JEE Mains 9 April 2019 Question Paper Shift 1 | JEE Main & Advanced Previous Year Papers PDF Download

 Page 1


Time : 3 hrs. M.M. : 360
Answers & Solutions
for for for for for
JEE (MAIN)-2019 (Online) Phase-2
Important Instructions :
1. The test is of 3 hours duration.
2. The Test Booklet consists of 90 questions. The maximum marks are 360.
3. There are three parts in the question paper A, B, C consisting of Physics, Chemistry and Mathematics
having 30 questions in each part of equal weightage.
4. Each question is allotted 4 (four) marks for each correct response. ¼ (one-fourth) marks will be deducted
for indicating incorrect response of each question. No deduction from the total score will be made if no
response is indicated for an item in the answer sheet.
5. There is only one correct response for each question.
(Physics, Chemistry and Mathematics)
09/04/2019
Morning
Page 2


Time : 3 hrs. M.M. : 360
Answers & Solutions
for for for for for
JEE (MAIN)-2019 (Online) Phase-2
Important Instructions :
1. The test is of 3 hours duration.
2. The Test Booklet consists of 90 questions. The maximum marks are 360.
3. There are three parts in the question paper A, B, C consisting of Physics, Chemistry and Mathematics
having 30 questions in each part of equal weightage.
4. Each question is allotted 4 (four) marks for each correct response. ¼ (one-fourth) marks will be deducted
for indicating incorrect response of each question. No deduction from the total score will be made if no
response is indicated for an item in the answer sheet.
5. There is only one correct response for each question.
(Physics, Chemistry and Mathematics)
09/04/2019
Morning
JEE (MAIN)-2019 (Online) Phase-2
PART–A : PHYSICS
1. Determine the charge on the capacitor in the
following circuit :
72 V
6 ??
4 ??
2 ??
10 ?? 10 F ?
(1) 200 ?C (2) 60 ?C
(3) 10 ?C (4) 2 ?C
Answer (1)
Sol. At steady state current through capacitor is
zero.
V
C
 = V
1
?? ?
10
53
VV
69
6 ?
72 V
2 ?
4 ? 10 ? V
1
??
??
?
1
572 3
V20 V
69
Q
1
= CV
1
= 200 ?C
2. The magnetic field of a plane electromagnetic
wave is given by :
B

 = 
0
ˆ
Bi

[cos(kz – ?t) + B
1
ˆ
j cos(kz + ?t)
where B
0
 = 3 × 10
–5 
T and B
1
 = 2 × 10
–6 
T.
The rms value of the force experienced by a
stationary charge Q = 10
–4
 C at z =0 is closest
to:
(1) 0.6 N (2) 0.9 N
(3) 3 × 10
–2 
N (4) 0.1 N
Answer (1)
Sol. ?

11
ECB
?

22
ECB
Also ?

12
EE
?
??
22
net 1 2
FEE
2
?
?
??? ? ?
4
86
10
310 3010
2
?
??
?
810
90 10 10
2
 0.6 N
3. A stationary horizontal disc is free to rotate
about its axis. When a torque is applied on it, its
kinetic energy as a function of ?, where ? is the
angle by which it has rotated, is given as k ?
2
. If
its moment of inertia is I then the angular
acceleration of the disc is:
(1)
2k
I
?
(2)
k
I
?
(3)
k
2I
?
(4)
k
4I
?
Answer (1)
Sol.
??
?
dE
d
?? ? 2k I
?
??
2k
I
4. The stream of a river is flowing with a speed of
2 km/h. A swimmer can swim at a speed of
4 km/h. What should be the direction of the
swimmer with respect to the flow of the river to
cross the river straight?
(1) 60° (2) 90°
(3) 150° (4) 120°
Answer (4)
Sol. Draw velocity diagram
?
?
v
r
v
sr
v
sg
?? ?
r
sr
v 1
sin
v2
? = 30°
? = 90 + ? = 120°
Page 3


