) M
–1
L
–3
T
4
A
2
(c) Permeability of free space, ?
0
(iii) M
–1
L
–2
T
4
A
2
(d) Electric field, E (iv) M
1
L
1
T
–2
A
–2
Choose the correct answer from the options given 
below 
(1) (a) ? (iii), (b) ? (ii), (c) ? (iv), (d) ? (i)
(2) (a) ? (iii), (b) ? (iv), (c) ? (ii), (d) ? (i)
(3) (a) ? (iv), (b) ? (ii), (c) ? (iii), (d) ? (i)
(4) (a) ? (iv), (b) ? (iii), (c) ? (ii), (d) ? (i)
Official Ans. by NTA (1) 
 
2 
 
7. Given below is the plot of a potential energy 
function U(x) for a system, in which a particle is in 
one dimensional motion, while a conservative 
force F(x) acts on it. Suppose that E
mech
 = 8 J, the 
incorrect statement for this system is : 
 
 
 
 
 
 
 
 
 
     
 
 
 
 (1) at x > x
4
, K.E. is constant throughout the region. 
  (2) at x < x
1
, K.E. is smallest and the particle is 
moving at the slowest speed. 
  (3) at x = x
2
, K.E. is greatest and the particle is 
moving at the fastest speed. 
 (4) at x = x
3
, K.E. = 4 J. 
 Official Ans. by NTA (2) 
8. A 100 ? resistance, a 0.1 ?F capacitor and an 
inductor are connected in series across a 250 V 
supply at variable frequency. Calculate the value of 
inductance of inductor at which resonance will 
occur. Given that the resonant frequency is 60 Hz. 
 (1) 0.70 H  (2) 70.3 mH 
  (3) 7.03 × 10
–5
 H (4) 70.3 H 
 Official Ans. by NTA (4) 
9. A simple pendulum of mass 'm', length 'l' and 
charge '+q' suspended in the electric field produced 
by two conducting parallel plates as shown. The 
value of deflection of pendulum in equilibrium 
position will be 
 
 
d 
–V
1
 
l 
m 
+q 
air 
t 
+V
2
 
Medium 
(K) 
 
 (1) 
1 1 2 1
12
C (V V ) q
tan
mg (C C )(d t)
?
?? ?
?
??
??
??
 
 (2) 
1 2 2 1
12
C (V V ) q
tan
mg (C C )(d t)
?
?? ?
?
??
??
??
 
  (3) 
1 2 1 2
12
C (V V ) q
tan
mg (C C )(d t)
?
?? ?
?
??
??
??
  
 (4) 
1 1 1 2
12
C (V V ) q
tan
mg (C C )(d t)
?
?? ?
?
??
??
??
 
 Official Ans. by NTA (3) 
10. Two Carnot engines A and B operate in series such 
that engine A absorbs heat at T
1
 and rejects heat to 
a sink at temperature T. Engine B absorbs half of 
the heat rejected by Engine A and rejects heat to 
the sink at T
3
. When workdone in both the cases is 
equal, to value of T is : 
 (1) 
13
23
TT
32
? (2) 
13
12
TT
33
? 
  (3) 
13
31
TT
23
? (4) 
13
21
TT
33
? 
 Official Ans. by NTA (4) 
11. Find the truth table for the function Y of A and B 
represented in the following figure. 
 
  
  
A 
B 
Y 
 
 (1) 
A B Y
000
0 1 1
1 0 0
1 1 0
  (2) 
A B Y
0 0 1
0 1 0
1 0 1
111
 
  (3) 
A B Y
000
0 1 0
1 0 0
111
 (4) 
A B Y
000
0 1 1
1 0 1
111
 
 Official Ans. by NTA (2) 
 
3 
12. Figure A and B shown two long straight wires of 
circular cross-section (a and b with a < b), carrying 
current I which is uniformly distributed across the 
cross-section. The magnitude of magnetic field B 
varies with radius r and can be represented as : 
 
a 
I 
Fig. A 
b 
I 
Fig. B 
 
 (1) 
 
B 
a 
b 
r O 
  (2) 
 
B 
a 
b 
r O 
 
  (3) 
 
B 
a 
b 
r O 
 (4) 
 
