JEE Advance 2023 Question Paper - 1 with Solutions | JEE Main & Advanced Previous Year Papers PDF Download

 Page 1


 
   
 
  
Answers & Solutions 
for 
JEE (Advanced)-2023 (Paper-1) 
  
SECTION 1 (Maximum Marks : 12) 
• This section contains THREE (03) questions. 
• Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four option(s) is(are) 
correct answer(s). 
• For each question, choose the option(s) corresponding to (all) the correct answer(s). 
• Answer to each question will be evaluated according to the following marking scheme: 
 Full Marks  : +4  ONLY if (all) the correct option(s) is(are) chosen; 
 Partial Marks  : +3  If all the four options are correct but ONLY three options are chosen; 
 Partial Marks  : + 2  If three or more options are correct but ONLY two options are chosen, both of which 
are correct; 
 Partial Marks  : +1 If two or more options are correct but ONLY one option is chosen and it is a correct 
option; 
 Zero Marks  : 0  If none of the options is chosen (i.e. the question is unanswered); 
 Negative Marks :  –2 In all other cases. 
Date: 04/06/2023 
Time : 3 hrs. Max. Marks: 180 
PART-I : PHYSICS 
Page 2


 
   
 
  
Answers & Solutions 
for 
JEE (Advanced)-2023 (Paper-1) 
  
SECTION 1 (Maximum Marks : 12) 
• This section contains THREE (03) questions. 
• Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four option(s) is(are) 
correct answer(s). 
• For each question, choose the option(s) corresponding to (all) the correct answer(s). 
• Answer to each question will be evaluated according to the following marking scheme: 
 Full Marks  : +4  ONLY if (all) the correct option(s) is(are) chosen; 
 Partial Marks  : +3  If all the four options are correct but ONLY three options are chosen; 
 Partial Marks  : + 2  If three or more options are correct but ONLY two options are chosen, both of which 
are correct; 
 Partial Marks  : +1 If two or more options are correct but ONLY one option is chosen and it is a correct 
option; 
 Zero Marks  : 0  If none of the options is chosen (i.e. the question is unanswered); 
 Negative Marks :  –2 In all other cases. 
Date: 04/06/2023 
Time : 3 hrs. Max. Marks: 180 
PART-I : PHYSICS 
 
 
   
  
1. A slide with a frictionless curved surface, which becomes horizontal at its lower end, is fixed on the terrace of a 
building of height 3h from the ground, as shown in the figure. A spherical ball of mass m is released on the slide 
from rest at a height h from the top of the terrace. The ball leaves the slide with a velocity 
00
ˆ u u x = and falls on 
the ground at a distance d from the building making an angle ? with the horizontal. It bounces off with a velocity 
v and reaches a maximum height h1. The acceleration due to gravity is g and the coefficient of restitution of the 
ground is 1/ 3. Which of the following statement(s) is(are) correct? 
 
 (A) 
0
ˆ 2 u ghx = (B) ˆˆ 2 ( – ) v gh x z = 
 (C) ? = 60° (D) 
1
/ 2 3 dh = 
Answer (A, C, D) 
Sol.  
 
0
2 u gh = 
Page 3


 
   
 
  
Answers & Solutions 
for 
JEE (Advanced)-2023 (Paper-1) 
  
SECTION 1 (Maximum Marks : 12) 
• This section contains THREE (03) questions. 
• Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four option(s) is(are) 
correct answer(s). 
• For each question, choose the option(s) corresponding to (all) the correct answer(s). 
• Answer to each question will be evaluated according to the following marking scheme: 
 Full Marks  : +4  ONLY if (all) the correct option(s) is(are) chosen; 
 Partial Marks  : +3  If all the four options are correct but ONLY three options are chosen; 
 Partial Marks  : + 2  If three or more options are correct but ONLY two options are chosen, both of which 
are correct; 
 Partial Marks  : +1 If two or more options are correct but ONLY one option is chosen and it is a correct 
option; 
 Zero Marks  : 0  If none of the options is chosen (i.e. the question is unanswered); 
 Negative Marks :  –2 In all other cases. 
Date: 04/06/2023 
Time : 3 hrs. Max. Marks: 180 
PART-I : PHYSICS 
 