Time : 3 hrs. M.M. : 360
Answers & Solutions
for for for for for
JEE (MAIN)-2019 (Online) Phase-2
Important Instructions :
1. The test is of 3 hours duration.
2. The Test Booklet consists of 90 questions. The maximum marks are 360.
3. There are three parts in the question paper A, B, C consisting of Physics, Chemistry and Mathematics
having 30 questions in each part of equal weightage.
4. Each question is allotted 4 (four) marks for each correct response. ¼ (one-fourth) marks will be deducted
for indicating incorrect response of each question. No deduction from the total score will be made if no
response is indicated for an item in the answer sheet.
5. There is only one correct response for each question.
(Physics, Chemistry and Mathematics)
09/04/2019
Morning
JEE (MAIN)-2019 (Online) Phase-2
PART–A : PHYSICS
1. Determine the charge on the capacitor in the
following circuit :
72 V
6 ??
4 ??
2 ??
10 ?? 10 F ?
(1) 200 ?C (2) 60 ?C
(3) 10 ?C (4) 2 ?C
Answer (1)
Sol. At steady state current through capacitor is
zero.
V
C
 = V
1
?? ?
10
53
VV
69
6 ?
72 V
2 ?
4 ? 10 ? V
1
??
??
?
1
572 3
V20 V
69
Q
1
= CV
1
= 200 ?C
2. The magnetic field of a plane electromagnetic
wave is given by :
B

 = 
0
ˆ
Bi

[cos(kz – ?t) + B
1
ˆ
j cos(kz + ?t)
where B
0
 = 3 × 10
–5 
T and B
1
 = 2 × 10
–6 
T.
The rms value of the force experienced by a
stationary charge Q = 10
–4
 C at z =0 is closest
to:
(1) 0.6 N (2) 0.9 N
(3) 3 × 10
–2 
N (4) 0.1 N
Answer (1)
Sol. ?

11
ECB
?

22
ECB
Also ?

12
EE
?
??
22
net 1 2
FEE
2
?
?
??? ? ?
4
86
10
310 3010
2
?
??
?
810
90 10 10
2
 0.6 N
3. A stationary horizontal disc is free to rotate
about its axis. When a torque is applied on it, its
kinetic energy as a function of ?, where ? is the
angle by which it has rotated, is given as k ?
2
. If
its moment of inertia is I then the angular
acceleration of the disc is:
(1)
2k
I
?
(2)
k
I
?
(3)
k
2I
?
(4)
k
4I
?
Answer (1)
Sol.
??
?
dE
d
?? ? 2k I
?
??
2k
I
4. The stream of a river is flowing with a speed of
2 km/h. A swimmer can swim at a speed of
4 km/h. What should be the direction of the
swimmer with respect to the flow of the river to
cross the river straight?
(1) 60° (2) 90°
(3) 150° (4) 120°
Answer (4)
Sol. Draw velocity diagram
?
?
v
r
v
sr
v
sg
?? ?
r
sr
v 1
sin
v2
? = 30°
? = 90 + ? = 120°
5. A uniform cable of mass ‘M’ and length ‘L’ is
placed on a horizontal surface such that its
th
1
n
??
??
??
 part is hanging below the edge of the
surface. To lift the hanging part of the cable
upto the surface, the work done should be:
(1)
2
MgL
n
(2) nMgL
(3)
2
MgL
2n
(4)
2
2MgL
n
Answer (3)
Sol.
?
1
M
m
n
?
??
i
ML
Ug
n2n
L/n
?
2
MgL
W
2n
6. A signal Acos ?t is transmitted using v
0
sin ?
0
t as
carrier wave. The correct amplitude modulated
(AM) signal is:
(1) ?? ??
00 0 0
AA
v sin t sin – t sin t
22
?? ? ? ? ? ??
(2) (v
0
 + A) cos ?t sin ?
0
t
(3) v
0
sin ?
0
t + Acos ?t
(4) v
0
sin[ ?
0
(1 + 0.01 Asin ?t)t]
Answer (1)
Sol. A= (v
o
 + Acos ?t) sin ?
o
t
= ? ? ??? ? ???
00 0 0
A
v sin( t) [sin( )t sin( )t]
2
7. The following bodies are made to roll up
(without slipping) the same inclined plane from
a horizontal plane : (i) a ring of radius R, (ii) a
solid cylinder of radius 
R
2
 and (iii) a solid
sphere of radius 
R
4
. If, in each case, the speed
of the center of mass at the bottom of the
incline is same, the ratio of the maximum
heights they climb is :
(1) 14 : 15 : 20 (2) 10 : 15 : 7
(3) 4 : 3 : 2 (4) 2 : 3 : 4
Answer (Bonus)
Sol.
2
p
1
mgh I
2
??
For ring ? 
22 2
1
2
1(2mr ) v v
h
2mg g (r)
?
??
?
For cylinder ? 
22
2
2
2
13 v 3v
hmr
22 4 g (r)
??
? ??
??
? ??
For sphere ? 
2
22
3
2
7
m(r)
1v7v
5
h
2 g 10 g (r)
?
?? ?
?
h
1
 : h
2
 : h
3
2 : 
3
2
: 
14
10
20 : 15 : 14
8. A wire of resistance R is bent to form a square
ABCD as shown in the figure. The effective
resistance between E and C is
(E is mid-point of arm CD)
AB
DC E
(1)
3
R
4
(2) R
(3)
1
R
16
(4)
7
R
64
Answer (4)
Sol.
12
R7R
R,R
88
??
eq
18 8
RR7R
??
eq
7R
R
64
?
9. In the density measurement of a cube, the
mass and edge length are measured as (10.00
± 0.10) kg and (0.10 ± 0.01) m, respectively. The
error in the measurement of density is
(1) 0.31 kg/m
3
(2) 0.01 kg/m
3
(3) 0.10 kg/m
3
(4) 0.07 kg/m
3
Answer (Bonus)
Page 4


