JEE Mains 26 August 2021 Question Paper Shift 1 | JEE Main & Advanced Previous Year Papers PDF Download

 Page 1


 
    1 
FINAL JEE –MAIN EXAMINATION – AUGUST, 2021 
(Held On Thursday 26
th
 August, 2021)             TIME : 9 : 00 AM  to  12 : 00 NOON 
PHYSICS 
 
TEST PAPER WITH SOLUTION 
 
 
 
 
 
 
 
SECTION-A 
1. The fractional change in the magnetic field 
intensity at a distance 'r' from centre on the axis of 
current carrying coil of radius 'a' to the magnetic 
field intensity at the centre of the same coil is : 
(Take r < a) 
 (1) 
2
2
3a
2 r
  (2) 
2
2
2a
3 r
  
 (3) 
2
2
2r
3 a
  (4) 
2
2
3r
2 a
  
 Official Ans. by NTA (4) 
Sol. 
? ?
2
0
axis 3/2
22
B
iR
2 R x
?
?
?
 
 
0
centre
B
i
2R
?
? 
 
0
centre
B
i
2a
?
?
? 
 
? ?
2
0
axis 3/2
22
B
ia
2 a r
?
?
?
?
 
 ? fractional change in magnetic field = 
 
? ?
2
00
3/2
22
3/2
2
0
2
i ia
2a
2 a r
1
1
i
r
1
2a
a
??
?
?
??
?
?? ??
?
?? ??
?? ??
 
 
22
22
3 r 3 r
11
2 a 2 a
??
? ? ? ?
??
??
 
 Note : 
3/2
22
22
r 3 r
11
a 2 a
?
? ? ? ?
? ? ?
? ? ? ?
? ? ? ?
  
 [True only if r << a] 
 Hence option (4) is the most suitable option 
2. The magnitude of vectors OA , OB and OC  in 
the given figure are equal. The direction of 
OA OB OC ??  with x-axis will be :- 
 
A 
y 
C 
O 
45° 30° 
60° 
B 
x 
 
 (1) 
1
(1 3 2)
tan
(1 3 2)
?
??
??
   
 (2)  
? ?
? ?
1
3 1 2
tan
1 3 2
?
??
??
   
 (3) 
? ?
? ?
1
3 1 2
tan
1 3 2
?
??
??
  
 (4) 
? ?
? ?
1
1 3 2
tan
1 3 2
?
??
??
  
 Official Ans. by NTA (1) 
Sol. 
 
B 
30° 
A 
C 
45° 
60° 
  
 Let magnitude be equal to ?. 
 
31
ˆ ˆ ˆ ˆ
OA cos30 i sin 30j i j
22
??
??
? ? ? ? ? ? ?
??
??
??
 
 
13
ˆ ˆ ˆ ˆ
OB cos60 i sin 60j i j
22
??
??
? ? ? ? ? ? ?
??
??
??
 
      
? ?
11
ˆ ˆ ˆ ˆ
OC cos 45 i sin 45j i j
22
??
??
? ? ? ? ? ? ? ? ?
??
??
??
 
 OA OB OC ? ? ? 
3 1 1 1 3 1
ˆˆ
ij
2 2 2 22
?? ? ? ? ?
?
? ? ? ? ? ?
?? ? ? ? ?
? ? ? ?
??
? ? ? ? ??
 
Page 2


 
    1 
FINAL JEE –MAIN EXAMINATION – AUGUST, 2021 
(Held On Thursday 26
th
 August, 2021)             TIME : 9 : 00 AM  to  12 : 00 NOON 
PHYSICS 
 
TEST PAPER WITH SOLUTION 
 
 
 
 
 
 
 
SECTION-A 
1. The fractional change in the magnetic field 
intensity at a distance 'r' from centre on the axis of 
current carrying coil of radius 'a' to the magnetic 
field intensity at the centre of the same coil is : 
(Take r < a) 
 (1) 
2
2
3a
2 r
  (2) 
2
2
2a
3 r
  
 (3) 
2
2
2r
3 a
  (4) 
2
2
3r
2 a
  
 Official Ans. by NTA (4) 
Sol. 
? ?
2
0
axis 3/2
22
B
iR
2 R x
?
?
?
 
 
0
centre
B
i
2R
?
? 
 
0
centre
B
i
2a
?
?
? 
 
? ?
2
0
axis 3/2
22
B
ia
2 a r
?
?
?
?
 
 ? fractional change in magnetic field = 
 
? ?
2
00
3/2
22
3/2
2
0
2
i ia
2a
2 a r
1
1
i
r
1
2a
a
??
?
?
??
?
?? ??
?
?? ??
?? ??
 
 
22
22
3 r 3 r
11
2 a 2 a
??
? ? ? ?
??
??
 
 Note : 
3/2
22
22
r 3 r
11
a 2 a
?
? ? ? ?
? ? ?
? ? ? ?
? ? ? ?
  
 [True only if r << a] 
 Hence option (4) is the most suitable option 
2. The magnitude of vectors OA , OB and OC  in 
the given figure are equal. The direction of 
OA OB OC ??  with x-axis will be :- 
 
A 
y 
C 
O 
45° 30° 
60° 
B 
x 
 
 (1) 
1
(1 3 2)
tan
(1 3 2)
?
??
??
   
 (2)  
? ?
? ?
1
3 1 2
tan
1 3 2
?
??
??
   
 (3) 
? ?
? ?
1
3 1 2
tan
1 3 2
?
??
??
  
 (4) 
? ?
? ?
1
1 3 2
tan
1 3 2
?
??
??
  
 Official Ans. by NTA (1) 
Sol. 
 
B 
30° 
A 
C 
45° 
60° 
  
 Let magnitude be equal to ?. 
 
31
ˆ ˆ ˆ ˆ
OA cos30 i sin 30j i j
22
??
??
? ? ? ? ? ? ?
??
??
??
 
