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

 Page 1


 
 
SECTION - A 
 
1. If ?
1
 and ?
?
 are the wavelengths of the third member of Lyman and first member of the Paschen 
series respectively, then the value of ?
1
 : ?
?
?is : 
 (1) 1 : 3 (2) 1 : 9  (3) 7 : 135 (4) 7 : 108 
Sol. (3) 
For Lyman series 
n
1
 = 1,  n
2
 = 4 
2
2 2
1 1 2
1 1 1
Rz
n n
? ?
? ?
? ?
? ?
?
? ?
 
2
2 2
1 1
1 1 1
Rz
1 4
? ?
? ?
? ?
? ?
?
? ?
 
2
1
1 15Rz
16
?
?
 
1 2
16
15Rz
? ? 
For paschen series 
n
1
 = 3,  n
2
 = 4 
2
2 2
2
1 1 1
Rz
3 4
? ?
? ?
? ?
?
? ?
 
2
2
1 16 9
Rz
9 16
? ? ?
?
? ?
? ?
? ?
 
2
2
1 7
Rz
9 16
? ?
?
? ?
? ?
? ?
 
2 2
9 16
7Rz
?
? ? 
So, 
 
2
1
2
2
16
15Rz
9 16
7Rz
?
?
? ?
 
 
16 7
15 9 16
?
?
? ?
 
 
7
135
? 
 
 
26
th
 Feb. 2021 | Shift - 1
PHYSICS
Page 2


 
 
SECTION - A 
 
1. If ?
1
 and ?
?
 are the wavelengths of the third member of Lyman and first member of the Paschen 
series respectively, then the value of ?
1
 : ?
?
?is : 
 (1) 1 : 3 (2) 1 : 9  (3) 7 : 135 (4) 7 : 108 
Sol. (3) 
For Lyman series 
n
1
 = 1,  n
2
 = 4 
2
2 2
1 1 2
1 1 1
Rz
n n
? ?
? ?
? ?
? ?
?
? ?
 
2
2 2
1 1
1 1 1
Rz
1 4
? ?
? ?
? ?
? ?
?
? ?
 
2
1
1 15Rz
16
?
?
 
1 2
16
15Rz
? ? 
For paschen series 
n
1
 = 3,  n
2
 = 4 
2
2 2
2
1 1 1
Rz
3 4
? ?
? ?
? ?
?
? ?
 
2
2
1 16 9
Rz
9 16
? ? ?
?
? ?
? ?
? ?
 
2
2
1 7
Rz
9 16
? ?
?
? ?
? ?
? ?
 
2 2
9 16
7Rz
?
? ? 
So, 
 
2
1
2
2
16
15Rz
9 16
7Rz
?
?
? ?
 
 
16 7
15 9 16
?
?
? ?
 
 
7
135
? 
 
 
26
th
 Feb. 2021 | Shift - 1
PHYSICS
 
 
2. The temperature ? at the junction of two insulating sheets, having thermal resistances R
1
 and 
R
2
 as well as top and bottom temperatures ?
1
 and ?
2
 (as shown in figure) is given by : 
 
?
2
R
2
R
1
?
?
1
R
1
 
 (1) 
1 2 2 1
1 2
R R
R R
? ? ?
?
 (2) 
1 2 2 1
2 1
R R
R R
? ? ?
?
 (3)
 
2 2 1 1
2 1
R R
R R
? ? ?
?
 (4) 
1 1 2 2
1 2
R R
R R
? ? ?
?
 
Sol. (1) 
 Temperature at the junction is ?. 
 so using the formula 
 
2 1
1 2
T T T T
R R
? ?
? 
 
2 1
2 1
R R
? ? ? ? ? ?
? 
 R
1
 ( ?
2
 – ?) = R
2
( ? ? ? ? ?
1
) 
 R
1
?
2
 – R
1
?
 
= R
2
? ? R
2
?
? ?
 R
1
?
 
