JEE Advanced 2018 Solved Paper - 2 PDF Download

 Page 1


1
Answers & Solutions
for for for for for
JEE (Advanced)-2018
Time : 3 hrs. Max. Marks: 180
PAPER - 2
PART-I : PHYSICS
SECTION - 1 (Maximum Marks : 24)
? This section contains SIX (06) questions.
? Each question has FOUR options for correct answer(s). ONE OR MORE THAN ONE of these four
option(s) is (are) correct option(s).
? For each question, choose the correct option(s) to answer the question.
? Answer to each question will be evaluated according to the following marking scheme:
Full Marks : +4 If only (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 options.
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.
For Example: If first, third and fourth are the ONLY three correct options for a question with second
option being an incorrect option; selecting only all the three correct options will result in +4 marks.
Selecting only two of the three correct options (e.g. the first and fourth options), without selecting
any incorrect option (second option in this case), will result in +2 marks. Selecting only one of the three
correct options (either first or third or fourth option), without selecting any incorrect option (second
option in this case), will result in +1 marks. Selecting any incorrect option(s) (second option in this
case), with or without selection of any correct option(s) will result in –2 marks.
Page 2


1
Answers & Solutions
for for for for for
JEE (Advanced)-2018
Time : 3 hrs. Max. Marks: 180
PAPER - 2
PART-I : PHYSICS
SECTION - 1 (Maximum Marks : 24)
? This section contains SIX (06) questions.
? Each question has FOUR options for correct answer(s). ONE OR MORE THAN ONE of these four
option(s) is (are) correct option(s).
? For each question, choose the correct option(s) to answer the question.
? Answer to each question will be evaluated according to the following marking scheme:
Full Marks : +4 If only (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 options.
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.
For Example: If first, third and fourth are the ONLY three correct options for a question with second
option being an incorrect option; selecting only all the three correct options will result in +4 marks.
Selecting only two of the three correct options (e.g. the first and fourth options), without selecting
any incorrect option (second option in this case), will result in +2 marks. Selecting only one of the three
correct options (either first or third or fourth option), without selecting any incorrect option (second
option in this case), will result in +1 marks. Selecting any incorrect option(s) (second option in this
case), with or without selection of any correct option(s) will result in –2 marks.
2
JEE (ADVANCED)-2018 (PAPER-2)
1. A particle of mass m is initially at rest at the origin. It is subjected to a force and starts moving along
the x-axis. Its kinetic energy K changes with time as dK/dt  = ? ? ? ? ?t, where ? ? ? ? ? is a positive constant of
appropriate dimensions. Which of the following statements is (are) true?
(A) The force applied on the particle is constant
(B) The speed of the particle is proportional to time
(C) The distance of the particle from the origin increases linearly with time
(D) The force is conservative
Answer (A, B, D)
Sol.
? ? ?
2
1dK dv
Kmv mv
2dt dt
given, ?? ? ??
dK dv
tmv t
dt dt
?
??
? ? ?
??
vt 22
00
vt
vdv tdt
m2m2
?
?
?vt
m
 ? 
?
??
dv
a
dt m
??? ? Fma m constant
??
? ? ?
2
dS t
tS
dt m m 2
2. Consider a thin square plate floating on a viscous liquid in a large tank. The height h of the liquid in
the tank is much less than the width of the tank. The floating plate is pulled horizontally with a
constant velocity u
0
. Which of the following statements is (are) true?
(A) The resistive force of liquid on the plate is inversely proportional to h
(B) The resistive force of liquid on the plate is independent of the area of the plate
(C) The tangential (shear) stress on the floor of the tank increases with u
0
(D) The tangential (shear) stress on the plate varies linearly with the viscosity ? ? ? ? ? of the liquid
Answer (A, C, D)
Sol. u
0
F
v
A
Plate
??
??
??
??
v
dv
FA
dz
Since height h of the liquid in tank is very small 
? ??
? ??
??
?
??
0
u dv v
dz z h
??
??
??
??
0
v
u
F()A
h
??
?? ? ??
??