 
13
ˆ ˆ ˆ ˆ
OB cos60 i sin 60j i j
22
??
??
? ? ? ? ? ? ?
??
??
??
 
      
? ?
11
ˆ ˆ ˆ ˆ
OC cos 45 i sin 45j i j
22
??
??
? ? ? ? ? ? ? ? ?
??
??
??
 
 OA OB OC ? ? ? 
3 1 1 1 3 1
ˆˆ
ij
2 2 2 22
?? ? ? ? ?
?
? ? ? ? ? ?
?? ? ? ? ?
? ? ? ?
??
? ? ? ? ??
 
 
2 
 
 
 ? Angle with x-axis 
 
11
1 3 1
2 6 2
22 2
tan tan
3 1 1 6 2 2
22 2
??
??
??
??
??
??
??
?
??
?? ??
??
??
??
??
 
 = 
1
1 3 2
tan
3 1 2
?
??
??
??
??
??
 
 Hence option (1) 
3. Car B overtakes another car A at a relative speed 
of 40 ms
–1
. How fast will the image of car B 
appear to move in the mirror of focal length 10 cm 
fitted in car A, when the car B is 1.9 m away from 
the car A? 
 (1) 4 ms
–1
  (2) 0.2 ms
–1
  
 (3) 40 ms
–1
  (4) 0.1 ms
–1
  
 Official Ans. by NTA (4) 
Sol. 
 
B 
V
B 
A 
V
A
 
 
 Mirror used is convex mirror (rear-view mirror) 
 
2
I/m O/m
V m V ? ? ? 
 Given, 
 
O/m
V 40m / s ? 
 
f 10 10
m
f u 10 190 200
? ? ?
??
 
 
I/m
1
V 40 0.1m / s
400
? ? ? ? ? ? 
 ? Car will appear to move with speed 0.1 m/s. 
 Hence option (4) 
4. Inside a uniform spherical shell : 
 (a) the gravitational field is zero 
 (b) the gravitational potential is zero 
 (c) the gravitational field is same everywhere 
 (d) the gravitation potential is same everywhere 
 (e) all of the above 
 Choose the most appropriate answer from the 
options given below :  
 (1) (a), (c) and (d) only 
 (2) (e) only  
 (3) (a), (b) and (c) only   
 (4) (b), (c) and (d) only  
 Official Ans. by NTA (1) 
Sol. Inside a spherical shell, gravitational field is zero 
and hence potential remains same everywhere  
 Hence option (1) 
5. Two narrow bores of diameter 5.0 mm and 8.0 mm 
are joined together to form a U-shaped tube open 
at both ends. If this U-tube contains water, what is 
the difference in the level of two limbs of the tube. 
 [Take surface tension of water T = 7.3 × 10
–2
 Nm
–1
, 
angle of contact = 0, g = 10 ms
–2
 and density of 
water = 1.0 × 10
3
 kg m
–3
] 
 (1) 3.62 mm  (2) 2.19 mm  
 (3) 5.34 mm  (4) 4.97 mm  
 Official Ans. by NTA (2) 
Sol. 
 
?h 
P
A 
x 
r
2
 r
1
 
P
B 
 
 We have P
A
 = P
B
. [Points A & B at same 
horizontal level] 
 ? ?
atm atm
12
2T 2T
P g x h P gx
rr
? ? ? ? ? ? ? ? ? ? 
 
12
11
g h 2T
rr
??
? ? ? ? ?
??
??
 
 
2
33
11
2 7.3 10
2.5 10 4 10
?
??
??
? ? ? ?
??
??
??
 
 
23
3
2 7.3 10 10 1 1
h
10 10 2.5 4
?
? ? ? ??
? ? ? ?
??
?
??
 
 = 2.19 × 10
–3
m = 2.19 mm 
 Hence option (2) 
6. An electric appliance supplies 6000 J/min heat to 
the system. If the system delivers a power of 90W. 
How long it would take to increase the internal 
energy by 2.5 × 10
3
 J ? 
 (1) 2.5 × 10
2
 s (2) 4.1 × 10
1
s  
 (3) 2.4 × 10
3 
s (4) 2.5 × 10
1
s  
 Official Ans. by NTA (1) 
Page 3


 
    1 
FINAL JEE –MAIN EXAMINATION – AUGUST, 2021 
(Held On Thursday 26
th
 August, 2021)             TIME : 9 : 00 AM  to  12 : 00 NOON 
PHYSICS 
 
TEST PAPER WITH SOLUTION 
 
 
 
 
 
 
 
SECTION-A 
1. The fractional change in the magnetic field 
intensity at a distance 'r' from centre on the axis of 
current carrying coil of radius 'a' to the magnetic 
field intensity at the centre of the same coil is : 
(Take r < a) 
 (1) 
2
2
3a
2 r
  (2) 
2
2
2a
3 r
  
 (3) 
2
2
2r
3 a
  (4) 
2
2
3r
2 a
  
 Official Ans. by NTA (4) 
Sol. 
? ?
2
0
axis 3/2
22
B
iR
2 R x
?
?
?
 
 
0
centre
B
i
2R
?
? 
 
0
centre
B
i
2a
?
?
? 
 
? ?
2
0
axis 3/2
22
B
ia
2 a r
?
?
?
?
 
 ? fractional change in magnetic field = 
 
? ?
2
00
3/2
22
3/2
2
0
2
i ia
2a
2 a r
1
1
i
r
1
2a
a
??
?
?
??
?
?? ??
?
?? ??
?? ??
 
 
22
22
3 r 3 r
11
2 a 2 a
??
? ? ? ?
??
??
 
 Note : 
3/2
22
22
r 3 r
11
a 2 a
?
? ? ? ?
? ? ?
? ? ? ?
? ? ? ?
  
 [True only if r << a] 
 Hence option (4) is the most suitable option 
2. The magnitude of vectors OA , OB and OC  in 
the given figure are equal. The direction of 
OA OB OC ??  with x-axis will be :- 
 
A 
y 
C 
O 
45° 30° 
60° 
B 
x 
 
 (1) 
1
(1 3 2)
tan
(1 3 2)
?
??
??
   