Time : 3 hrs. M.M. : 360
Answers & Solutions
for for for for for
JEE (MAIN)-2019 (Online) Phase-2
Important Instructions :
1. The test is of 3 hours duration.
2. The Test Booklet consists of 90 questions. The maximum marks are 360.
3. There are three parts in the question paper A, B, C consisting of Physics, Chemistry and Mathematics
having 30 questions in each part of equal weightage.
4. Each question is allotted 4 (four) marks for each correct response. ¼ (one-fourth) marks will be deducted
for indicating incorrect response of each question. No deduction from the total score will be made if no
response is indicated for an item in the answer sheet.
5. There is only one correct response for each question.
(Physics, Chemistry and Mathematics)
09/04/2019
Morning
JEE (MAIN)-2019 (Online) Phase-2
PART–A : PHYSICS
1. Determine the charge on the capacitor in the
following circuit :
72 V
6 ??
4 ??
2 ??
10 ?? 10 F ?
(1) 200 ?C (2) 60 ?C
(3) 10 ?C (4) 2 ?C
Answer (1)
Sol. At steady state current through capacitor is
zero.
V
C
 = V
1
?? ?
10
53
VV
69
6 ?
72 V
2 ?
4 ? 10 ? V
1
??
??
?
1
572 3
V20 V
69
Q
1
= CV
1
= 200 ?C
2. The magnetic field of a plane electromagnetic
wave is given by :
B

 = 
0
ˆ
Bi

[cos(kz – ?t) + B
1
ˆ
j cos(kz + ?t)
where B
0
 = 3 × 10
–5 
T and B
1
 = 2 × 10
–6 
T.
The rms value of the force experienced by a
stationary charge Q = 10
–4
 C at z =0 is closest
to:
(1) 0.6 N (2) 0.9 N
(3) 3 × 10
–2 
N (4) 0.1 N
Answer (1)
Sol. ?