B 
b 
a 
r O 
 
 Official Ans. by NTA (3) 
13. Two identical particles of mass 1 kg each go round 
a circle of radius R, under the action of their 
mutual gravitational attraction. The angular speed 
of each particle is : 
 (1) 
3
G
2R
 (2) 
3
1G
2
R
  (3) 
11
2R G
 (4) 
3
2G
R
 
 Official Ans. by NTA (2) 
14. Consider the following statements : 
 A. Atoms of each element emit characteristics 
spectrum. 
 B. According to Bohr's Postulate, an electron in a 
hydrogen atom, revolves in a certain stationary 
orbit. 
 C. The density of nuclear matter depends on the 
size of the nucleus. 
 D. A free neutron is stable but a free proton decay 
is possible. 
 E. Radioactivity is an indication of the instability 
of nuclei. 
 Choose the correct answer from the options given 
below : 
 (1)  A, B, C, D and E 
 (2) A, B and E only 
  (3) B and D only 
 (4) A, C and E only 
 Official Ans. by NTA (2) 
15. What will be the magnitude of electric field at 
point O as shown in figure? Each side of the figure 
is l and perpendicular to each other? 
 
A( –q) 
B 
(+)q 
l 
l 
O 
l 
l l 
l 
l 
l 
E 
(2q) 
F 
(q) 
H 
 ( –q) 
G(2q) 
(2q) 
C D 
(+q) 
 
 (1) 
2
0
1q
4??
l
   
 (2) 
? ?
2
0
1q
2 2 1
4
(2 )
?
??
l
 
  (3) 
2
0
q
4 (2 ) ?? l
 
 (4) 
? ?
2
0
1 2q
2
4
2
??
l
 
 Official Ans. by NTA (2) 
16. A physical quantity 'y' is represented by the 
formula y = m
2
r
–4
g
x
3
2
?
l  
 If the percentage errors found in y, m, r, l and g are 
18, 1, 0.5, 4 and p respectively, then find the value 
of x and p. 
 (1) 5 and ± 2  (2) 4 and ± 3 
  (3) 
16
3
 and ± 
3
2
 (4) 8 and ± 2 
 Official Ans. by NTA (3) 
17. An automobile of mass 'm' accelerates starting 
from origin and initially at rest, while the engine 
supplies constant power P. The position is given as 
a function of time by : 
 (1) 
1
3
2
2
9P
t
8m
??
??
??
  (2) 
1
2
2
3
8P
t
9m
??
??
??
 
  (3) 
1
3
2
2
9m
t
8P
??
??
??
 (4) 
1
3
2
2
8P
t
9m
??
??
??
 
 Official Ans. by NTA (4) 
Page 4


 1 
FINAL JEE –MAIN EXAMINATION – JULY, 2021 
(Held On Tuesday 27
th
 July, 2021)   TIME : 3 : 00 PM  to 6 : 00 PM
PHYSICS TEST PAPER WITH ANSWER 
 