 (2)  
? ?
? ?
1
3 1 2
tan
1 3 2
?
??
??
   
 (3) 
? ?
? ?
1
3 1 2
tan
1 3 2
?
??
??
  
 (4) 
? ?
? ?
1
1 3 2
tan
1 3 2
?
??
??
  
 Official Ans. by NTA (1) 
Sol. 
 
B 
30° 
A 
C 
45° 
60° 
  
 Let magnitude be equal to ?. 
 
31
ˆ ˆ ˆ ˆ
OA cos30 i sin 30j i j
22
??
??
? ? ? ? ? ? ?
??
??
??
 
 
13
ˆ ˆ ˆ ˆ
OB cos60 i sin 60j i j
22
??
??
? ? ? ? ? ? ?
??
??
??
 
      
? ?
11
ˆ ˆ ˆ ˆ
OC cos 45 i sin 45j i j
22
??
??
? ? ? ? ? ? ? ? ?
??
??
??
 
 OA OB OC ? ? ? 
3 1 1 1 3 1
ˆˆ
ij
2 2 2 22
?? ? ? ? ?
?
? ? ? ? ? ?
?? ? ? ? ?
? ? ? ?
??
? ? ? ? ??
 
 
2 
 
 
 ? Angle with x-axis 
 
11
1 3 1
2 6 2
22 2
tan tan
3 1 1 6 2 2
22 2
??
??
??
??
??
??
??
?
??
?? ??
??
??
??
??
 
 = 
1
1 3 2
tan
3 1 2
?
??
??
??
??
??
 
 Hence option (1) 
3. Car B overtakes another car A at a relative speed 
of 40 ms
–1
. How fast will the image of car B 
appear to move in the mirror of focal length 10 cm 
fitted in car A, when the car B is 1.9 m away from 
the car A? 
 (1) 4 ms
–1
  (2) 0.2 ms
–1
  
 (3) 40 ms
–1
  (4) 0.1 ms
–1
  
 Official Ans. by NTA (4) 
Sol. 
 
B 
V
B 
A 
V
A
 
 
 Mirror used is convex mirror (rear-view mirror) 
 
2
I/m O/m
V m V ? ? ? 
 Given, 
 
O/m
V 40m / s ? 
 
f 10 10
m
f u 10 190 200
? ? ?
??
 
 
I/m
1
V 40 0.1m / s
400
? ? ? ? ? ? 
 ? Car will appear to move with speed 0.1 m/s. 
 Hence option (4) 
4. Inside a uniform spherical shell : 
 (a) the gravitational field is zero 
 (b) the gravitational potential is zero 
 (c) the gravitational field is same everywhere 
 (d) the gravitation potential is same everywhere 
 (e) all of the above 
 Choose the most appropriate answer from the 
options given below :  
 (1) (a), (c) and (d) only 
 (2) (e) only  
 (3) (a), (b) and (c) only   
 (4) (b), (c) and (d) only  
 Official Ans. by NTA (1) 
Sol. Inside a spherical shell, gravitational field is zero 
and hence potential remains same everywhere  
 Hence option (1) 
5. Two narrow bores of diameter 5.0 mm and 8.0 mm 
are joined together to form a U-shaped tube open 
at both ends. If this U-tube contains water, what is 
the difference in the level of two limbs of the tube. 
 [Take surface tension of water T = 7.3 × 10
–2
 Nm
–1
, 
angle of contact = 0, g = 10 ms
–2
 and density of 
water = 1.0 × 10
3
 kg m
–3
] 
 (1) 3.62 mm  (2) 2.19 mm  
 (3) 5.34 mm  (4) 4.97 mm  
 Official Ans. by NTA (2) 
Sol. 
 
?h 
P
A 
x 
r
2
 r
1
 
P
B 
 
 We have P
A
 = P
B
. [Points A & B at same 
horizontal level] 
 ? ?
atm atm
12
2T 2T
P g x h P gx
rr
? ? ? ? ? ? ? ? ? ? 
 
12
11
g h 2T
rr
??
? ? ? ? ?
??
??
 
 
2
33
11
2 7.3 10
2.5 10 4 10
?
??
??
? ? ? ?
??
??
??
 
 
23
3
2 7.3 10 10 1 1
h
10 10 2.5 4
?
? ? ? ??
? ? ? ?
??
?
??
 
 = 2.19 × 10
–3
m = 2.19 mm 
 Hence option (2) 
6. An electric appliance supplies 6000 J/min heat to 
the system. If the system delivers a power of 90W. 
How long it would take to increase the internal 
energy by 2.5 × 10
3
 J ? 
 (1) 2.5 × 10
2
 s (2) 4.1 × 10
1
s  
 (3) 2.4 × 10
3 
s (4) 2.5 × 10
1
s  
 Official Ans. by NTA (1) 
 
 
3 
 
 
Sol. Q U W ? ? ? ? ? 
 
Q U W
t t t
? ? ?
??
? ? ?
 
 
3
6000 J 2.5 10
90
60 sec t
?
??
?
 
 ?t = 250 sec 
 Option (1) 
7. An inductor coil stores 64 J of magnetic field 
energy and dissipates energy at the rate of 640 W 
when a current of 8A is passed through it. If this 
coil is joined across an ideal battery, find the time 
constant of the circuit in seconds : 
 (1) 0.4 (2) 0.8 (3) 0.125 (4) 0.2  
 Official Ans. by NTA (4) 
Sol. 
2
1
U Li 64 L 2
2
? ? ? ? 
 i
2
R = 640 
 
? ?
2
640
R 10
8
?? 
 