11
ECB
?

22
ECB
Also ?

12
EE
?
??
22
net 1 2
FEE
2
?
?
??? ? ?
4
86
10
310 3010
2
?
??
?
810
90 10 10
2
 0.6 N
3. A stationary horizontal disc is free to rotate
about its axis. When a torque is applied on it, its
kinetic energy as a function of ?, where ? is the
angle by which it has rotated, is given as k ?
2
. If
its moment of inertia is I then the angular
acceleration of the disc is:
(1)
2k
I
?
(2)
k
I
?
(3)
k
2I
?
(4)
k
4I
?
Answer (1)
Sol.
??
?
dE
d
?? ? 2k I
?
??
2k
I
4. The stream of a river is flowing with a speed of
2 km/h. A swimmer can swim at a speed of
4 km/h. What should be the direction of the
swimmer with respect to the flow of the river to
cross the river straight?
(1) 60° (2) 90°
(3) 150° (4) 120°
Answer (4)
Sol. Draw velocity diagram
?
?
v
r
v
sr
v
sg
?? ?
r
sr
v 1
sin
v2
? = 30°
? = 90 + ? = 120°
5. A uniform cable of mass ‘M’ and length ‘L’ is
placed on a horizontal surface such that its
th
1
n
??
??
??
 part is hanging below the edge of the
surface. To lift the hanging part of the cable
upto the surface, the work done should be:
(1)
2
MgL
n
(2) nMgL
(3)
2
MgL
2n
(4)
2
2MgL
n
Answer (3)
Sol.
?
1
M
m
n
?
??
i
ML
Ug
n2n
L/n
?
2
MgL
W
2n
6. A signal Acos ?t is transmitted using v
0
sin ?
0
t as
carrier wave. The correct amplitude modulated
(AM) signal is:
(1) ?? ??
00 0 0
AA
v sin t sin – t sin t
22
?? ? ? ? ? ??
(2) (v
0
 + A) cos ?t sin ?
0
t
(3) v
0
sin ?
0
t + Acos ?t
(4) v
0
sin[ ?
0
(1 + 0.01 Asin ?t)t]
Answer (1)
Sol. A= (v
o
 + Acos ?t) sin ?
o
t
= ? ? ??? ? ???
00 0 0
A
v sin( t) [sin( )t sin( )t]
2
7. The following bodies are made to roll up
(without slipping) the same inclined plane from
a horizontal plane : (i) a ring of radius R, (ii) a
solid cylinder of radius 
R
2
 and (iii) a solid
sphere of radius 
R
4
. If, in each case, the speed
of the center of mass at the bottom of the
incline is same, the ratio of the maximum
heights they climb is :
(1) 14 : 15 : 20 (2) 10 : 15 : 7
(3) 4 : 3 : 2 (4) 2 : 3 : 4
Answer (Bonus)
Sol.
2
p
1
mgh I
2
??
For ring ? 
22 2
1
2
1(2mr ) v v
h
2mg g (r)
?
??
?
For cylinder ? 
22
2
2
2
13 v 3v
hmr
22 4 g (r)
??
? ??
??
? ??
For sphere ? 
2
22
3
2
7
m(r)
1v7v
5
h
2 g 10 g (r)
?
?? ?
?
h
1
 : h
2
 : h
3
2 : 
3
2
: 
14
10
20 : 15 : 14
8. A wire of resistance R is bent to form a square
ABCD as shown in the figure. The effective
resistance between E and C is
(E is mid-point of arm CD)
AB
DC E
(1)
3
R
4
(2) R
(3)
1
R
16
(4)
7
R
64
Answer (4)
Sol.
12
R7R
R,R
88
??
eq
18 8
RR7R
??
eq
7R
R
64
?
9. In the density measurement of a cube, the
mass and edge length are measured as (10.00
± 0.10) kg and (0.10 ± 0.01) m, respectively. The
error in the measurement of density is
(1) 0.31 kg/m
3
(2) 0.01 kg/m
3
(3) 0.10 kg/m
3
(4) 0.07 kg/m
3
Answer (Bonus)
Sol. ?? ? ?
3
3
10
M/V 10,000kg/m
(0.1)
???
??
??
?
??
ddMdV
MV
d 0.1 0.03
10,000 10 0.1
?
??
d ? = 3100 kg/m
3
10. A rectangular coil (Dimension 5 cm × 2.5 cm)
with 100 turns, carrying a current of 3 A in the
clock-wise direction, is kept centered at the
origin and in the X-Z plane. A magnetic field of
1 T is applied along X-axis. If the coil is tilted
through 45° about Z-axis, then the torque on
the coil is
(1) 0.55 Nm (2) 0.27 Nm
(3) 0.42 Nm (4) 0.38 Nm
Answer (2)
Sol. MB ?? ?