??
vv0v v
1
F,Fu,FA,F
h
Page 3


1
Answers & Solutions
for for for for for
JEE (Advanced)-2018
Time : 3 hrs. Max. Marks: 180
PAPER - 2
PART-I : PHYSICS
SECTION - 1 (Maximum Marks : 24)
? This section contains SIX (06) questions.
? Each question has FOUR options for correct answer(s). ONE OR MORE THAN ONE of these four
option(s) is (are) correct option(s).
? For each question, choose the correct option(s) to answer the question.
? Answer to each question will be evaluated according to the following marking scheme:
Full Marks : +4 If only (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 options.
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.
For Example: If first, third and fourth are the ONLY three correct options for a question with second
option being an incorrect option; selecting only all the three correct options will result in +4 marks.
Selecting only two of the three correct options (e.g. the first and fourth options), without selecting
any incorrect option (second option in this case), will result in +2 marks. Selecting only one of the three
correct options (either first or third or fourth option), without selecting any incorrect option (second
option in this case), will result in +1 marks. Selecting any incorrect option(s) (second option in this
case), with or without selection of any correct option(s) will result in –2 marks.
2
JEE (ADVANCED)-2018 (PAPER-2)
1. A particle of mass m is initially at rest at the origin. It is subjected to a force and starts moving along
the x-axis. Its kinetic energy K changes with time as dK/dt  = ? ? ? ? ?t, where ? ? ? ? ? is a positive constant of
appropriate dimensions. Which of the following statements is (are) true?
(A) The force applied on the particle is constant
(B) The speed of the particle is proportional to time
(C) The distance of the particle from the origin increases linearly with time
(D) The force is conservative
Answer (A, B, D)
Sol.
? ? ?
2
1dK dv
Kmv mv
2dt dt
given, ?? ? ??
dK dv
tmv t
dt dt
?
??
? ? ?
??
vt 22
00
vt
vdv tdt
m2m2
?
?
?vt
m
 ? 
?
??
dv
a
dt m
??? ? Fma m constant
??
? ? ?
2
dS t
tS
dt m m 2
2. Consider a thin square plate floating on a viscous liquid in a large tank. The height h of the liquid in
the tank is much less than the width of the tank. The floating plate is pulled horizontally with a
constant velocity u
0
. Which of the following statements is (are) true?
(A) The resistive force of liquid on the plate is inversely proportional to h
(B) The resistive force of liquid on the plate is independent of the area of the plate
(C) The tangential (shear) stress on the floor of the tank increases with u
0
(D) The tangential (shear) stress on the plate varies linearly with the viscosity ? ? ? ? ? of the liquid
Answer (A, C, D)
Sol. u
0
F
v
A
Plate
??
??
??
??
v
dv
FA
dz
Since height h of the liquid in tank is very small 
? ??
? ??
??
?
??
0
u dv v
dz z h
??
??
??
??
0
v
u
F()A
h
??
?? ? ??
??
??
vv0v v
1
F,Fu,FA,F
h
3
JEE (ADVANCED)-2018 (PAPER-2)
3. An infinitely long thin non-conducting wire is parallel to the z-axis and carries a uniform line charge
density ? ? ? ? ?. It pierces a thin non-conducting spherical shell of radius R in such a way that the arc PQ
subtends an angle 120° at the centre O of the spherical shell, as shown in the figure. The permittivity
of free space is ? ? ? ? ?
0
. Which of the following statements is (are) true?
?
P
R
O
Q
120°
z
(A) The electric flux through the shell is 
0
3R ?
?
(B) The z-component of the electric field is zero at all the points on the surface of the shell
(C) The electric flux through the shell is 
0
2R ?
?
(D) The electric field is normal to the surface of the shell at all points
Answer (A, B)
Sol. PQ = (2) R sin 60°
?
P
R
O
Q
120°
z
R
??
3
(2R) 3R
2
??
?? enclosed
Q3R ??
We have ??
?
enclosed
0
q
?
??
?
??
??
??
?
?? 0
3R
Also electric filed is perpendicular to wire so Z-component will be zero.
