JEE Mains 12 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)
12/04/2019
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)
12/04/2019
Morning
PART–A : PHYSICS
1. The value of numerical aperture of the
objective lens of a microscope is 1.25. If light
of wavelength 5000 Å is used, the minimum
separation between two points, to be seen as
distinct, will be :
(1) 0.24 ?m (2) 0.38 ?m
(3) 0.48 ?m (4) 0.12 ?m
Answer (1)
Sol.
min
1.22
D
?
??
D
1.25
2f
?
10
min
1.22 f 1.22 5000 10
d
D2.50
?
?? ?
??
 
 
= 0.24 ?m
2. A circular disc of radius b has a hole of radius
a at its centre (see figure). If the mass per unit
area of the disc varies as 
0
,
r
? ??
??
??
 then the
radius of gyration of the disc about its axis
passing through the centre is :
(1)
ab
2
?
(2)
22
ab ab
2
??
(3)
ab
3
?
(4)
22
ab ab
3
??
Answer (4)
Sol. ?
00
2 rdr dm
rr
??
?? ? ? ?
? m = ?
0
2 ? (b – a)
b
233 0
0
a
2
I2rdr (ba )
3
??
?? ? ? ?
?
?
2233 0
0
2
mk I 2 (b a)k (b a )
3
??
? ? ?? ? ? ?
?
22 2
1
k(b aba)
3
?? ?
?
33
1(ba )
k
3b a
?
?
?
3. A shell is fired from a fixed artillery gun with
an initial speed u such that it hits the target on
the ground at a distance R from it. If
t
1
 and t
2
 are the values of the time taken by it
to hit the target in two possible ways, the
product  t
1
t
2
 is :
(1)
R
2g
(2)
2R
g
(3)
R
g
(4)
R
4g
Answer (2)
Sol. For same horizontal range.
2
1
usin2
R
g
?
??? ?
?
2
 = (90 – ?)
so12
2usin 2ucos
tandt
gg
??
??
?
2
12
2
u4sin cos
tt
g
??
?
?
2
12
2
2u sin2 2R
tt
g g
?
??
4. The resistive network shown below is
connected to a D.C. source of 16 V. The power
consumed by the network is 4 Watt. The value
of R is :
(1) 8 ? (2) 1 ?
(3) 16 ? (4) 6 ?
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)
12/04/2019
Morning
PART–A : PHYSICS
1. The value of numerical aperture of the
objective lens of a microscope is 1.25. If light
of wavelength 5000 Å is used, the minimum
separation between two points, to be seen as
distinct, will be :
(1) 0.24 ?m (2) 0.38 ?m
(3) 0.48 ?m (4) 0.12 ?m
Answer (1)
Sol.
min
1.22
D
?
??
D
1.25
2f
?
10
min
1.22 f 1.22 5000 10
d
D2.50
?
?? ?
??
 