4
1
100 3 5 2.5 10 1
2
0.27Nm
?
?? ? ? ? ? ? ?
?
11. A simple pendulum oscillating in air has
period T . The bob of the pendulum is completely
immersed in a non-viscous liquid. The density
of the liquid is 
1
th
16
 of the material of the bob.
If the bob is inside liquid all the time, its period
of oscillation in this liquid is :
(1)
1
2T
14
(2)
1
4T
15
(3)
1
4T
14
(4)
1
2T
10
Answer (2)
Sol.
eff
l
T2
g
??
eff
eff
g T
Tg
?
?
?
eff
g 15
gg
16 16
? ?? ?
T16
T15
?
?
12. The total number of turns and cross-section
area in a solenoid is fixed. However, its length
L is varied by adjusting the separation between
windings. The inductance of solenoid will be
proportional to
(1) 1/L (2) L
(3) 1/L
2
(4) L
2
Answer (1)
Sol. B = ?
0
ni
? = ?
0
ni(nL) A
(Inductance) L ? = ?
0
n
2
L A
N
L
??
??
??
??
0
N
LNA
L
??
? ??
??
??
1
L
L
? ?
13. For a given gas at 1 atm pressure, rms speed
of the molecules is 200 m/s at 127°C. At 2 atm
pressure and at 227°C, the rms speed of the
molecules will be:
(1) 100 5 m/s (2) 100 m/s
(3) 80 5 m/s (4) 80 m/s
Answer (1)
Sol.
? VT
?
11
22
VT
VT
?
2
200 400
V500
??
2
5
V 200 100 5m/s
4
14. A capacitor with capacitance 5 ?F is charged
to 5 ?C. If the plates are pulled apart to reduce
the capacitance to 2 ?F, how much work is
done?
(1) 2.55 × 10
–6
 J (2) 6.25 × 10
–6
 J
(3) 3.75 × 10
–6
 J (4) 2.16 × 10
–6
 J
Answer (3)
Page 5


Time : 3 hrs. M.M. : 360
Answers & Solutions
for for for for for
JEE (MAIN)-2019 (Online) Phase-2
Important Instructions :
1. The test is of 3 hours duration.
2. The Test Booklet consists of 90 questions. The maximum marks are 360.
3. There are three parts in the question paper A, B, C consisting of Physics, Chemistry and Mathematics
having 30 questions in each part of equal weightage.
4. Each question is allotted 4 (four) marks for each correct response. ¼ (one-fourth) marks will be deducted
for indicating incorrect response of each question. No deduction from the total score will be made if no
response is indicated for an item in the answer sheet.
5. There is only one correct response for each question.
(Physics, Chemistry and Mathematics)
09/04/2019
Morning
JEE (MAIN)-2019 (Online) Phase-2
PART–A : PHYSICS
1. Determine the charge on the capacitor in the
following circuit :
72 V
6 ??
4 ??
2 ??
10 ?? 10 F ?
(1) 200 ?C (2) 60 ?C
(3) 10 ?C (4) 2 ?C
Answer (1)
Sol. At steady state current through capacitor is
zero.
V
C
 = V
1
?? ?
10
53
VV
69
6 ?
72 V
2 ?
4 ? 10 ? V
1
??
??
?
1
572 3
V20 V
69
Q
1
= CV
1
= 200 ?C
2. The magnetic field of a plane electromagnetic
wave is given by :
B

 = 
0
ˆ
Bi

[cos(kz – ?t) + B
1
ˆ
j cos(kz + ?t)
where B
0
 = 3 × 10
–5 
T and B
1
 = 2 × 10
–6 
T.
The rms value of the force experienced by a
stationary charge Q = 10
–4
 C at z =0 is closest
to:
(1) 0.6 N (2) 0.9 N
(3) 3 × 10
–2 
N (4) 0.1 N
Answer (1)
Sol. ?