 
SECTION-A 
1. An electron and proton are separated by a large
distance. The electron starts approaching the
proton with energy 3 eV. The proton captures the
electrons and forms a hydrogen atom in second
excited state. The resulting photon is incident on a
photosensitive metal of threshold wavelength
4000 Å. What is the maximum kinetic energy of
the emitted photoelectron?
(1) 7.61 eV
(2) 1.41 eV
(3) 3.3 eV
(4) No photoelectron would be emitted
Official Ans. by NTA (2) 
2. The expected graphical representation of the
variation of angle of deviation '?' with angle of
incidence 'i' in a prism is :
(1) 
?
(2) 
?
(3) 
?
(4) 
?
Official Ans. by NTA (2) 
3. A raindrop with radius R = 0.2 mm falls from a
cloud at a height h = 2000 m above the ground.
Assume that the drop is spherical throughout its
fall and the force of buoyance may be neglected,
then the terminal speed attained by the raindrop is :
[Density of water f
w
 = 1000 kg m
–3
 and Density of
air f
a
 = 1.2 kg m
–3
, g = 10 m/s
2
Coefficient of viscosity of air = 1.8 × 10
–5
 Nsm
–2
]
(1) 250.6 ms
–1
(2) 43.56 ms
–1
(3) 4.94 ms
–1
(4) 14.4 ms
–1
Official Ans. by NTA (3) 
4. One mole of an ideal gas is taken through an
adiabatic process where the temperature rises from
27°C to 37°C. If the ideal gas is composed of
polyatomic molecule that has 4 vibrational modes,
which of the following is true?
[R = 8.314 J mol
–1
 k
–1
]
(1) work done by the gas is close to 332 J
(2) work done on the gas is close to 582 J
(3) work done by the gas is close to 582 J
(4) work done on the gas is close to 332 J
Official Ans. by NTA (2) 
5. An object of mass 0.5 kg is executing simple
harmonic motion. It amplitude is 5 cm and time
period (T) is 0.2 s. What will be the potential
energy of the object at an instant  
T
ts
4
? starting 
from mean position. Assume that the initial phase
of the oscillation is zero.
(1) 0.62 J (2) 6.2 × 10
–3
 J
(3) 1.2 × 10
3
 J (4) 6.2 × 10
3
 J
Official Ans. by NTA (1) 
6. Match List I with List II.
       List-I List-II 
(a) Capacitance, C (i) M
1
L
1
T
–3
A
–1
(b) Permittivity of free space, ?
0
(ii) M
–1
L
–3
T
4
A
2
(c) Permeability of free space, ?
0
(iii) M
–1
L
–2
T
4
A
2
(d) Electric field, E (iv) M
1
L
1
T
–2
A
–2
Choose the correct answer from the options given 
below 
(1) (a) ? (iii), (b) ? (ii), (c) ? (iv), (d) ? (i)
(2) (a) ? (iii), (b) ? (iv), (c) ? (ii), (d) ? (i)
(3) (a) ? (iv), (b) ? (ii), (c) ? (iii), (d) ? (i)
(4) (a) ? (iv), (b) ? (iii), (c) ? (ii), (d) ? (i)
Official Ans. by NTA (1) 
 
2 
 
7. Given below is the plot of a potential energy 
function U(x) for a system, in which a particle is in 
one dimensional motion, while a conservative 
force F(x) acts on it. Suppose that E
mech
 = 8 J, the 
incorrect statement for this system is : 
 
 
 
 
 
 
 
 
 
     
 
 
 
 (1) at x > x
4
, K.E. is constant throughout the region. 
  (2) at x < x
1
, K.E. is smallest and the particle is 
moving at the slowest speed. 
  (3) at x = x
2
, K.E. is greatest and the particle is 
moving at the fastest speed. 
 (4) at x = x
3
, K.E. = 4 J. 
 Official Ans. by NTA (2) 
8. A 100 ? resistance, a 0.1 ?F capacitor and an 
inductor are connected in series across a 250 V 
supply at variable frequency. Calculate the value of 
inductance of inductor at which resonance will 
occur. Given that the resonant frequency is 60 Hz. 
 (1) 0.70 H  (2) 70.3 mH 
  (3) 7.03 × 10
–5
 H (4) 70.3 H 
 Official Ans. by NTA (4) 
9. A simple pendulum of mass 'm', length 'l' and 
charge '+q' suspended in the electric field produced 
by two conducting parallel plates as shown. The 
value of deflection of pendulum in equilibrium 
position will be 
 
 
d 
–V
1
 
l 
m 
+q 
air 
t 
+V
2
 
Medium 
(K) 
 
 (1) 
1 1 2 1
12
C (V V ) q
tan
mg (C C )(d t)
?
?? ?
?
??
??
??
 
 (2) 
1 2 2 1
12
C (V V ) q
tan
mg (C C )(d t)
?
?? ?
?
??
??
??
 
  (3) 
1 2 1 2
12
C (V V ) q
tan
mg (C C )(d t)
?
?? ?
?
??
??
??
  
 (4) 
1 1 1 2
12
C (V V ) q
tan
mg (C C )(d t)
?
?? ?
?
??
??
??
 
 Official Ans. by NTA (3) 
10. Two Carnot engines A and B operate in series such 
that engine A absorbs heat at T
1
 and rejects heat to 
a sink at temperature T. Engine B absorbs half of 
the heat rejected by Engine A and rejects heat to 
the sink at T
3
. When workdone in both the cases is 
equal, to value of T is : 
 (1) 
13
23
TT
32
? (2) 
13
12
TT
33
? 
  (3) 
13
31
TT
23
? (4) 
13
21
TT
33
? 
 Official Ans. by NTA (4) 
11. Find the truth table for the function Y of A and B 
represented in the following figure. 
 