 
= 0.24 ?m
2. A circular disc of radius b has a hole of radius
a at its centre (see figure). If the mass per unit
area of the disc varies as 
0
,
r
? ??
??
??
 then the
radius of gyration of the disc about its axis
passing through the centre is :
(1)
ab
2
?
(2)
22
ab ab
2
??
(3)
ab
3
?
(4)
22
ab ab
3
??
Answer (4)
Sol. ?
00
2 rdr dm
rr
??
?? ? ? ?
? m = ?
0
2 ? (b – a)
b
233 0
0
a
2
I2rdr (ba )
3
??
?? ? ? ?
?
?
2233 0
0
2
mk I 2 (b a)k (b a )
3
??
? ? ?? ? ? ?
?
22 2
1
k(b aba)
3
?? ?
?
33
1(ba )
k
3b a
?
?
?
3. A shell is fired from a fixed artillery gun with
an initial speed u such that it hits the target on
the ground at a distance R from it. If
t
1
 and t
2
 are the values of the time taken by it
to hit the target in two possible ways, the
product  t
1
t
2
 is :
(1)
R
2g
(2)
2R
g
(3)
R
g
(4)
R
4g
Answer (2)
Sol. For same horizontal range.
2
1
usin2
R
g
?
??? ?
?
2
 = (90 – ?)
so12
2usin 2ucos
tandt
gg
??
??
?
2
12
2
u4sin cos
tt
g
??
?
?
2
12
2
2u sin2 2R
tt
g g
?
??
4. The resistive network shown below is
connected to a D.C. source of 16 V. The power
consumed by the network is 4 Watt. The value
of R is :
(1) 8 ? (2) 1 ?
(3) 16 ? (4) 6 ?
Answer (1)
Sol. R
eq
 = 2R + R + 4R + R = 8R
2
eq
v1616
P4watt
R8R
?
? ? ?
16 16
RR8
48
?
? ? ??
?
5. In a double slit experiment, when a thin film of
thickness t having refractive index ? is
introduced in front of one of the slits, the
maximum at the centre of the fringe pattern
shifts by one fringe width. The value of t is
( ? is the wavelength of the light used) :
(1)
2
( 1)
?
??
(2)
2( 1)
?
??
(3)
(21)
?
??
(4)
( 1)
?
??
Answer (4)
Sol. ?t – t = ?
? t( ? – 1) = ?
?
t
( 1)
?
?
??
6. A galvanometer of resistance 100 ? has 50
divisions on its scale and has sensitivity of
20 ?A/division. It is to be converted to a
voltmeter with three ranges, of 0-2 V, 0-10 V
and 0-20 V. The appropriate circuit to do so is :
(1)
(2)
(3)
(4)
Answer (1)
Sol. For R
1
? I
g
 = 10
–3
 A
? 10
–3
(R
1
 + 100) = 2 V ? R
1
 = 1900 ?
For R
2
10
–3
(R
1
 + R
2
 + 100) = 10 V
? R
1
 + R
2
2
 = 8000 ?
For R
3
10
–3
(R
1
 + R
2
 + R
3
 + 100) = 20 V
? R
1
 + R
2
 + R
3
 + 100 = 20 × 1000
? R
3
 = 10000 ?
7. A point dipole 
0
ˆ pp x ??

 is kept at the origin.
The potential and electric field due to this
dipole on the y-axis at a distance d are,
respectively : (Take V = 0 at infinity)
(1)
23
00
|p| p
,
4d 4d ?? ??

(2)
23
00
|p| p
,
4d 4d
?
?? ??

(3)
3
0
p
0,
4d
?
??

(4)
3
0
p
0,
4d ??

Answer (3)
Sol.
2
3
p
EK 3cos 1
r
???


?? = ?/2  (0, d, 0)
?
3
kp
E
d
?
?


 + 100 = 10000
? R
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)
12/04/2019
Morning
PART–A : PHYSICS
1. The value of numerical aperture of the
objective lens of a microscope is 1.25. If light
of wavelength 5000 Å is used, the minimum
separation between two points, to be seen as
distinct, will be :
(1) 0.24 ?m (2) 0.38 ?m
(3) 0.48 ?m (4) 0.12 ?m
Answer (1)
Sol.
min
1.22
D
?
??
D
1.25
2f
?
10
min
1.22 f 1.22 5000 10
d
D2.50
?
?? ?
??
 