Page 4


1
Answers & Solutions
for for for for for
JEE (Advanced)-2018
Time : 3 hrs. Max. Marks: 180
PAPER - 2
PART-I : PHYSICS
SECTION - 1 (Maximum Marks : 24)
? This section contains SIX (06) questions.
? Each question has FOUR options for correct answer(s). ONE OR MORE THAN ONE of these four
option(s) is (are) correct option(s).
? For each question, choose the correct option(s) to answer the question.
? Answer to each question will be evaluated according to the following marking scheme:
Full Marks : +4 If only (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 options.
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.
For Example: If first, third and fourth are the ONLY three correct options for a question with second
option being an incorrect option; selecting only all the three correct options will result in +4 marks.
Selecting only two of the three correct options (e.g. the first and fourth options), without selecting
any incorrect option (second option in this case), will result in +2 marks. Selecting only one of the three
correct options (either first or third or fourth option), without selecting any incorrect option (second
option in this case), will result in +1 marks. Selecting any incorrect option(s) (second option in this
case), with or without selection of any correct option(s) will result in –2 marks.
2
JEE (ADVANCED)-2018 (PAPER-2)
1. A particle of mass m is initially at rest at the origin. It is subjected to a force and starts moving along
the x-axis. Its kinetic energy K changes with time as dK/dt  = ? ? ? ? ?t, where ? ? ? ? ? is a positive constant of
appropriate dimensions. Which of the following statements is (are) true?
(A) The force applied on the particle is constant
(B) The speed of the particle is proportional to time
(C) The distance of the particle from the origin increases linearly with time
(D) The force is conservative
Answer (A, B, D)
Sol.
? ? ?
2
1dK dv
Kmv mv
2dt dt
given, ?? ? ??
dK dv
tmv t
dt dt
?
??
? ? ?
??
vt 22
00
vt
vdv tdt
m2m2
?
?
?vt
m
 ? 
?
??
dv
a
dt m
??? ? Fma m constant
??
? ? ?
2
dS t
tS
dt m m 2
2. Consider a thin square plate floating on a viscous liquid in a large tank. The height h of the liquid in
the tank is much less than the width of the tank. The floating plate is pulled horizontally with a
constant velocity u
0
. Which of the following statements is (are) true?
(A) The resistive force of liquid on the plate is inversely proportional to h
(B) The resistive force of liquid on the plate is independent of the area of the plate
(C) The tangential (shear) stress on the floor of the tank increases with u
0
(D) The tangential (shear) stress on the plate varies linearly with the viscosity ? ? ? ? ? of the liquid
Answer (A, C, D)
Sol. u
0
F
v
A
Plate
??
??
??
??
v
dv
FA
dz
Since height h of the liquid in tank is very small 
? ??
? ??
??
?
??
0
u dv v
dz z h
??
??
??
??
0
v
u
F()A
h
??
?? ? ??
??
??
vv0v v
1
F,Fu,FA,F
h
3
JEE (ADVANCED)-2018 (PAPER-2)
3. An infinitely long thin non-conducting wire is parallel to the z-axis and carries a uniform line charge
density ? ? ? ? ?. It pierces a thin non-conducting spherical shell of radius R in such a way that the arc PQ
subtends an angle 120° at the centre O of the spherical shell, as shown in the figure. The permittivity
of free space is ? ? ? ? ?
0
. Which of the following statements is (are) true?
?
P
R
O
Q
120°
z
(A) The electric flux through the shell is 
0
3R ?
?
(B) The z-component of the electric field is zero at all the points on the surface of the shell
(C) The electric flux through the shell is 
0
2R ?
?
(D) The electric field is normal to the surface of the shell at all points
Answer (A, B)
Sol. PQ = (2) R sin 60°
?
P
R
O
Q
120°
z
R
??
3
(2R) 3R
2
??
?? enclosed
Q3R ??
We have ??
?
enclosed
0
q
?
??
?
??
??
??
?
?? 0
3R
Also electric filed is perpendicular to wire so Z-component will be zero.