  
  
A 
B 
Y 
 
 (1) 
A B Y
000
0 1 1
1 0 0
1 1 0
  (2) 
A B Y
0 0 1
0 1 0
1 0 1
111
 
  (3) 
A B Y
000
0 1 0
1 0 0
111
 (4) 
A B Y
000
0 1 1
1 0 1
111
 
 Official Ans. by NTA (2) 
 
3 
12. Figure A and B shown two long straight wires of 
circular cross-section (a and b with a < b), carrying 
current I which is uniformly distributed across the 
cross-section. The magnitude of magnetic field B 
varies with radius r and can be represented as : 
 
a 
I 
Fig. A 
b 
I 
Fig. B 
 
 (1) 
 
B 
a 
b 
r O 
  (2) 
 
B 
a 
b 
r O 
 
  (3) 
 
B 
a 
b 
r O 
 (4) 
 
B 
b 
a 
r O 
 
 Official Ans. by NTA (3) 
13. Two identical particles of mass 1 kg each go round 
a circle of radius R, under the action of their 
mutual gravitational attraction. The angular speed 
of each particle is : 
 (1) 
3
G
2R
 (2) 
3
1G
2
R
  (3) 
11
2R G
 (4) 
3
2G
R
 
 Official Ans. by NTA (2) 
14. Consider the following statements : 
 A. Atoms of each element emit characteristics 
spectrum. 
 B. According to Bohr's Postulate, an electron in a 
hydrogen atom, revolves in a certain stationary 
orbit. 
 C. The density of nuclear matter depends on the 
size of the nucleus. 
 D. A free neutron is stable but a free proton decay 
is possible. 
 E. Radioactivity is an indication of the instability 
of nuclei. 
 Choose the correct answer from the options given 
below : 
 (1)  A, B, C, D and E 
 (2) A, B and E only 
  (3) B and D only 
 (4) A, C and E only 
 Official Ans. by NTA (2) 
15. What will be the magnitude of electric field at 
point O as shown in figure? Each side of the figure 
is l and perpendicular to each other? 
 
A( –q) 
B 
(+)q 
l 
l 
O 
l 
l l 
l 
l 
l 
E 
(2q) 
F 
(q) 
H 
 ( –q) 
G(2q) 
(2q) 
C D 
(+q) 
 
 (1) 
2
0
1q
4??
l
   
 (2) 
? ?
2
0
1q
2 2 1
4
(2 )
?
??
l
 
  (3) 
2
0
q
4 (2 ) ?? l
 
 (4) 
? ?
2
0
1 2q
2
4
2
??
l
 
 Official Ans. by NTA (2) 
16. A physical quantity 'y' is represented by the 
formula y = m
2
r
–4
g
x
3
2
?
l  
 If the percentage errors found in y, m, r, l and g are 
18, 1, 0.5, 4 and p respectively, then find the value 
of x and p. 
 (1) 5 and ± 2  (2) 4 and ± 3 
  (3) 
16
3
 and ± 
3
2
 (4) 8 and ± 2 
 Official Ans. by NTA (3) 
17. An automobile of mass 'm' accelerates starting 
from origin and initially at rest, while the engine 
supplies constant power P. The position is given as 
a function of time by : 
 (1) 
1
3
2
2
9P
t
8m
??
??
??
  (2) 
1
2
2
3
8P
t
9m
??
??
??
 
  (3) 
1
3
2
2
9m
t
8P
??
??
??
 (4) 
1
3
2
2
8P
t
9m
??
??
??
 
 Official Ans. by NTA (4) 
 
4 
18. The planet Mars has two moons, if one of them has 
a period 7 hours, 30 minutes and an orbital radius 
of 9.0 × 10
3
 km. Find the mass of Mars. 
 
2
11 1 2 2
4
Given 6 10 N m kg
G
??
??
???
??
??
??
??
 
 (1) 5.96 × 10
19
 kg  (2) 3.25 × 10
21
 kg 
  (3) 7.02 × 10
25
 kg (4) 6.00 × 10
23
 kg 
 Official Ans. by NTA (4) 
19. A particle of mass M originally at rest is subjected 
to a force whose direction is constant but 
magnitude varies with time according to the 
relation 
2
0
tT
F F 1
T
??
? ??
????
??
?? ??
??
 