L1
0.2
R5
? ? ? ? 
 Option (4) 
8. A series LCR circuit driven by 300 V at a 
frequency of 50 Hz contains a resistance R = 3 k ?, 
an inductor of inductive reactance X
L
 = 250 ?? 
and an unknown capacitor. The value of 
capacitance to maximize the average power should 
be : (Take ?
2
 = 10) 
 (1) 4 µF (2) 25 µF (3) 400 µF (4) 40 µF 
 Official Ans. by NTA (1) 
Sol. For maximum average power  
 
LC
XX ? 
 
? ?
1
250
2 50 C
??
?
 
 
6
C 4 10
?
?? 
 Option (1) 
9. Identify the logic operation carried out by the 
given circuit :- 
 
A 
B 
Y 
X 
Z 
 
 (1) OR  (2) AND (3) NOR (4) NAND  
 Official Ans. by NTA (3) 
Sol. 
A B X Y Z
1 1 0 0 0
1 0 0 1 0
0 1 1 0 0
0 0 1 1 1
 
 Option (3) 
10. A particular hydrogen like ion emits radiation of 
frequency 2.92 × 10
15
 Hz when it makes transition 
from n = 3 to n = 1. The frequency in Hz of 
radiation emitted in transition from n = 2 to n = 1 
will be : 
 (1) 0.44 × 10
15
 (2) 6.57 × 10
15
  
 (3) 4.38 × 10
15
 (4) 2.46 × 10
15
  
 Official Ans. by NTA (4) 
Sol. 
1 2
11
nf k
13
??
??
??
??
 
 
2 2
1
nf k 1
2
??
??
??
??
 
 
15 1
2
2
f 8 / 9
f 2.46 10
f 3/ 4
? ? ? ? 
 Option (4) 
11. In a photoelectric experiment ultraviolet light of 
wavelength 280 nm is used with lithium cathode 
having work function ? = 2.5 eV. If the wavelength 
of incident light is switched to 400 nm, find out the 
change in the stopping potential. (h = 6.63 × 10
–34
 Js, 
c = 3 × 10
8
 ms
–1
) 
 (1) 1.3 V (2) 1.1 V (3) 1.9 V (4) 0.6 V  
 Official Ans. by NTA (1) 
Sol. 
max S
hc
KE eV ? ? ? ?
?
 
 
S
1240
eV 2.5 1.93eV
280
? ? ? ? 
 
1
S
V 1.93V ?? … (i) 
 
2
S
1240
eV 2.5 0.6eV
400
? ? ? ? 
 
2
S
V 0.6V ?? … (ii) 
 
12
SS
V V V 1.93 0.6 1.33V ? ? ? ? ? ? 
 Option (1)  
Page 4


 
    1 
FINAL JEE –MAIN EXAMINATION – AUGUST, 2021 
(Held On Thursday 26
th
 August, 2021)             TIME : 9 : 00 AM  to  12 : 00 NOON 
PHYSICS 
 
TEST PAPER WITH SOLUTION 
 
 
 
 
 
 
 
SECTION-A 
1. The fractional change in the magnetic field 
intensity at a distance 'r' from centre on the axis of 
current carrying coil of radius 'a' to the magnetic 
field intensity at the centre of the same coil is : 
(Take r < a) 
 (1) 
2
2
3a
2 r
  (2) 
2
2
2a
3 r
  
 (3) 
2
2
2r
3 a
  (4) 
2
2
3r
2 a
  
 Official Ans. by NTA (4) 
Sol. 
? ?
2
0
axis 3/2
22
B
iR
2 R x
?
?
?
 
 
0
centre
B
i
2R
?
? 
 
0
centre
B
i
2a
?
?
? 
 
? ?
2
0
axis 3/2
22
B
ia
2 a r
?
?
?
?
 
 ? fractional change in magnetic field = 
 
? ?
2
00
3/2
22
3/2
2
0
2
i ia
2a
2 a r
1
1
i
r
1
2a
a
??
?
?
??
?
?? ??
?
?? ??
?? ??
 
 
22
22
3 r 3 r
11
2 a 2 a
??
? ? ? ?
??
??
 
 Note : 
3/2
22
22
r 3 r
11
a 2 a
?
? ? ? ?
? ? ?
? ? ? ?
? ? ? ?
  
 [True only if r << a] 
 Hence option (4) is the most suitable option 
2. The magnitude of vectors OA , OB and OC  in 
the given figure are equal. The direction of 
OA OB OC ??  with x-axis will be :- 
 
A 
y 
C 
O 
45° 30° 
60° 
B 
x 
 
 (1) 
1
(1 3 2)
tan
(1 3 2)
?
??
??
   
 (2)  
? ?
? ?
1
3 1 2
tan
1 3 2
?
??
??
   
 (3) 
? ?
? ?
1
3 1 2
tan
1 3 2
?
??
??
  
 (4) 
? ?
? ?
1
1 3 2
tan
1 3 2
?
??
??
  
 Official Ans. by NTA (1) 
Sol. 
 
B 
30° 
A 
C 
45° 
60° 
  
 Let magnitude be equal to ?. 
 
31
ˆ ˆ ˆ ˆ
OA cos30 i sin 30j i j
22
??
??
? ? ? ? ? ? ?
??
??
??
 
 
13
ˆ ˆ ˆ ˆ
OB cos60 i sin 60j i j
22
??
??
? ? ? ? ? ? ?
??
??
??
 
      
? ?
11
ˆ ˆ ˆ ˆ
OC cos 45 i sin 45j i j
22
??
??
? ? ? ? ? ? ? ? ?
??
??
??
 
 OA OB OC ? ? ? 
3 1 1 1 3 1
ˆˆ
ij
2 2 2 22
?? ? ? ? ?
?
? ? ? ? ? ?
?? ? ? ? ?
? ? ? ?
??
? ? ? ? ??
 
 
2 
 
 
 ? Angle with x-axis 
 
11
1 3 1
2 6 2
22 2
tan tan
3 1 1 6 2 2
22 2
??
??
??
??
??
??
??
?
??
?? ??
??
??
??
??
 
 = 
1
1 3 2
tan
3 1 2
?
??
??
??
??
??
 