4
JEE (ADVANCED)-2018 (PAPER-2)
4. A wire is bent in the shape of a right angled triangle and is placed in front of a concave mirror of focal
length f, as shown in the figure. Which of the figures shown in the four options qualitatively represent( s)
the shape of the image of the bent wire? (These figures are not to scale).
45°
f
f
2
(A)
?
? > 45°
(B)
?
(C)
?
0 < < 45° ?? 
(D)
?
Answer (D)
Sol. Image of point A
f/2
B
A
Q
(f – x)
x
C P O
?? ? ?
? ??
?
??
??
11 1
vf
f vf
2
? ?? ? ?
?
AB
AB
I f
I2AB
f
AB
2
For Height of PQ
?
?? ??? ? ?
?? ? ?
11 1 1 1 1 f(fx)
v
v(fx) f v (fx) f x
?
? ??
?? ?
??
??
??
PQ
I f(fx) f
PQ x{(fx)} x
?
PQ
f f2(AB)x
IPQ
xx f
??? ? ??
??? ? ??? ?     
2(AB)x
PQ
f
??
?
??
??
?
I
PQ
 = 2AB
(Size of image is independent of x. So, final image will be of same height terminating at infinity)
Page 5


1
Answers & Solutions
for for for for for
JEE (Advanced)-2018
Time : 3 hrs. Max. Marks: 180
PAPER - 2
PART-I : PHYSICS
SECTION - 1 (Maximum Marks : 24)
? This section contains SIX (06) questions.
? Each question has FOUR options for correct answer(s). ONE OR MORE THAN ONE of these four
option(s) is (are) correct option(s).
? For each question, choose the correct option(s) to answer the question.
? Answer to each question will be evaluated according to the following marking scheme:
Full Marks : +4 If only (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 options.
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.
For Example: If first, third and fourth are the ONLY three correct options for a question with second
option being an incorrect option; selecting only all the three correct options will result in +4 marks.
Selecting only two of the three correct options (e.g. the first and fourth options), without selecting
any incorrect option (second option in this case), will result in +2 marks. Selecting only one of the three
correct options (either first or third or fourth option), without selecting any incorrect option (second
option in this case), will result in +1 marks. Selecting any incorrect option(s) (second option in this
case), with or without selection of any correct option(s) will result in –2 marks.
2
JEE (ADVANCED)-2018 (PAPER-2)
1. A particle of mass m is initially at rest at the origin. It is subjected to a force and starts moving along
the x-axis. Its kinetic energy K changes with time as dK/dt  = ? ? ? ? ?t, where ? ? ? ? ? is a positive constant of
appropriate dimensions. Which of the following statements is (are) true?
(A) The force applied on the particle is constant
(B) The speed of the particle is proportional to time
(C) The distance of the particle from the origin increases linearly with time
(D) The force is conservative
Answer (A, B, D)
Sol.
? ? ?
2
1dK dv
Kmv mv
2dt dt
given, ?? ? ??
dK dv
tmv t
dt dt
?
??
? ? ?
??
vt 22
00
vt
vdv tdt
m2m2
?
?
?vt
m
 ? 
?
??
dv
a
dt m
??? ? Fma m constant
??
? ? ?
2
dS t
tS
dt m m 2
2. Consider a thin square plate floating on a viscous liquid in a large tank. The height h of the liquid in
the tank is much less than the width of the tank. The floating plate is pulled horizontally with a
constant velocity u
0
. Which of the following statements is (are) true?
(A) The resistive force of liquid on the plate is inversely proportional to h
(B) The resistive force of liquid on the plate is independent of the area of the plate
(C) The tangential (shear) stress on the floor of the tank increases with u
0
(D) The tangential (shear) stress on the plate varies linearly with the viscosity ? ? ? ? ? of the liquid
Answer (A, C, D)
Sol. u
0
F
v
A
Plate
??
??
??
??
v
dv
FA
dz
Since height h of the liquid in tank is very small 
? ??
? ??
??
?
??
0
u dv v
dz z h
??
??
??
??
0
v
u
F()A
h
??
?? ? ??
??