 
   
  
1. A slide with a frictionless curved surface, which becomes horizontal at its lower end, is fixed on the terrace of a 
building of height 3h from the ground, as shown in the figure. A spherical ball of mass m is released on the slide 
from rest at a height h from the top of the terrace. The ball leaves the slide with a velocity 
00
ˆ u u x = and falls on 
the ground at a distance d from the building making an angle ? with the horizontal. It bounces off with a velocity 
v and reaches a maximum height h1. The acceleration due to gravity is g and the coefficient of restitution of the 
ground is 1/ 3. Which of the following statement(s) is(are) correct? 
 
 (A) 
0
ˆ 2 u ghx = (B) ˆˆ 2 ( – ) v gh x z = 
 (C) ? = 60° (D) 
1
/ 2 3 dh = 
Answer (A, C, D) 
Sol.  
 
0
2 u gh = 
   
 
 
   
  
 2 (3 )
z
v g h = 
 tan 3
z
v
u
? = = 
 60 ? = ? 
 
( )
00
33
2 2 (2)
hh
d u T u gh
gg
? ? ? ?
= = =
? ? ? ?
? ? ? ?
 
 Velocity after collision, only velocity along z-direction change 
 
1
2
z
v ev gh == 
 
10
ˆˆ
v v k u i =+ 
 
ˆˆ
2gh i k
??
=+
??
 
 
2
1
1
2
v
hh
g
== 
 Finally, 
0
2 , 60 , 2 3
d
u gh
h
= ? = ? = 
2. A plane polarized blue light ray is incident on a prism such that there is no reflection from the surface of the 
prism. The angle of deviation of the emergent ray is ? = 60° (see Figure-1). The angle of minimum deviation for 
red light from the same prism is ?min = 30° (see Figure-2). The refractive index of the prism material for blue light 
is 3. Which of the following statement(s) is(are) correct? 
 
 (A) The blue light is polarized in the plane of incidence. 
 (B) The angle of the prism is 45°. 
 (C) The refractive index of the material of the prism for red light is 2. 
 (D) The angle of refraction for blue light in air at the exit plane of the prism is 60°. 
Answer (A, C, D) 
Page 4


 
   
 
  
Answers & Solutions 
for 
JEE (Advanced)-2023 (Paper-1) 
  
SECTION 1 (Maximum Marks : 12) 
• This section contains THREE (03) questions. 
• Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four option(s) is(are) 
correct answer(s). 
• For each question, choose the option(s) corresponding to (all) the correct answer(s). 
• Answer to each question will be evaluated according to the following marking scheme: 
 Full Marks  : +4  ONLY if (all) the correct option(s) is(are) chosen; 
 Partial Marks  : +3  If all the four options are correct but ONLY three options are chosen; 
 Partial Marks  : + 2  If three or more options are correct but ONLY two options are chosen, both of which 
are correct; 
 Partial Marks  : +1 If two or more options are correct but ONLY one option is chosen and it is a correct 
option; 
 Zero Marks  : 0  If none of the options is chosen (i.e. the question is unanswered); 
 Negative Marks :  –2 In all other cases. 
Date: 04/06/2023 
Time : 3 hrs. Max. Marks: 180 
PART-I : PHYSICS 
 
 
   
  
1. A slide with a frictionless curved surface, which becomes horizontal at its lower end, is fixed on the terrace of a 
building of height 3h from the ground, as shown in the figure. A spherical ball of mass m is released on the slide 
from rest at a height h from the top of the terrace. The ball leaves the slide with a velocity 
00
ˆ u u x = and falls on 
the ground at a distance d from the building making an angle ? with the horizontal. It bounces off with a velocity 
v and reaches a maximum height h1. The acceleration due to gravity is g and the coefficient of restitution of the 
ground is 1/ 3. Which of the following statement(s) is(are) correct? 
 