 Hence option (1) 
3. Car B overtakes another car A at a relative speed 
of 40 ms
–1
. How fast will the image of car B 
appear to move in the mirror of focal length 10 cm 
fitted in car A, when the car B is 1.9 m away from 
the car A? 
 (1) 4 ms
–1
  (2) 0.2 ms
–1
  
 (3) 40 ms
–1
  (4) 0.1 ms
–1
  
 Official Ans. by NTA (4) 
Sol. 
 
B 
V
B 
A 
V
A
 
 
 Mirror used is convex mirror (rear-view mirror) 
 
2
I/m O/m
V m V ? ? ? 
 Given, 
 
O/m
V 40m / s ? 
 
f 10 10
m
f u 10 190 200
? ? ?
??
 
 
I/m
1
V 40 0.1m / s
400
? ? ? ? ? ? 
 ? Car will appear to move with speed 0.1 m/s. 
 Hence option (4) 
4. Inside a uniform spherical shell : 
 (a) the gravitational field is zero 
 (b) the gravitational potential is zero 
 (c) the gravitational field is same everywhere 
 (d) the gravitation potential is same everywhere 
 (e) all of the above 
 Choose the most appropriate answer from the 
options given below :  
 (1) (a), (c) and (d) only 
 (2) (e) only  
 (3) (a), (b) and (c) only   
 (4) (b), (c) and (d) only  
 Official Ans. by NTA (1) 
Sol. Inside a spherical shell, gravitational field is zero 
and hence potential remains same everywhere  
 Hence option (1) 
5. Two narrow bores of diameter 5.0 mm and 8.0 mm 
are joined together to form a U-shaped tube open 
at both ends. If this U-tube contains water, what is 
the difference in the level of two limbs of the tube. 
 [Take surface tension of water T = 7.3 × 10
–2
 Nm
–1
, 
angle of contact = 0, g = 10 ms
–2
 and density of 
water = 1.0 × 10
3
 kg m
–3
] 
 (1) 3.62 mm  (2) 2.19 mm  
 (3) 5.34 mm  (4) 4.97 mm  
 Official Ans. by NTA (2) 
Sol. 
 
?h 
P
A 
x 
r
2
 r
1
 
P
B 
 
 We have P
A
 = P
B
. [Points A & B at same 
horizontal level] 
 ? ?
atm atm
12
2T 2T
P g x h P gx
rr
? ? ? ? ? ? ? ? ? ? 
 
12
11
g h 2T
rr
??
? ? ? ? ?
??
??
 
 
2
33
11
2 7.3 10
2.5 10 4 10
?
??
??
? ? ? ?
??
??
??
 
 
23
3
2 7.3 10 10 1 1
h
10 10 2.5 4
?
? ? ? ??
? ? ? ?
??
?
??
 
 = 2.19 × 10
–3
m = 2.19 mm 
 Hence option (2) 
6. An electric appliance supplies 6000 J/min heat to 
the system. If the system delivers a power of 90W. 
How long it would take to increase the internal 
energy by 2.5 × 10
3
 J ? 
 (1) 2.5 × 10
2
 s (2) 4.1 × 10
1
s  
 (3) 2.4 × 10
3 
s (4) 2.5 × 10
1
s  
 Official Ans. by NTA (1) 
 
 
3 
 
 
Sol. Q U W ? ? ? ? ? 
 
Q U W
t t t
? ? ?
??
? ? ?
 
 
3
6000 J 2.5 10
90
60 sec t
?
??
?
 
 ?t = 250 sec 
 Option (1) 
7. An inductor coil stores 64 J of magnetic field 
energy and dissipates energy at the rate of 640 W 
when a current of 8A is passed through it. If this 
coil is joined across an ideal battery, find the time 
constant of the circuit in seconds : 
 (1) 0.4 (2) 0.8 (3) 0.125 (4) 0.2  
 Official Ans. by NTA (4) 
Sol. 
2
1
U Li 64 L 2
2
? ? ? ? 
 i
2
R = 640 
 
? ?
2
640
R 10
8
?? 
 
L1
0.2
R5
? ? ? ? 
 Option (4) 
8. A series LCR circuit driven by 300 V at a 
frequency of 50 Hz contains a resistance R = 3 k ?, 
an inductor of inductive reactance X
L
 = 250 ?? 
and an unknown capacitor. The value of 
capacitance to maximize the average power should 
be : (Take ?
2
 = 10) 
 (1) 4 µF (2) 25 µF (3) 400 µF (4) 40 µF 
 Official Ans. by NTA (1) 
Sol. For maximum average power  
 
LC
XX ? 
 
? ?
1
250
2 50 C
??
?
 
 
6
C 4 10
?
?? 
 Option (1) 
9. Identify the logic operation carried out by the 
given circuit :- 
 
A 
B 
Y 
X 
Z 
 
 (1) OR  (2) AND (3) NOR (4) NAND  
 Official Ans. by NTA (3) 
Sol. 
A B X Y Z
1 1 0 0 0
1 0 0 1 0
0 1 1 0 0
0 0 1 1 1
 
 Option (3) 
10. A particular hydrogen like ion emits radiation of 
frequency 2.92 × 10
15
 Hz when it makes transition 
from n = 3 to n = 1. The frequency in Hz of 
radiation emitted in transition from n = 2 to n = 1 
will be : 
 (1) 0.44 × 10
15
 (2) 6.57 × 10
15
  
 (3) 4.38 × 10
15
 (4) 2.46 × 10
15
  
 Official Ans. by NTA (4) 
Sol. 
1 2
11
nf k
13
??
??
??
??
 
 
2 2
1
nf k 1
2
??
??
??
??
 