 Where F
0
 and T are constants. The force acts only 
for the time interval 2T. The velocity v of the 
particle after time 2T is : 
 (1) 2F
0
T / M  (2) F
0
T / 2M 
  (3) 4F
0
T / 3M (4) F
0
T / 3M 
 Official Ans. by NTA (3) 
20. The resistance of a conductor at 15°C is 16 ? and 
at 100°C is 20?. What will be the temperature 
coefficient of resistance of the conductor? 
 (1) 0.010°C
–1
  (2) 0.033°C
–1
 
  (3) 0.003°C
–1
 (4) 0.042°C
–1
 
 Official Ans. by NTA (3) 
 
SECTION-B 
1. In the given figure, two wheels P and Q are 
connected by a belt B. The radius of P is three 
times as that of Q. In case of same rotational 
kinetic energy, the ratio of rotational inertias 
1
2
I
I
??
??
??
 
will be x : 1. The value of x will be _____. 
 
3R 
R 
B 
P 
Q 
 
 Official Ans. by NTA (9) 
2. The difference in the number of waves when 
yellow light propagates through air and vacuum 
columns of the same thickness is one. The 
thickness of the air column is ______ mm. 
[Refractive index of air = 1.0003, wavelength of 
yellow light in vacuum = 6000 Å] 
 Official Ans. by NTA (2) 
3. The maximum amplitude for an amplitude 
modulated wave is found to be 12V while the 
minimum amplitude is found to be 3V. The 
modulation index is 0.6x where x is ______. 
 Official Ans. by NTA (1) 
4. In the given figure the magnetic flux through  the 
loop increases according to the relation  
?
B
(t) = 10t
2
+ 20t, where ?
B
 is in milliwebers and t 
is in seconds. 
 The magnitude of current through R = 2? resistor 
at t = 5 s is ______ mA. 
 
R=2? 
× × × × × 
× × × × × 
× × × × × 
× × × × × 
 
 Official Ans. by NTA (60) 
5. A particle executes simple harmonic motion 
represented by displacement function as 
x(t) = A sin (?t + ?) 
If the position and velocity of the particle at  
t = 0 s are 2 cm and 2? cm s
–1
 respectively, then its 
amplitude is x 2 cm where the value of x is ____.  
 Official Ans. by NTA (2) 
6. A swimmer wants to cross a river from point A to 
point B. Line AB makes an angle of 30° with the 
flow of river. Magnitude of velocity of the 
swimmer is same as that of the river. The angle ? 
with the line AB should be ____°, so that the 
swimmer reaches point B. 
 
30° 
? 
B 
A 
 
 Official Ans. by NTA (30) 
Page 5


 1 
FINAL JEE –MAIN EXAMINATION – JULY, 2021 
(Held On Tuesday 27
th
 July, 2021)   TIME : 3 : 00 PM  to 6 : 00 PM
PHYSICS TEST PAPER WITH ANSWER 
 