??
vv0v v
1
F,Fu,FA,F
h
3
JEE (ADVANCED)-2018 (PAPER-2)
3. An infinitely long thin non-conducting wire is parallel to the z-axis and carries a uniform line charge
density ? ? ? ? ?. It pierces a thin non-conducting spherical shell of radius R in such a way that the arc PQ
subtends an angle 120° at the centre O of the spherical shell, as shown in the figure. The permittivity
of free space is ? ? ? ? ?
0
. Which of the following statements is (are) true?
?
P
R
O
Q
120°
z
(A) The electric flux through the shell is 
0
3R ?
?
(B) The z-component of the electric field is zero at all the points on the surface of the shell
(C) The electric flux through the shell is 
0
2R ?
?
(D) The electric field is normal to the surface of the shell at all points
Answer (A, B)
Sol. PQ = (2) R sin 60°
?
P
R
O
Q
120°
z
R
??
3
(2R) 3R
2
??
?? enclosed
Q3R ??
We have ??
?
enclosed
0
q
?
??
?
??
??
??
?
?? 0
3R
Also electric filed is perpendicular to wire so Z-component will be zero.
4
JEE (ADVANCED)-2018 (PAPER-2)
4. A wire is bent in the shape of a right angled triangle and is placed in front of a concave mirror of focal
length f, as shown in the figure. Which of the figures shown in the four options qualitatively represent( s)
the shape of the image of the bent wire? (These figures are not to scale).
45°
f
f
2
(A)
?
? > 45°
(B)
?
(C)
?
0 < < 45° ?? 
(D)
?
Answer (D)
Sol. Image of point A
f/2
B
A
Q
(f – x)
x
C P O
?? ? ?
? ??
?
??
??
11 1
vf
f vf
2
? ?? ? ?
?
AB
AB
I f
I2AB
f
AB
2
For Height of PQ
?
?? ??? ? ?
?? ? ?
11 1 1 1 1 f(fx)
v
v(fx) f v (fx) f x
?
? ??
?? ?
??
??
??
PQ
I f(fx) f
PQ x{(fx)} x
?
PQ
f f2(AB)x
IPQ
xx f
??? ? ??
??? ? ??? ?     
2(AB)x
PQ
f
??
?
??
??
?
I
PQ
 = 2AB
(Size of image is independent of x. So, final image will be of same height terminating at infinity)
5
JEE (ADVANCED)-2018 (PAPER-2)
5. In a radioactive decay chain, 
232
90
Th
 nucleus decays to 
212
82
Pb
 nucleus. Let N
?
 and N
?
 be the number
of  ? ? ? ? ?  and ? ? ? ? ?
–  
particles,  respectively,  emitted  in  this  decay  process.  Which  of  the following
statements is (are) true?
(A)
?
? N5
(B)
?
? N6
(C)
?
? N2
(D)
?
? N4
Answer (A, C)
Sol.
?? ?
?
?? ? ? ?
Decay AA4
ZZ2
XY
Decay AA
ZZ11
XX
?
??
?
????? ?
?? ?
232 212
90 82
Th Pb
No. of ?-particles emitted 
?
??
232 212
5
4
Since Z decreases by (90 – 82) = 8 only
Hence no. of ?
–
 decay = 2
6. In an experiment to measure the speed of sound by a resonating air column, a tuning fork of frequency
500 Hz is used. The length of the air column is varied by changing the level of water in the resonance
tube. Two successive resonances are heard at air columns of length 50.7 cm and 83.9 cm. Which of
the following statements is (are) true?
(A) The speed of sound determined from this experiment is 332 ms
–1
(B) The end correction in this experiment is 0.9 cm
(C) The wavelength of the sound wave is 66.4 cm
(D) The resonance at 50.7 cm corresponds to the fundamental harmonic
Answer (A, B, C)
Sol.
?
?? (2n–1) 50.7 e
4
?? 2(n 1)–1 83.9 e
4
?
?? ?
?
?
?? 83.9–50.7 33.2cm
2
?? = 66.4 cm
v = ?f = 66.4 × 500 × 10
–2
 m/s = 332 m/s
For, n = 2, e = – 0.9 cm