 
15 1
2
2
f 8 / 9
f 2.46 10
f 3/ 4
? ? ? ? 
 Option (4) 
11. In a photoelectric experiment ultraviolet light of 
wavelength 280 nm is used with lithium cathode 
having work function ? = 2.5 eV. If the wavelength 
of incident light is switched to 400 nm, find out the 
change in the stopping potential. (h = 6.63 × 10
–34
 Js, 
c = 3 × 10
8
 ms
–1
) 
 (1) 1.3 V (2) 1.1 V (3) 1.9 V (4) 0.6 V  
 Official Ans. by NTA (1) 
Sol. 
max S
hc
KE eV ? ? ? ?
?
 
 
S
1240
eV 2.5 1.93eV
280
? ? ? ? 
 
1
S
V 1.93V ?? … (i) 
 
2
S
1240
eV 2.5 0.6eV
400
? ? ? ? 
 
2
S
V 0.6V ?? … (ii) 
 
12
SS
V V V 1.93 0.6 1.33V ? ? ? ? ? ? 
 Option (1)  
 
4 
 
 
12. In the given figure, the emf of the cell is 2.2 V and 
if internal resistance is 0.6 ?. Calculate the power 
dissipated in the whole circuit : 
 
 
 
4 ? 
2 ?    
 8 ? 
 8 ? 
2.2 V, r=0.6 ? 
B A 
 4 ? 
 
 (1) 1.32 W  (2) 0.65 W  
 (3) 2.2 W  (4) 4.4 W  
 Official Ans. by NTA (3) 
Sol. 
 
 
4 ? 
2 ?    
 8 ? 
 8 ? 
2.2 V, r=0.6 ? 
B A 
 4 ?  4 ? 
 
 ? 
 
4 ? 
 
12 ? 
6 ? 
2.2 V 
r = 0.6 ? 
 
 
 
 
 8 ? 
 
 
eq
1 1 1 1 1 6 3 2 4 15
R 4 8 12 6 24 24
? ? ?
? ? ? ? ? ? 
 
eq T
24
R 1.6 R 1.6 0.6 2.2
15
? ? ? ? ? ? ? 
 
? ?
2
2
T
2.2
V
P 2.2W
R 2.2
? ? ? 
 Option (3) 
13. A solid metal sphere of radius R having charge q is 
enclosed inside the concentric spherical shell of 
inner radius a and outer radius b as shown in 
figure. The approximate variation electric field E 
as a function of distance r from centre O is given 
by 
 
O R b 
a 
 
 (1) 
 
r R a b 
  
 (2) 
 
r R a b 
  
 (3) 
 
r R a b 
 
 (4) 
 
r R a b 
 
 Official Ans. by NTA (1) 
 Official Ans. by ALLEN (1 or 2) 
Sol. Considering outer spherical shell is non-
conducting 
 Electric field inside a metal sphere is zero. 
 r < R ? E = 0 
 
2
kQ
r R E
r
? ? ? 
Page 5


 
    1 
FINAL JEE –MAIN EXAMINATION – AUGUST, 2021 
(Held On Thursday 26
th
 August, 2021)             TIME : 9 : 00 AM  to  12 : 00 NOON 
PHYSICS 
 
TEST PAPER WITH SOLUTION 
 
 
 
 
 
 
 
SECTION-A 
1. The fractional change in the magnetic field 
intensity at a distance 'r' from centre on the axis of 
current carrying coil of radius 'a' to the magnetic 
field intensity at the centre of the same coil is : 
(Take r < a) 
 (1) 
2
2
3a
2 r
  (2) 
2
2
2a
3 r
  
 (3) 
2
2
2r
3 a
  (4) 
2
2
3r
2 a
  
 Official Ans. by NTA (4) 
Sol. 
? ?
2
0
axis 3/2
22
B
iR
2 R x
?
?
?
 
 
0
centre
B
i
2R
?
? 
 
0
centre
B
i
2a
?
?
? 
 
? ?
2
0
axis 3/2
22
B
ia
2 a r
?
?
?
?
 
 ? fractional change in magnetic field = 
 
? ?
2
00
3/2
22
3/2
2
0
2
i ia
2a
2 a r
1
1
i
r
1
2a
a
??
?
?
??
?
?? ??
?
?? ??
?? ??
 
 
22
22
3 r 3 r
11
2 a 2 a
??
? ? ? ?
??
??
 
 Note : 
3/2
22
22
r 3 r
11
a 2 a
?
? ? ? ?
? ? ?
? ? ? ?
? ? ? ?
  
 [True only if r << a] 
 Hence option (4) is the most suitable option 
2. The magnitude of vectors OA , OB and OC  in 
the given figure are equal. The direction of 
OA OB OC ??  with x-axis will be :- 
 
A 
y 
C 
O 
45° 30° 
60° 
B 
x 
 
 (1) 
1
(1 3 2)
tan
(1 3 2)
?
??
??
   
 (2)  
? ?
? ?
1
3 1 2
tan
1 3 2
?
??
??
   
 (3) 
? ?
? ?
1
3 1 2
tan
1 3 2
?
??
??
  
 (4) 
? ?
? ?
1
1 3 2
tan
1 3 2
?
??
??
  
 Official Ans. by NTA (1) 
Sol. 
 
B 
30° 
A 
C 
45° 
60° 
  
 Let magnitude be equal to ?. 
 
31
ˆ ˆ ˆ ˆ
OA cos30 i sin 30j i j
22
??
??
? ? ? ? ? ? ?
??
??
??
 
 
13
ˆ ˆ ˆ ˆ
OB cos60 i sin 60j i j
22
??
??
? ? ? ? ? ? ?
??
??
??
 
      
? ?
11
ˆ ˆ ˆ ˆ
OC cos 45 i sin 45j i j
22
??
??
? ? ? ? ? ? ? ? ?
??
??
??
 
 OA OB OC ? ? ? 
3 1 1 1 3 1
ˆˆ
ij
2 2 2 22
?? ? ? ? ?
?
? ? ? ? ? ?
?? ? ? ? ?
? ? ? ?
??
? ? ? ? ??
 
 
2 
 
 
 ? Angle with x-axis 
 
11
1 3 1
2 6 2
22 2
tan tan
3 1 1 6 2 2
22 2
??
??
??
??
??
??
??
?
??
?? ??
??
??
??
??
 