 
SECTION-A 
1. An electron and proton are separated by a large
distance. The electron starts approaching the
proton with energy 3 eV. The proton captures the
electrons and forms a hydrogen atom in second
excited state. The resulting photon is incident on a
photosensitive metal of threshold wavelength
4000 Å. What is the maximum kinetic energy of
the emitted photoelectron?
(1) 7.61 eV
(2) 1.41 eV
(3) 3.3 eV
(4) No photoelectron would be emitted
Official Ans. by NTA (2) 
2. The expected graphical representation of the
variation of angle of deviation '?' with angle of
incidence 'i' in a prism is :
(1) 
?
(2) 
?
(3) 
?
(4) 
?
Official Ans. by NTA (2) 
3. A raindrop with radius R = 0.2 mm falls from a
cloud at a height h = 2000 m above the ground.
Assume that the drop is spherical throughout its
fall and the force of buoyance may be neglected,
then the terminal speed attained by the raindrop is :
[Density of water f
w
 = 1000 kg m
–3
 and Density of
air f
a
 = 1.2 kg m
–3
, g = 10 m/s
2
Coefficient of viscosity of air = 1.8 × 10
–5
 Nsm
–2
]
(1) 250.6 ms
–1
(2) 43.56 ms
–1
(3) 4.94 ms
–1
(4) 14.4 ms
–1
Official Ans. by NTA (3) 
4. One mole of an ideal gas is taken through an
adiabatic process where the temperature rises from
27°C to 37°C. If the ideal gas is composed of
polyatomic molecule that has 4 vibrational modes,
which of the following is true?
[R = 8.314 J mol
–1
 k
–1
]
(1) work done by the gas is close to 332 J
(2) work done on the gas is close to 582 J
(3) work done by the gas is close to 582 J
(4) work done on the gas is close to 332 J
Official Ans. by NTA (2) 
5. An object of mass 0.5 kg is executing simple
harmonic motion. It amplitude is 5 cm and time
period (T) is 0.2 s. What will be the potential
energy of the object at an instant  
T
ts
4
? starting 
from mean position. Assume that the initial phase
of the oscillation is zero.
(1) 0.62 J (2) 6.2 × 10
–3
 J
(3) 1.2 × 10
3
 J (4) 6.2 × 10
3
 J
Official Ans. by NTA (1) 
6. Match List I with List II.
       List-I List-II 
(a) Capacitance, C (i) M
1
L
1
T
–3
A
–1
(b) Permittivity of free space, ?
0
(ii) M
–1
L
–3
T
4
A
2
(c) Permeability of free space, ?
0
(iii) M
–1
L
–2
T
4
A
2
(d) Electric field, E (iv) M
1
L
1
T
–2
A
–2
Choose the correct answer from the options given 
below 
(1) (a) ? (iii), (b) ? (ii), (c) ? (iv), (d) ? (i)
(2) (a) ? (iii), (b) ? (iv), (c) ? (ii), (d) ? (i)
(3) (a) ? (iv), (b) ? (ii), (c) ? (iii), (d) ? (i)
(4) (a) ? (iv), (b) ? (iii), (c) ? (ii), (d) ? (i)
Official Ans. by NTA (1) 
 
2 
 
7. Given below is the plot of a potential energy 
function U(x) for a system, in which a particle is in 
one dimensional motion, while a conservative 
force F(x) acts on it. Suppose that E
mech
 = 8 J, the 
incorrect statement for this system is : 
 
 
 
 
 
 
 
 
 
     
 
 
 
 (1) at x > x
4
, K.E. is constant throughout the region. 
  (2) at x < x
1
, K.E. is smallest and the particle is 
moving at the slowest speed. 
  (3) at x = x
2
, K.E. is greatest and the particle is 
moving at the fastest speed. 
 (4) at x = x
3
, K.E. = 4 J. 
 Official Ans. by NTA (2) 
8. A 100 ? resistance, a 0.1 ?F capacitor and an 
inductor are connected in series across a 250 V 
supply at variable frequency. Calculate the value of 
inductance of inductor at which resonance will 
occur. Given that the resonant frequency is 60 Hz. 
 (1) 0.70 H  (2) 70.3 mH 
  (3) 7.03 × 10
–5
 H (4) 70.3 H 
 Official Ans. by NTA (4) 
9. A simple pendulum of mass 'm', length 'l' and 
charge '+q' suspended in the electric field produced 
by two conducting parallel plates as shown. The 
value of deflection of pendulum in equilibrium 
position will be 
 
 
d 
–V
1
 
l 
m 
+q 
air 
t 
+V
2
 
Medium 
(K) 
 
 (1) 
1 1 2 1
12
C (V V ) q
tan
mg (C C )(d t)
?
?? ?
?
??
??
??
 
 (2) 
1 2 2 1
12
C (V V ) q
tan
mg (C C )(d t)
?
?? ?
?
??
??
??
 
  (3) 
1 2 1 2
12
C (V V ) q
tan
mg (C C )(d t)
?
?? ?
?
??
??
??
  
 (4) 
1 1 1 2
12
C (V V ) q
tan
mg (C C )(d t)
?
?? ?
?
??
??
??
 
 Official Ans. by NTA (3) 
10. Two Carnot engines A and B operate in series such 
that engine A absorbs heat at T
1
 and rejects heat to 
a sink at temperature T. Engine B absorbs half of 
the heat rejected by Engine A and rejects heat to 
the sink at T
3
. When workdone in both the cases is 
equal, to value of T is : 
 (1) 
13
23
TT
32
? (2) 
13
12
TT
33
? 
  (3) 
13
31
TT
23
? (4) 
13
21
TT
33
? 
 Official Ans. by NTA (4) 
11. Find the truth table for the function Y of A and B 
represented in the following figure. 
 