11
ECB
?

22
ECB
Also ?

12
EE
?
??
22
net 1 2
FEE
2
?
?
??? ? ?
4
86
10
310 3010
2
?
??
?
810
90 10 10
2
 0.6 N
3. A stationary horizontal disc is free to rotate
about its axis. When a torque is applied on it, its
kinetic energy as a function of ?, where ? is the
angle by which it has rotated, is given as k ?
2
. If
its moment of inertia is I then the angular
acceleration of the disc is:
(1)
2k
I
?
(2)
k
I
?
(3)
k
2I
?
(4)
k
4I
?
Answer (1)
Sol.
??
?
dE
d
?? ? 2k I
?
??
2k
I
4. The stream of a river is flowing with a speed of
2 km/h. A swimmer can swim at a speed of
4 km/h. What should be the direction of the
swimmer with respect to the flow of the river to
cross the river straight?
(1) 60° (2) 90°
(3) 150° (4) 120°
Answer (4)
Sol. Draw velocity diagram
?
?
v
r
v
sr
v
sg
?? ?
r
sr
v 1
sin
v2
? = 30°
? = 90 + ? = 120°
5. A uniform cable of mass ‘M’ and length ‘L’ is
placed on a horizontal surface such that its
th
1
n
??
??
??
 part is hanging below the edge of the
surface. To lift the hanging part of the cable
upto the surface, the work done should be:
(1)
2
MgL
n
(2) nMgL
(3)
2
MgL
2n
(4)
2
2MgL
n
Answer (3)
Sol.
?
1
M
m
n
?
??
i
ML
Ug
n2n
L/n
?
2
MgL
W
2n
6. A signal Acos ?t is transmitted using v
0
sin ?
0
t as
carrier wave. The correct amplitude modulated
(AM) signal is:
(1) ?? ??
00 0 0
AA
v sin t sin – t sin t
22
?? ? ? ? ? ??
(2) (v
0
 + A) cos ?t sin ?
0
t
(3) v
0
sin ?
0
t + Acos ?t
(4) v
0
sin[ ?
0
(1 + 0.01 Asin ?t)t]
Answer (1)
Sol. A= (v
o
 + Acos ?t) sin ?
o
t
= ? ? ??? ? ???
00 0 0
A
v sin( t) [sin( )t sin( )t]
2
7. The following bodies are made to roll up
(without slipping) the same inclined plane from
a horizontal plane : (i) a ring of radius R, (ii) a
solid cylinder of radius 
R
2
 and (iii) a solid
sphere of radius 
R
4
. If, in each case, the speed
of the center of mass at the bottom of the
incline is same, the ratio of the maximum
heights they climb is :
(1) 14 : 15 : 20 (2) 10 : 15 : 7
(3) 4 : 3 : 2 (4) 2 : 3 : 4
Answer (Bonus)
Sol.
2
p
1
mgh I
2
??
For ring ? 
22 2
1
2
1(2mr ) v v
h
2mg g (r)
?
??
?
For cylinder ? 
22
2
2
2
13 v 3v
hmr
22 4 g (r)
??
? ??
??
? ??
For sphere ? 
2
22
3
2
7
m(r)
1v7v
5
h
2 g 10 g (r)
?
?? ?
?
h
1
 : h
2
 : h
3
2 : 
3
2
: 
14
10
20 : 15 : 14
8. A wire of resistance R is bent to form a square
ABCD as shown in the figure. The effective
resistance between E and C is
(E is mid-point of arm CD)
AB
DC E
(1)
3
R
4
(2) R
(3)
1
R
16
(4)
7
R
64
Answer (4)
Sol.
12
R7R
R,R
88
??
eq
18 8
RR7R
??
eq
7R
R
64
?
9. In the density measurement of a cube, the
mass and edge length are measured as (10.00
± 0.10) kg and (0.10 ± 0.01) m, respectively. The
error in the measurement of density is
(1) 0.31 kg/m
3
(2) 0.01 kg/m
3
(3) 0.10 kg/m
3
(4) 0.07 kg/m
3
Answer (Bonus)
Sol. ?? ? ?
3
3
10
M/V 10,000kg/m
(0.1)
???
??
??
?
??
ddMdV
MV
d 0.1 0.03
10,000 10 0.1
?
??
d ? = 3100 kg/m
3
10. A rectangular coil (Dimension 5 cm × 2.5 cm)
with 100 turns, carrying a current of 3 A in the
clock-wise direction, is kept centered at the
origin and in the X-Z plane. A magnetic field of
1 T is applied along X-axis. If the coil is tilted
through 45° about Z-axis, then the torque on
the coil is
(1) 0.55 Nm (2) 0.27 Nm
(3) 0.42 Nm (4) 0.38 Nm
Answer (2)
Sol. MB ?? ?