 = 
1
1 3 2
tan
3 1 2
?
??
??
??
??
??
 
 Hence option (1) 
3. Car B overtakes another car A at a relative speed 
of 40 ms
–1
. How fast will the image of car B 
appear to move in the mirror of focal length 10 cm 
fitted in car A, when the car B is 1.9 m away from 
the car A? 
 (1) 4 ms
–1
  (2) 0.2 ms
–1
  
 (3) 40 ms
–1
  (4) 0.1 ms
–1
  
 Official Ans. by NTA (4) 
Sol. 
 
B 
V
B 
A 
V
A
 
 
 Mirror used is convex mirror (rear-view mirror) 
 
2
I/m O/m
V m V ? ? ? 
 Given, 
 
O/m
V 40m / s ? 
 
f 10 10
m
f u 10 190 200
? ? ?
??
 
 
I/m
1
V 40 0.1m / s
400
? ? ? ? ? ? 
 ? Car will appear to move with speed 0.1 m/s. 
 Hence option (4) 
4. Inside a uniform spherical shell : 
 (a) the gravitational field is zero 
 (b) the gravitational potential is zero 
 (c) the gravitational field is same everywhere 
 (d) the gravitation potential is same everywhere 
 (e) all of the above 
 Choose the most appropriate answer from the 
options given below :  
 (1) (a), (c) and (d) only 
 (2) (e) only  
 (3) (a), (b) and (c) only   
 (4) (b), (c) and (d) only  
 Official Ans. by NTA (1) 
Sol. Inside a spherical shell, gravitational field is zero 
and hence potential remains same everywhere  
 Hence option (1) 
5. Two narrow bores of diameter 5.0 mm and 8.0 mm 
are joined together to form a U-shaped tube open 
at both ends. If this U-tube contains water, what is 
the difference in the level of two limbs of the tube. 
 [Take surface tension of water T = 7.3 × 10
–2
 Nm
–1
, 
angle of contact = 0, g = 10 ms
–2
 and density of 
water = 1.0 × 10
3
 kg m
–3
] 
 (1) 3.62 mm  (2) 2.19 mm  
 (3) 5.34 mm  (4) 4.97 mm  
 Official Ans. by NTA (2) 
Sol. 
 
?h 
P
A 
x 
r
2
 r
1
 
P
B 
 
 We have P
A
 = P
B
. [Points A & B at same 
horizontal level] 
 ? ?
atm atm
12
2T 2T
P g x h P gx
rr
? ? ? ? ? ? ? ? ? ? 
 
12
11
g h 2T
rr
??
? ? ? ? ?
??
??
 
 
2
33
11
2 7.3 10
2.5 10 4 10
?
??
??
? ? ? ?
??
??
??
 
 
23
3
2 7.3 10 10 1 1
h
10 10 2.5 4
?
? ? ? ??
? ? ? ?
??
?
??
 
 = 2.19 × 10
–3
m = 2.19 mm 
 Hence option (2) 
6. An electric appliance supplies 6000 J/min heat to 
the system. If the system delivers a power of 90W. 
How long it would take to increase the internal 
energy by 2.5 × 10
3
 J ? 
 (1) 2.5 × 10
2
 s (2) 4.1 × 10
1
s  
 (3) 2.4 × 10
3 
s (4) 2.5 × 10
1
s  
 Official Ans. by NTA (1) 
 
 
3 
 
 
Sol. Q U W ? ? ? ? ? 
 
Q U W
t t t
? ? ?
??
? ? ?
 
 
3
6000 J 2.5 10
90
60 sec t
?
??
?
 
 ?t = 250 sec 
 Option (1) 
7. An inductor coil stores 64 J of magnetic field 
energy and dissipates energy at the rate of 640 W 
when a current of 8A is passed through it. If this 
coil is joined across an ideal battery, find the time 
constant of the circuit in seconds : 
 (1) 0.4 (2) 0.8 (3) 0.125 (4) 0.2  
 Official Ans. by NTA (4) 
Sol. 
2
1
U Li 64 L 2
2
? ? ? ? 
 i
2
R = 640 
 
? ?
2
640
R 10
8
?? 
 
L1
0.2
R5
? ? ? ? 
 Option (4) 
8. A series LCR circuit driven by 300 V at a 
frequency of 50 Hz contains a resistance R = 3 k ?, 
an inductor of inductive reactance X
L
 = 250 ?? 
and an unknown capacitor. The value of 
capacitance to maximize the average power should 
be : (Take ?
2
 = 10) 
 (1) 4 µF (2) 25 µF (3) 400 µF (4) 40 µF 
 Official Ans. by NTA (1) 
Sol. For maximum average power  
 
LC
XX ? 
 
? ?
1
250
2 50 C
??
?
 
 
6
C 4 10
?
?? 
 Option (1) 
9. Identify the logic operation carried out by the 
given circuit :- 
 
A 
B 
Y 
X 
Z 
 
 (1) OR  (2) AND (3) NOR (4) NAND  
 Official Ans. by NTA (3) 
Sol. 
A B X Y Z
1 1 0 0 0
1 0 0 1 0
0 1 1 0 0
0 0 1 1 1
 
 Option (3) 
10. A particular hydrogen like ion emits radiation of 
frequency 2.92 × 10
15
 Hz when it makes transition 
from n = 3 to n = 1. The frequency in Hz of 
radiation emitted in transition from n = 2 to n = 1 
will be : 
 (1) 0.44 × 10
15
 (2) 6.57 × 10
15
  
 (3) 4.38 × 10
15
 (4) 2.46 × 10
15
  
 Official Ans. by NTA (4) 
Sol. 
1 2
11
nf k
13
??
??
??
??
 
 
2 2
1
nf k 1
2
??
??
??
??
 