 (A) 
0
ˆ 2 u ghx = (B) ˆˆ 2 ( – ) v gh x z = 
 (C) ? = 60° (D) 
1
/ 2 3 dh = 
Answer (A, C, D) 
Sol.  
 
0
2 u gh = 
   
 
 
   
  
 2 (3 )
z
v g h = 
 tan 3
z
v
u
? = = 
 60 ? = ? 
 
( )
00
33
2 2 (2)
hh
d u T u gh
gg
? ? ? ?
= = =
? ? ? ?
? ? ? ?
 
 Velocity after collision, only velocity along z-direction change 
 
1
2
z
v ev gh == 
 
10
ˆˆ
v v k u i =+ 
 
ˆˆ
2gh i k
??
=+
??
 
 
2
1
1
2
v
hh
g
== 
 Finally, 
0
2 , 60 , 2 3
d
u gh
h
= ? = ? = 
2. A plane polarized blue light ray is incident on a prism such that there is no reflection from the surface of the 
prism. The angle of deviation of the emergent ray is ? = 60° (see Figure-1). The angle of minimum deviation for 
red light from the same prism is ?min = 30° (see Figure-2). The refractive index of the prism material for blue light 
is 3. Which of the following statement(s) is(are) correct? 
 
 (A) The blue light is polarized in the plane of incidence. 
 (B) The angle of the prism is 45°. 
 (C) The refractive index of the material of the prism for red light is 2. 
 (D) The angle of refraction for blue light in air at the exit plane of the prism is 60°. 
Answer (A, C, D) 
 
 
   
  
Sol. For no reflection 
  
 tan 3 i = 
  i = 60 
 
1
1
sin
3, 30
sin
i
r
r
= = ? 
 ? = i + e – r1 – r2 = 60° 
 
2
60 30 er = ? = ? 
 60 A=? 
 For red light, 
 
sin
2
2
sin
2
m
A
A
+? ??
??
??
? = =
??
??
??
 
3. In a circuit shown in the figure, the capacitor C is initially uncharged and the key K is open. In this condition, a 
current of 1 A flows through the 1 ? resistor. The key is closed at time t = t
0
. Which of the following statement(s) 
is(are) correct? 
 [Given : e
–1
 = 0.36] 
 
 (A) The value of the resistance R is 3 ?. 
 (B) For t < t
0
, the value of current I
1
 is 2 A. 
 (C) At t = t
0
 + 7.2 ?s, the current in the capacitor is 0.6 A. 
 (D) For t ? ?, the charge on the capacitor is 12 ?C. 
Answer (A, B, C, D) 
Page 5


 
   
 
  
Answers & Solutions 
for 
JEE (Advanced)-2023 (Paper-1) 
  
SECTION 1 (Maximum Marks : 12) 
• This section contains THREE (03) questions. 
• Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four option(s) is(are) 
correct answer(s). 
• For each question, choose the option(s) corresponding to (all) the correct answer(s). 
• Answer to each question will be evaluated according to the following marking scheme: 
 Full Marks  : +4  ONLY if (all) the correct option(s) is(are) chosen; 
 Partial Marks  : +3  If all the four options are correct but ONLY three options are chosen; 
 Partial Marks  : + 2  If three or more options are correct but ONLY two options are chosen, both of which 
are correct; 
 Partial Marks  : +1 If two or more options are correct but ONLY one option is chosen and it is a correct 
option; 
 Zero Marks  : 0  If none of the options is chosen (i.e. the question is unanswered); 
 Negative Marks :  –2 In all other cases. 
Date: 04/06/2023 
Time : 3 hrs. Max. Marks: 180 
PART-I : PHYSICS 
 
 
   
  
1. A slide with a frictionless curved surface, which becomes horizontal at its lower end, is fixed on the terrace of a 
building of height 3h from the ground, as shown in the figure. A spherical ball of mass m is released on the slide 
from rest at a height h from the top of the terrace. The ball leaves the slide with a velocity 
00
ˆ u u x = and falls on 
the ground at a distance d from the building making an angle ? with the horizontal. It bounces off with a velocity 
v and reaches a maximum height h1. The acceleration due to gravity is g and the coefficient of restitution of the 
ground is 1/ 3. Which of the following statement(s) is(are) correct? 
 