+ R
2
? = R
1
?
? ?
 + R
2
?
1
 
 
1 2 2 1
1 2
R R
R R
? ? ?
? ?
?
  
  
3. In a Young's double slit experiment two slits are separated by 2 mm and the screen is placed 
one meter away. When a light of wavelength 500 nm is used, the fringe separation will be :  
 (1) 0.75 mm (2) 0.50 mm (3) 1 mm (4) 0.25 mm 
Sol. (4) 
 Fringe width ( ?) = 
D
d
?
 
  d = 2×10
–3
m 
  ? = 500×10
–9
m 
  D = 1m 
 Now 
? ? ? =
9
3
500 10 1
2 10
?
?
? ?
?
 
  ? = 
4
5
10
2
?
? 
? = 2.5 × 10
-4
 
? ?= 0.25 mm 
Page 3


 
 
SECTION - A 
 
1. If ?
1
 and ?
?
 are the wavelengths of the third member of Lyman and first member of the Paschen 
series respectively, then the value of ?
1
 : ?
?
?is : 
 (1) 1 : 3 (2) 1 : 9  (3) 7 : 135 (4) 7 : 108 
Sol. (3) 
For Lyman series 
n
1
 = 1,  n
2
 = 4 
2
2 2
1 1 2
1 1 1
Rz
n n
? ?
? ?
? ?
? ?
?
? ?
 
2
2 2
1 1
1 1 1
Rz
1 4
? ?
? ?
? ?
? ?
?
? ?
 
2
1
1 15Rz
16
?
?
 
1 2
16
15Rz
? ? 
For paschen series 
n
1
 = 3,  n
2
 = 4 
2
2 2
2
1 1 1
Rz
3 4
? ?
? ?
? ?
?
? ?
 
2
2
1 16 9
Rz
9 16
? ? ?
?
? ?
? ?
? ?
 
2
2
1 7
Rz
9 16
? ?
?
? ?
? ?
? ?
 
2 2
9 16
7Rz
?
? ? 
So, 
 
2
1
2
2
16
15Rz
9 16
7Rz
?
?
? ?
 
 
16 7
15 9 16
?
?
? ?
 
 
7
135
? 
 
 
26
th
 Feb. 2021 | Shift - 1
PHYSICS
 
 
2. The temperature ? at the junction of two insulating sheets, having thermal resistances R
1
 and 
R
2
 as well as top and bottom temperatures ?
1
 and ?
2
 (as shown in figure) is given by : 
 
?
2
R
2
R
1
?
?
1
R
1
 
 (1) 
1 2 2 1
1 2
R R
R R
? ? ?
?
 (2) 
1 2 2 1
2 1
R R
R R
? ? ?
?
 (3)
 
2 2 1 1
2 1
R R
R R
? ? ?
?
 (4) 
1 1 2 2
1 2
R R
R R
? ? ?
?
 
Sol. (1) 
 Temperature at the junction is ?. 
 so using the formula 
 
2 1
1 2
T T T T
R R
? ?
? 
 
2 1
2 1
R R
? ? ? ? ? ?
? 
 R
1
 ( ?
2
 – ?) = R
2
( ? ? ? ? ?
1
) 
 R
1
?
2
 – R
1
?
 
= R
2
? ? R
2
?
? ?
 R
1
?
 
+ R
2
? = R
1
?
? ?
 + R
2
?
1
 
 
1 2 2 1
1 2
R R
R R
? ? ?
? ?
?
  
  
3. In a Young's double slit experiment two slits are separated by 2 mm and the screen is placed 
one meter away. When a light of wavelength 500 nm is used, the fringe separation will be :  
 (1) 0.75 mm (2) 0.50 mm (3) 1 mm (4) 0.25 mm 
Sol. (4) 
 Fringe width ( ?) = 
D
d
?
 
  d = 2×10
–3
m 
  ? = 500×10
–9
m 
  D = 1m 
 Now 
? ? ? =
9
3
500 10 1
2 10
?
?
? ?
?
 