4
1
100 3 5 2.5 10 1
2
0.27Nm
?
?? ? ? ? ? ? ?
?
11. A simple pendulum oscillating in air has
period T . The bob of the pendulum is completely
immersed in a non-viscous liquid. The density
of the liquid is 
1
th
16
 of the material of the bob.
If the bob is inside liquid all the time, its period
of oscillation in this liquid is :
(1)
1
2T
14
(2)
1
4T
15
(3)
1
4T
14
(4)
1
2T
10
Answer (2)
Sol.
eff
l
T2
g
??
eff
eff
g T
Tg
?
?
?
eff
g 15
gg
16 16
? ?? ?
T16
T15
?
?
12. The total number of turns and cross-section
area in a solenoid is fixed. However, its length
L is varied by adjusting the separation between
windings. The inductance of solenoid will be
proportional to
(1) 1/L (2) L
(3) 1/L
2
(4) L
2
Answer (1)
Sol. B = ?
0
ni
? = ?
0
ni(nL) A
(Inductance) L ? = ?
0
n
2
L A
N
L
??
??
??
??
0
N
LNA
L
??
? ??
??
??
1
L
L
? ?
13. For a given gas at 1 atm pressure, rms speed
of the molecules is 200 m/s at 127°C. At 2 atm
pressure and at 227°C, the rms speed of the
molecules will be:
(1) 100 5 m/s (2) 100 m/s
(3) 80 5 m/s (4) 80 m/s
Answer (1)
Sol.
? VT
?
11
22
VT
VT
?
2
200 400
V500
??
2
5
V 200 100 5m/s
4
14. A capacitor with capacitance 5 ?F is charged
to 5 ?C. If the plates are pulled apart to reduce
the capacitance to 2 ?F, how much work is
done?
(1) 2.55 × 10
–6
 J (2) 6.25 × 10
–6
 J
(3) 3.75 × 10
–6
 J (4) 2.16 × 10
–6
 J
Answer (3)
Sol.
?
2
i
1
Q
U
2C
?
2
f
2
Q
U
2C
??
??
??
??
2
21
Q1 1
W
2C C
??
??
??
??
2
(5) 1 1
22 5
W = 3.75 ?J
15. Following figure shows two processes A and B
for a gas. If ?Q
A 
and
 
?Q
B
  are the amount of
heat absorbed by the system in two cases, and
?U
A
 and ?U
B
 are changes in internal energies,
respectively, then:
f
A
B
f
i
(1) ?Q
A 
> ?Q
B
,??U
A
 = ?U
B
(2) ?Q
A 
= ?Q
B
;??U
A
 = ?U
B
(3) ?Q
A 
> ?Q
B
,??U
A
 > ?U
B
(4) ?Q
A 
< ?Q
B
,??U
A
 < ?U
B
Answer (1)
Sol. ?W
A
 > ?W
B
?U
A
 > ?U
B
From first law of thermodynamics,
?Q = ?U + ?W
?Q
A 
> ?Q
B
16. A concave mirror for face viewing has focal
length of 0.4 m. The distance at which you hold
the mirror from your face in order to see your
image upright with a magnification of 5 is:
(1) 0.32 m (2) 0.24 m
(3) 1.60 m (4) 0.16 m
Answer (1)
Sol.
???
11 1
VU 40
??
V
5
U
?? ??
11 1
5U U 40
U = – 32 cm
17. A solid sphere of mass ‘M’ and radius ‘a’ is
surrounded by a uniform concentric spherical
shell of thickness 2a and mass 2M. The
gravitational field at distance ‘3a’ from the
centre will be:
(1)
2
GM
9a
(2)
2
2GM
9a
(3)
2
GM
3a
(4)
2
2GM
3a
Answer (3)
Sol.
??
22
GM 2GM
E
(3a) (3a)
?
2
GM
E
3a
18. A moving coil galvanometer has resistance
50 ? and it indicates full deflection at 4 mA
current. A voltmeter is made using this
galvanometer and a 5 k ??resistance. The
maximum voltage, that can be measured using
this voltmeter, will be close to:
(1) 10 V (2) 20 V
(3) 15 V (4) 40 V
Answer (2)
Sol. V = I
g
 (R
s
 +  R
g
)
= 4 × 10
–3
 [5050]
? 20 V
19. The pressure wave, P = 0.01sin[1000 t – 3x]Nm
–2
,
corresponds to the sound produced by a
vibrating blade on a day when atmospheric
temperature is 0°C. On some other day when
temperature is T, the speed of sound produced
by the same blade and at the same frequency
is found to be 336 ms
–1
. Approximate value of
T is :
(1) 4°C (2) 12°C
(3) 15°C (4) 11°C
Answer (1)
Sol.
1
1000
Vm/s
3
?