  
  
A 
B 
Y 
 
 (1) 
A B Y
000
0 1 1
1 0 0
1 1 0
  (2) 
A B Y
0 0 1
0 1 0
1 0 1
111
 
  (3) 
A B Y
000
0 1 0
1 0 0
111
 (4) 
A B Y
000
0 1 1
1 0 1
111
 
 Official Ans. by NTA (2) 
 
3 
12. Figure A and B shown two long straight wires of 
circular cross-section (a and b with a < b), carrying 
current I which is uniformly distributed across the 
cross-section. The magnitude of magnetic field B 
varies with radius r and can be represented as : 
 
a 
I 
Fig. A 
b 
I 
Fig. B 
 
 (1) 
 
B 
a 
b 
r O 
  (2) 
 
B 
a 
b 
r O 
 
  (3) 
 
B 
a 
b 
r O 
 (4) 
 
B 
b 
a 
r O 
 
 Official Ans. by NTA (3) 
13. Two identical particles of mass 1 kg each go round 
a circle of radius R, under the action of their 
mutual gravitational attraction. The angular speed 
of each particle is : 
 (1) 
3
G
2R
 (2) 
3
1G
2
R
  (3) 
11
2R G
 (4) 
3
2G
R
 
 Official Ans. by NTA (2) 
14. Consider the following statements : 
 A. Atoms of each element emit characteristics 
spectrum. 
 B. According to Bohr's Postulate, an electron in a 
hydrogen atom, revolves in a certain stationary 
orbit. 
 C. The density of nuclear matter depends on the 
size of the nucleus. 
 D. A free neutron is stable but a free proton decay 
is possible. 
 E. Radioactivity is an indication of the instability 
of nuclei. 
 Choose the correct answer from the options given 
below : 
 (1)  A, B, C, D and E 
 (2) A, B and E only 
  (3) B and D only 
 (4) A, C and E only 
 Official Ans. by NTA (2) 
15. What will be the magnitude of electric field at 
point O as shown in figure? Each side of the figure 
is l and perpendicular to each other? 
 
A( –q) 
B 
(+)q 
l 
l 
O 
l 
l l 
l 
l 
l 
E 
(2q) 
F 
(q) 
H 
 ( –q) 
G(2q) 
(2q) 
C D 
(+q) 
 
 (1) 
2
0
1q
4??
l
   
 (2) 
? ?
2
0
1q
2 2 1
4
(2 )
?
??
l
 
  (3) 
2
0
q
4 (2 ) ?? l
 
 (4) 
? ?
2
0
1 2q
2
4
2
??
l
 
 Official Ans. by NTA (2) 
16. A physical quantity 'y' is represented by the 
formula y = m
2
r
–4
g
x
3
2
?
l  
 If the percentage errors found in y, m, r, l and g are 
18, 1, 0.5, 4 and p respectively, then find the value 
of x and p. 
 (1) 5 and ± 2  (2) 4 and ± 3 
  (3) 
16
3
 and ± 
3
2
 (4) 8 and ± 2 
 Official Ans. by NTA (3) 
17. An automobile of mass 'm' accelerates starting 
from origin and initially at rest, while the engine 
supplies constant power P. The position is given as 
a function of time by : 
 (1) 
1
3
2
2
9P
t
8m
??
??
??
  (2) 
1
2
2
3
8P
t
9m
??
??
??
 
  (3) 
1
3
2
2
9m
t
8P
??
??
??
 (4) 
1
3
2
2
8P
t
9m
??
??
??
 
 Official Ans. by NTA (4) 
 
4 
18. The planet Mars has two moons, if one of them has 
a period 7 hours, 30 minutes and an orbital radius 
of 9.0 × 10
3
 km. Find the mass of Mars. 
 
2
11 1 2 2
4
Given 6 10 N m kg
G
??
??
???
??
??
??
??
 
 (1) 5.96 × 10
19
 kg  (2) 3.25 × 10
21
 kg 
  (3) 7.02 × 10
25
 kg (4) 6.00 × 10
23
 kg 
 Official Ans. by NTA (4) 
19. A particle of mass M originally at rest is subjected 
to a force whose direction is constant but 
magnitude varies with time according to the 
relation 
2
0
tT
F F 1
T
??
? ??
????
??
?? ??
??
 