  ? = 
4
5
10
2
?
? 
? = 2.5 × 10
-4
 
? ?= 0.25 mm 
 
 
4. Given below are two statements : one is labelled as Assertion A and the other is labelled as 
Reason R. 
 Assertion A :  An electron microscope can achieve better resolving power than an optical 
microscope. 
 Reason R :  The de Broglie's wavelength of the electrons emitted from an electron gun is 
much less than wavelength of visible light. 
 In the light of the above statements, choose the correct answer from the options given below: 
 (1) A is true but R is false. 
 (2) Both A and R are true but R is NOT the correct explanation of A. 
 (3) Both A and R are true and R is the correct explanation of A. 
 (4) A is false but R is true. 
Sol. (3) 
Resolution limit ? ?
1.22
d
?
? ? ? 
Resolution power 
1
Resolution limit
? 
? ? ? ? ? ? ?
? ? ? ?Power ? ?
  
5. Four identical solid spheres each of mass 'm' and radius 'a' are placed with their centres on the 
four corners of a square of side 'b'. The moment of inertia of  the system about one side of 
square where the axis of rotation is parallel to the  plane of the square is : 
 (1)
 
4
5
ma
2
 (2) 
8
5
ma
2
 + mb
2
 (3) 
4
5
ma
2
 + 2mb
2
 (4) 
8
5
ma
2
 + 2mb
2
 
Sol. (4) 
 
 
a
?
a
?
 
a
?
a
?
b b
b
 
 I = 
2
5
 ma
2
 + 
2
5
 ma
2
 + 
2 2
2
ma mb
5
? ?
?
? ?
? ?
+ 
2 2
2
ma mb
5
? 
 I = 4 ×
2
5
 ma
2
 + 2mb
2
 
 = 
8
5
ma
2
 + 2mb
2
 
 
Page 4


 
 
SECTION - A 
 
1. If ?
1
 and ?
?
 are the wavelengths of the third member of Lyman and first member of the Paschen 
series respectively, then the value of ?
1
 : ?
?
?is : 
 (1) 1 : 3 (2) 1 : 9  (3) 7 : 135 (4) 7 : 108 
Sol. (3) 
For Lyman series 
n
1
 = 1,  n
2
 = 4 
2
2 2
1 1 2
1 1 1
Rz
n n
? ?
? ?
? ?
? ?
?
? ?
 
2
2 2
1 1
1 1 1
Rz
1 4
? ?
? ?
? ?
? ?
?
? ?
 
2
1
1 15Rz
16
?
?
 
1 2
16
15Rz
? ? 
For paschen series 
n
1
 = 3,  n
2
 = 4 
2
2 2
2
1 1 1
Rz
3 4
? ?
? ?
? ?
?
? ?
 
2
2
1 16 9
Rz
9 16
? ? ?
?
? ?
? ?
? ?
 
2
2
1 7
Rz
9 16
? ?
?
? ?
? ?
? ?
 
2 2
9 16
7Rz
?
? ? 
So, 
 
2
1
2
2
16
15Rz
9 16
7Rz
?
?
? ?
 
 
16 7
15 9 16
?
?
? ?
 
 
7
135
? 
 
 
26
th
 Feb. 2021 | Shift - 1
PHYSICS
 
 
2. The temperature ? at the junction of two insulating sheets, having thermal resistances R
1
 and 
R
2
 as well as top and bottom temperatures ?
1
 and ?
2
 (as shown in figure) is given by : 
 
?
2
R
2
R
1
?
?
1
R
1
 
 (1) 
1 2 2 1
1 2
R R
R R
? ? ?
?
 (2) 
1 2 2 1
2 1
R R
R R
? ? ?
?
 (3)
 
2 2 1 1
2 1
R R
R R
? ? ?
?
 (4) 
1 1 2 2
1 2
R R
R R
? ? ?
?
 