 
15 1
2
2
f 8 / 9
f 2.46 10
f 3/ 4
? ? ? ? 
 Option (4) 
11. In a photoelectric experiment ultraviolet light of 
wavelength 280 nm is used with lithium cathode 
having work function ? = 2.5 eV. If the wavelength 
of incident light is switched to 400 nm, find out the 
change in the stopping potential. (h = 6.63 × 10
–34
 Js, 
c = 3 × 10
8
 ms
–1
) 
 (1) 1.3 V (2) 1.1 V (3) 1.9 V (4) 0.6 V  
 Official Ans. by NTA (1) 
Sol. 
max S
hc
KE eV ? ? ? ?
?
 
 
S
1240
eV 2.5 1.93eV
280
? ? ? ? 
 
1
S
V 1.93V ?? … (i) 
 
2
S
1240
eV 2.5 0.6eV
400
? ? ? ? 
 
2
S
V 0.6V ?? … (ii) 
 
12
SS
V V V 1.93 0.6 1.33V ? ? ? ? ? ? 
 Option (1)  
 
4 
 
 
12. In the given figure, the emf of the cell is 2.2 V and 
if internal resistance is 0.6 ?. Calculate the power 
dissipated in the whole circuit : 
 
 
 
4 ? 
2 ?    
 8 ? 
 8 ? 
2.2 V, r=0.6 ? 
B A 
 4 ? 
 
 (1) 1.32 W  (2) 0.65 W  
 (3) 2.2 W  (4) 4.4 W  
 Official Ans. by NTA (3) 
Sol. 
 
 
4 ? 
2 ?    
 8 ? 
 8 ? 
2.2 V, r=0.6 ? 
B A 
 4 ?  4 ? 
 
 ? 
 
4 ? 
 
12 ? 
6 ? 
2.2 V 
r = 0.6 ? 
 
 
 
 
 8 ? 
 
 
eq
1 1 1 1 1 6 3 2 4 15
R 4 8 12 6 24 24
? ? ?
? ? ? ? ? ? 
 
eq T
24
R 1.6 R 1.6 0.6 2.2
15
? ? ? ? ? ? ? 
 
? ?
2
2
T
2.2
V
P 2.2W
R 2.2
? ? ? 
 Option (3) 
13. A solid metal sphere of radius R having charge q is 
enclosed inside the concentric spherical shell of 
inner radius a and outer radius b as shown in 
figure. The approximate variation electric field E 
as a function of distance r from centre O is given 
by 
 
O R b 
a 
 
 (1) 
 
r R a b 
  
 (2) 
 
r R a b 
  
 (3) 
 
r R a b 
 
 (4) 
 
r R a b 
 
 Official Ans. by NTA (1) 
 Official Ans. by ALLEN (1 or 2) 
Sol. Considering outer spherical shell is non-
conducting 
 Electric field inside a metal sphere is zero. 
 r < R ? E = 0 
 
2
kQ
r R E
r
? ? ? 
 
 
5 
 
 
 
 
r r=R 
 
E 
 
 Option (2) 
 Considering outer spherical shell is conducting 
 
 
b 
a 
+Q 
R 
–Q 
+Q 
 
 r < R, E = 0 
 R r a ?? 
2
kQ
E
r
? 
 a r b ?? , E = 0 
 rb ? 
2
kQ
E
r
? 
 
 
r=a r=R 
E 
r 
r=b 
 
 Option (1) 
14. The rms speeds of the molecules of Hydrogen, 
Oxygen and Carbondioxide at the same 
temperature are V
H
, V
O
 and V
C
 respectively then : 
 (1) V
H
 > V
O
 > V
C
 (2) V
C
 > V
O
 > V
H
 
 (3) V
H
 = V
O
 > V
C
 (4) V
H
 = V
O
 = V
C
  
 Official Ans. by NTA (1) 
Sol. 
RMS
W
3RT
V
M
? 
 At the same temperature 
RMS
w
1
V
M
? 
 
H O C
V V V ? ? ? 
 Option (1) 
15. In a Screw Gauge, fifth division of the circular 
scale coincides with the reference line when the 
ratchet is closed. There are 50 divisions on the 
circular scale, and the main scale moves by  
0.5 mm on a complete rotation. For a particular 
observation the reading on the main scale is 5 mm 
and the 20
th
 division of the circular scale coincides 
with reference line. Calculate the true reading. 
 (1) 5.00 mm  (2) 5.25 mm 
 (3) 5.15 mm  (4) 5.20 mm 
 Official Ans. by NTA (3) 
Sol. Least count (L.C) = 
0.5
50
 
 True reading 
0.5 0.5
5 20 5
50 50
? ? ? ? ? 
 ? ?
0.5
5 15 5.15mm
50
? ? ?  
 Option (3) 
16. What equal length of an iron wire and a  
copper-nickel alloy wire, each of 2 mm diameter 
connected parallel to give an equivalent resistance 
of 3 ?? 
 (Given resistivities of iron and copper-nickel alloy 
wire are 12 ?? cm and 51 ?? cm respectively) 
 (1) 82 m  (2) 97 m  
 (3) 110 m  (4) 90 m  
 Official Ans. by NTA (2) 
Sol. 
12
12
RR
3
RR
?
?
 
 
? ?
? ?
? ?
? ?
? ?
6 2 6 2
22
66
62
2
6
12 10 10 4 51 10 10 4
2 10 2 10
63 10 10 4
2 10
? ? ? ?
??
??
?
? ? ? ? ? ?
?
? ? ? ?
? ? ? ?
??
 
 97m ?? 
 Option (2) 
17. The initial mass of a rocket is 1000 kg. Calculate at 
what rate the fuel should be burnt so that the rocket 
is given an acceleration of 20 ms
–2
. The gases 
come out at a relative speed of 500 ms
–1
 with 
respect to the rocket :[Use g = 10 m/s
2
] 
 (1) 6.0 × 10
2
 kg s
–1
 (2) 500 kg s
–1
  
 (3) 10 kg s
–1
  (4) 60 kg s
–1
  
 Official Ans. by NTA (4)