 Where F
0
 and T are constants. The force acts only 
for the time interval 2T. The velocity v of the 
particle after time 2T is : 
 (1) 2F
0
T / M  (2) F
0
T / 2M 
  (3) 4F
0
T / 3M (4) F
0
T / 3M 
 Official Ans. by NTA (3) 
20. The resistance of a conductor at 15°C is 16 ? and 
at 100°C is 20?. What will be the temperature 
coefficient of resistance of the conductor? 
 (1) 0.010°C
–1
  (2) 0.033°C
–1
 
  (3) 0.003°C
–1
 (4) 0.042°C
–1
 
 Official Ans. by NTA (3) 
 
SECTION-B 
1. In the given figure, two wheels P and Q are 
connected by a belt B. The radius of P is three 
times as that of Q. In case of same rotational 
kinetic energy, the ratio of rotational inertias 
1
2
I
I
??
??
??
 
will be x : 1. The value of x will be _____. 
 
3R 
R 
B 
P 
Q 
 
 Official Ans. by NTA (9) 
2. The difference in the number of waves when 
yellow light propagates through air and vacuum 
columns of the same thickness is one. The 
thickness of the air column is ______ mm. 
[Refractive index of air = 1.0003, wavelength of 
yellow light in vacuum = 6000 Å] 
 Official Ans. by NTA (2) 
3. The maximum amplitude for an amplitude 
modulated wave is found to be 12V while the 
minimum amplitude is found to be 3V. The 
modulation index is 0.6x where x is ______. 
 Official Ans. by NTA (1) 
4. In the given figure the magnetic flux through  the 
loop increases according to the relation  
?
B
(t) = 10t
2
+ 20t, where ?
B
 is in milliwebers and t 
is in seconds. 
 The magnitude of current through R = 2? resistor 
at t = 5 s is ______ mA. 
 
R=2? 
× × × × × 
× × × × × 
× × × × × 
× × × × × 
 
 Official Ans. by NTA (60) 
5. A particle executes simple harmonic motion 
represented by displacement function as 
x(t) = A sin (?t + ?) 
If the position and velocity of the particle at  
t = 0 s are 2 cm and 2? cm s
–1
 respectively, then its 
amplitude is x 2 cm where the value of x is ____.  
 Official Ans. by NTA (2) 
6. A swimmer wants to cross a river from point A to 
point B. Line AB makes an angle of 30° with the 
flow of river. Magnitude of velocity of the 
swimmer is same as that of the river. The angle ? 
with the line AB should be ____°, so that the 
swimmer reaches point B. 
 
30° 
? 
B 
A 
 
 Official Ans. by NTA (30) 
 
5 
7. For the circuit shown, the value of current at time  
t = 3.2 s will be ______ A. 
 
 
 
 
 
    
 
 
 
 
 
± 
R=1? 
5V 
V(t) 
I 
Figure-2 
 
 [Voltage distribution V(t) is shown by Fig. (1) and 
the circuit is shown in Fig. (2)] 
 Official Ans. by NTA (1) 
8. A small block slides down from the top of 
hemisphere of radius R = 3 m as shown in the 
figure. The height 'h' at which the block will lose 
contact with the surface of the sphere is ____m. 
 (Assume there is no friction between the block and 
the hemisphere) 
 
(R –h) A 
O 
R 
h 
? 
 
 Official Ans. by NTA (2)  
9. The K
?
 X-ray of molybdenum has wavelength 
0.071 nm. If the energy of a molybdenum atoms 
with a K electron knocked out is 27.5 keV, the 
energy of this atom when an L electron is knocked 
out will be ______ keV. (Round off to the nearest 
integer) 
 [h = 4.14 × 10
–15
 eVs, c = 3 × 10
8
 ms
–1
] 
 Official Ans. by NTA (10) 
10. The water is filled upto height of 12 m in a tank 
having vertical sidewalls. A hole is made in one of 
the walls at a depth 'h' below the water level. The 
value of 'h' for which the emerging stream of water 
strikes the ground at the maximum range is ___ m. 
 Official Ans. by NTA (6)