Sol. (1) 
 Temperature at the junction is ?. 
 so using the formula 
 
2 1
1 2
T T T T
R R
? ?
? 
 
2 1
2 1
R R
? ? ? ? ? ?
? 
 R
1
 ( ?
2
 – ?) = R
2
( ? ? ? ? ?
1
) 
 R
1
?
2
 – R
1
?
 
= R
2
? ? R
2
?
? ?
 R
1
?
 
+ R
2
? = R
1
?
? ?
 + R
2
?
1
 
 
1 2 2 1
1 2
R R
R R
? ? ?
? ?
?
  
  
3. In a Young's double slit experiment two slits are separated by 2 mm and the screen is placed 
one meter away. When a light of wavelength 500 nm is used, the fringe separation will be :  
 (1) 0.75 mm (2) 0.50 mm (3) 1 mm (4) 0.25 mm 
Sol. (4) 
 Fringe width ( ?) = 
D
d
?
 
  d = 2×10
–3
m 
  ? = 500×10
–9
m 
  D = 1m 
 Now 
? ? ? =
9
3
500 10 1
2 10
?
?
? ?
?
 
  ? = 
4
5
10
2
?
? 
? = 2.5 × 10
-4
 
? ?= 0.25 mm 
 
 
4. Given below are two statements : one is labelled as Assertion A and the other is labelled as 
Reason R. 
 Assertion A :  An electron microscope can achieve better resolving power than an optical 
microscope. 
 Reason R :  The de Broglie's wavelength of the electrons emitted from an electron gun is 
much less than wavelength of visible light. 
 In the light of the above statements, choose the correct answer from the options given below: 
 (1) A is true but R is false. 
 (2) Both A and R are true but R is NOT the correct explanation of A. 
 (3) Both A and R are true and R is the correct explanation of A. 
 (4) A is false but R is true. 
Sol. (3) 
Resolution limit ? ?
1.22
d
?
? ? ? 
Resolution power 
1
Resolution limit
? 
? ? ? ? ? ? ?
? ? ? ?Power ? ?
  
5. Four identical solid spheres each of mass 'm' and radius 'a' are placed with their centres on the 
four corners of a square of side 'b'. The moment of inertia of  the system about one side of 
square where the axis of rotation is parallel to the  plane of the square is : 
 (1)
 
4
5
ma
2
 (2) 
8
5
ma
2
 + mb
2
 (3) 
4
5
ma
2
 + 2mb
2
 (4) 
8
5
ma
2
 + 2mb
2
 
Sol. (4) 
 
 
a
?
a
?
 
a
?
a
?
b b
b
 
 I = 
2
5
 ma
2
 + 
2
5
 ma
2
 + 
2 2
2
ma mb
5
? ?
?
? ?
? ?
+ 
2 2
2
ma mb
5
? 
 I = 4 ×
2
5
 ma
2
 + 2mb
2
 
 = 
8
5
ma
2
 + 2mb
2
 
 
 
 
6. The normal density of a material is ? and its bulk modulus of elasticity is K. The magnitude of 
increase in density of material, when a pressure P is applied uniformly on all sides, will be : 
 (1) 
K
P
?
 (2) 
K
P ?
 (3) 
PK
?
 (4) 
P
K
?
 
Sol. (4) 
 Bulk modulus 
P pv
K
v v
v
? ? ? ?
? ?
? ?
 
 We know, 
M
V
? ? 
 So, 
v
v
? ? ? ?
?
?
 
  
P P
K
? ? ? ?
? ?
? ? ? ? ? ?
?
? ?
?
? ?
 
  
P
K
? ?
? ? ? 
  
P
K
?
? ? ? 
 