 (A) 
0
ˆ 2 u ghx = (B) ˆˆ 2 ( – ) v gh x z = 
 (C) ? = 60° (D) 
1
/ 2 3 dh = 
Answer (A, C, D) 
Sol.  
 
0
2 u gh = 
   
 
 
   
  
 2 (3 )
z
v g h = 
 tan 3
z
v
u
? = = 
 60 ? = ? 
 
( )
00
33
2 2 (2)
hh
d u T u gh
gg
? ? ? ?
= = =
? ? ? ?
? ? ? ?
 
 Velocity after collision, only velocity along z-direction change 
 
1
2
z
v ev gh == 
 
10
ˆˆ
v v k u i =+ 
 
ˆˆ
2gh i k
??
=+
??
 
 
2
1
1
2
v
hh
g
== 
 Finally, 
0
2 , 60 , 2 3
d
u gh
h
= ? = ? = 
2. A plane polarized blue light ray is incident on a prism such that there is no reflection from the surface of the 
prism. The angle of deviation of the emergent ray is ? = 60° (see Figure-1). The angle of minimum deviation for 
red light from the same prism is ?min = 30° (see Figure-2). The refractive index of the prism material for blue light 
is 3. Which of the following statement(s) is(are) correct? 
 
 (A) The blue light is polarized in the plane of incidence. 
 (B) The angle of the prism is 45°. 
 (C) The refractive index of the material of the prism for red light is 2. 
 (D) The angle of refraction for blue light in air at the exit plane of the prism is 60°. 
Answer (A, C, D) 
 
 
   
  
Sol. For no reflection 
  
 tan 3 i = 
  i = 60 
 
1
1
sin
3, 30
sin
i
r
r
= = ? 
 ? = i + e – r1 – r2 = 60° 
 
2
60 30 er = ? = ? 
 60 A=? 
 For red light, 
 
sin
2
2
sin
2
m
A
A
+? ??
??
??
? = =
??
??
??
 
3. In a circuit shown in the figure, the capacitor C is initially uncharged and the key K is open. In this condition, a 
current of 1 A flows through the 1 ? resistor. The key is closed at time t = t
0
. Which of the following statement(s) 
is(are) correct? 
 [Given : e
–1
 = 0.36] 
 
 (A) The value of the resistance R is 3 ?. 
 (B) For t < t
0
, the value of current I
1
 is 2 A. 
 (C) At t = t
0
 + 7.2 ?s, the current in the capacitor is 0.6 A. 
 (D) For t ? ?, the charge on the capacitor is 12 ?C. 
Answer (A, B, C, D) 
   
 
 
   
  
Sol. 15 – IR = 6 
 I
1
 [3] = 6 
 
1
2A I = 
 I = I
1
 + 1 = 3 
 15 – 3R = 6 
 ? 3 R=? 
 Eq. circuit is 
 
eq
1 1 1
1
33 R
= + + 
 
eq
3
5
R =? 
 E
eq
 = 5 + 5 + 0 = 10  
 
eq
3
10 6 V
5
E = ? = 
 Current in circuit is 
/
6
3
3
5
t CR
e
-
??
+
??
??
  
  
–6
6
7.2 10
2 10 3 6
65
18
e
-
?
-
? ? ?
?
= 
  
1
30 30
0.36
18 18
e
-
= ? = ? 
  0.6 A = 
 At steady state, voltage across capacitor = 6 V 
 Q = 6 × 2 = 12? C 
SECTION 2 (Maximum Marks : 12) 
• This section contains FOUR (04) questions. 
• Each question has FOUR options (A), (B), (C) and (D). ONLY ONE of these four options is the correct answer. 
• For each question, choose the option corresponding to the correct answer. 
• Answer to each question will be evaluated according to the following marking scheme: 
 Full Marks  : +3 If ONLY the correct option is chosen; 
 Zero Marks  : 0 If none of the options is chosen (i.e. the question is unanswered); 
 Negative Marks  : -1 In all other cases.