7. LED is constructed from Ga-As-P semiconducting material. The energy gap of this LED is 1.9 eV. 
Calculate the wavelength of light emitted and its colour. 
 [h=6.63×10
–34 
Js and c=3×10
8
 ms
–1
] 
 (1) 654 nm and red colour (2) 1046 nm and blue colour 
 (3) 1046 nm and red colour (4) 654 nm and orange colour 
Sol. (1) 
 We know that 
hc
E ?
?
 
 
? ?
? ?
1240 in eV
hc
E E in eV
? ? ? 
 
1240
1.9
? ? 
 = 652.63 nm  ? 654 nm 
 Wavelength of red light is 620 nm to 750 nm 
 So, answer is 1. 
  
 
 
Page 5


 
 
SECTION - A 
 
1. If ?
1
 and ?
?
 are the wavelengths of the third member of Lyman and first member of the Paschen 
series respectively, then the value of ?
1
 : ?
?
?is : 
 (1) 1 : 3 (2) 1 : 9  (3) 7 : 135 (4) 7 : 108 
Sol. (3) 
For Lyman series 
n
1
 = 1,  n
2
 = 4 
2
2 2
1 1 2
1 1 1
Rz
n n
? ?
? ?
? ?
? ?
?
? ?
 
2
2 2
1 1
1 1 1
Rz
1 4
? ?
? ?
? ?
? ?
?
? ?
 
2
1
1 15Rz
16
?
?
 
1 2
16
15Rz
? ? 
For paschen series 
n
1
 = 3,  n
2
 = 4 
2
2 2
2
1 1 1
Rz
3 4
? ?
? ?
? ?
?
? ?
 
2
2
1 16 9
Rz
9 16
? ? ?
?
? ?
? ?
? ?
 
2
2
1 7
Rz
9 16
? ?
?
? ?
? ?
? ?
 
2 2
9 16
7Rz
?
? ? 
So, 
 
2
1
2
2
16
15Rz
9 16
7Rz
?
?
? ?
 
 
16 7
15 9 16
?
?
? ?
 
 
7
135
? 
 
 
26
th
 Feb. 2021 | Shift - 1
PHYSICS
 
 
2. The temperature ? at the junction of two insulating sheets, having thermal resistances R
1
 and 
R
2
 as well as top and bottom temperatures ?
1
 and ?
2
 (as shown in figure) is given by : 
 
?
2
R
2
R
1
?
?
1
R
1
 
 (1) 
1 2 2 1
1 2
R R
R R
? ? ?
?
 (2) 
1 2 2 1
2 1
R R
R R
? ? ?
?
 (3)
 
2 2 1 1
2 1
R R
R R
? ? ?
?
 (4) 
1 1 2 2
1 2
R R
R R
? ? ?
?
 
Sol. (1) 
 Temperature at the junction is ?. 
 so using the formula 
 
2 1
1 2
T T T T
R R
? ?
? 
 
2 1
2 1
R R
? ? ? ? ? ?
? 
 R
1
 ( ?
2
 – ?) = R
2
( ? ? ? ? ?
1
) 
 R
1
?
2
 – R
1
?
 
= R
2
? ? R
2
?
? ?
 R
1
?
 
+ R
2
? = R
1
?
? ?
 + R
2
?
1
 
 
1 2 2 1
1 2
R R
R R
? ? ?
? ?
?
  
  
3. In a Young's double slit experiment two slits are separated by 2 mm and the screen is placed 
one meter away. When a light of wavelength 500 nm is used, the fringe separation will be :  
 (1) 0.75 mm (2) 0.50 mm (3) 1 mm (4) 0.25 mm 
Sol. (4) 
 Fringe width ( ?) = 
D
d
?
 
  d = 2×10
–3
m 
  ? = 500×10
–9
m 
  D = 1m 
 Now 
? ? ? =
9
3
500 10 1
2 10
?
?
? ?
?
 
  ? = 
4
5
10
2
?
? 
? = 2.5 × 10
-4
 
? ?= 0.25 mm 
 
 
4. Given below are two statements : one is labelled as Assertion A and the other is labelled as 
Reason R. 
 Assertion A :  An electron microscope can achieve better resolving power than an optical 
microscope. 
 Reason R :  The de Broglie's wavelength of the electrons emitted from an electron gun is 
much less than wavelength of visible light. 
 In the light of the above statements, choose the correct answer from the options given below: 
 (1) A is true but R is false. 
 (2) Both A and R are true but R is NOT the correct explanation of A. 
 (3) Both A and R are true and R is the correct explanation of A. 
 (4) A is false but R is true. 
Sol. (3) 
Resolution limit ? ?
1.22
d
?
? ? ? 
Resolution power 
1
Resolution limit
? 
? ? ? ? ? ? ?
? ? ? ?Power ? ?
  
5. Four identical solid spheres each of mass 'm' and radius 'a' are placed with their centres on the 
four corners of a square of side 'b'. The moment of inertia of  the system about one side of 
square where the axis of rotation is parallel to the  plane of the square is : 
 (1)
 
4
5
ma
2
 (2) 
8
5
ma
2
 + mb
2
 (3) 
4
5
ma
2
 + 2mb
2
 (4) 
8
5
ma
2
 + 2mb
2
 
Sol. (4) 
 
 
a
?
a
?
 
a
?
a
?
b b
b
 
 I = 
2
5
 ma
2
 + 
2
5
 ma
2
 + 
2 2
2
ma mb
5
? ?
?
? ?
? ?
+ 
2 2
2
ma mb
5
? 
 I = 4 ×
2
5
 ma
2
 + 2mb
2
 
 = 
8
5
ma
2
 + 2mb
2
 
 
 
 
6. The normal density of a material is ? and its bulk modulus of elasticity is K. The magnitude of 
increase in density of material, when a pressure P is applied uniformly on all sides, will be : 
 (1) 
K
P
?
 (2) 
K
P ?
 (3) 
PK
?
 (4) 
P
K
?
 
Sol. (4) 
 Bulk modulus 
P pv
K
v v
v
? ? ? ?
? ?
? ?
 
 We know, 
M
V
? ? 
 So, 
v
v
? ? ? ?
?
?
 
  
P P
K
? ? ? ?
? ?
? ? ? ? ? ?
?
? ?
?
? ?
 
  
P
K
? ?
? ? ? 
  
P
K
?
? ? ? 
 
7. LED is constructed from Ga-As-P semiconducting material. The energy gap of this LED is 1.9 eV. 
Calculate the wavelength of light emitted and its colour. 
 [h=6.63×10
–34 
Js and c=3×10
8
 ms
–1
] 
 (1) 654 nm and red colour (2) 1046 nm and blue colour 
 (3) 1046 nm and red colour (4) 654 nm and orange colour 
Sol. (1) 
 We know that 
hc
E ?
?
 
 
? ?
? ?
1240 in eV
hc
E E in eV
? ? ? 
 
1240
1.9
? ? 
 = 652.63 nm  ? 654 nm 
 Wavelength of red light is 620 nm to 750 nm 
 So, answer is 1. 
  
 
 
 
 
8. Five equal resistances are connected in a network as shown in figure. The net resistance 
between the points A and B is : 
 
R
R
R
R A
B
R
D 
E C 
 
 (1) 
3R
2
 (2) 
R
2
 (3) R (4) 2R 
Sol. (3) 
 It is balanced wheat stone bridge 
 
 
A B
R R
R R
R
o
E
D
 
 So, we know that 
  R
1
R
4
 = R
2
R
3
 
  
3 1
2 4
R R
R R
? 
 
 
A B
R R
R R
 
 
 
2R 
2R
B A
 
 Req ? 
2R 2R
2R 2R
?
?
 
 
2
4R
R
4R
? ?