 
= 0.24 ?m
2. A circular disc of radius b has a hole of radius
a at its centre (see figure). If the mass per unit
area of the disc varies as 
0
,
r
? ??
??
??
 then the
radius of gyration of the disc about its axis
passing through the centre is :
(1)
ab
2
?
(2)
22
ab ab
2
??
(3)
ab
3
?
(4)
22
ab ab
3
??
Answer (4)
Sol. ?
00
2 rdr dm
rr
??
?? ? ? ?
? m = ?
0
2 ? (b – a)
b
233 0
0
a
2
I2rdr (ba )
3
??
?? ? ? ?
?
?
2233 0
0
2
mk I 2 (b a)k (b a )
3
??
? ? ?? ? ? ?
?
22 2
1
k(b aba)
3
?? ?
?
33
1(ba )
k
3b a
?
?
?
3. A shell is fired from a fixed artillery gun with
an initial speed u such that it hits the target on
the ground at a distance R from it. If
t
1
 and t
2
 are the values of the time taken by it
to hit the target in two possible ways, the
product  t
1
t
2
 is :
(1)
R
2g
(2)
2R
g
(3)
R
g
(4)
R
4g
Answer (2)
Sol. For same horizontal range.
2
1
usin2
R
g
?
??? ?
?
2
 = (90 – ?)
so12
2usin 2ucos
tandt
gg
??
??
?
2
12
2
u4sin cos
tt
g
??
?
?
2
12
2
2u sin2 2R
tt
g g
?
??
4. The resistive network shown below is
connected to a D.C. source of 16 V. The power
consumed by the network is 4 Watt. The value
of R is :
(1) 8 ? (2) 1 ?
(3) 16 ? (4) 6 ?
Answer (1)
Sol. R
eq
 = 2R + R + 4R + R = 8R
2
eq
v1616
P4watt
R8R
?
? ? ?
16 16
RR8
48
?
? ? ??
?
5. In a double slit experiment, when a thin film of
thickness t having refractive index ? is
introduced in front of one of the slits, the
maximum at the centre of the fringe pattern
shifts by one fringe width. The value of t is
( ? is the wavelength of the light used) :
(1)
2
( 1)
?
??
(2)
2( 1)
?
??
(3)
(21)
?
??
(4)
( 1)
?
??
Answer (4)
Sol. ?t – t = ?
? t( ? – 1) = ?
?
t
( 1)
?
?
??
6. A galvanometer of resistance 100 ? has 50
divisions on its scale and has sensitivity of
20 ?A/division. It is to be converted to a
voltmeter with three ranges, of 0-2 V, 0-10 V
and 0-20 V. The appropriate circuit to do so is :
(1)
(2)
(3)
(4)
Answer (1)
Sol. For R
1
? I
g
 = 10
–3
 A
? 10
–3
(R
1
 + 100) = 2 V ? R
1
 = 1900 ?
For R
2
10
–3
(R
1
 + R
2
 + 100) = 10 V
? R
1
 + R
2
2
 = 8000 ?
For R
3
10
–3
(R
1
 + R
2
 + R
3
 + 100) = 20 V
? R
1
 + R
2
 + R
3
 + 100 = 20 × 1000
? R
3
 = 10000 ?
7. A point dipole 
0
ˆ pp x ??

 is kept at the origin.
The potential and electric field due to this
dipole on the y-axis at a distance d are,
respectively : (Take V = 0 at infinity)
(1)
23
00
|p| p
,
4d 4d ?? ??

(2)
23
00
|p| p
,
4d 4d
?
?? ??

(3)
3
0
p
0,
4d
?
??

(4)
3
0
p
0,
4d ??

Answer (3)
Sol.
2
3
p
EK 3cos 1
r
???


?? = ?/2  (0, d, 0)
?
3
kp
E
d
?
?


 + 100 = 10000
? R
JEE (MAIN)-2019 (Online) Phase-2
8. A magnetic compass needle oscillates
30 times per minute at a place where the dip
is 45°, and 40 times per minute where the dip
is 30°. If B
1
 and B
2
 are respectively the total
magnetic field due to the earth at the two
places, then the ratio B
1
/B
2
 is best given by :
(1) 2.2 (2) 0.7
(3) 3.6 (4) 1.8
Answer (2)
Sol. T
1
 = 2 sec., T
2
 = 3/2
For place (1), 
1
1
H1
B
BBcos45
2
???
For place (2), 
2
2
H2
B3
BBcos30
2
???
?
H
I
T2
MB
?? ?
2
1
H
1
2H
B
T
TB
?
2
1
B3 2 44
92B
? ?
? ?
1
2
B 69
B216
?
?
?
1
2
B
0.68 0.7.
B
? ??
9. An electromagnetic wave is represented by
the electric field
????

0
ˆ EEnsin[ t (6y 8z)]. Taking unit vectors in
x, y and z directions to be 
ˆ ˆˆ
i, j,k, the direction
of propogation ˆ s, is:
(1)
ˆ ˆ
3j 4k
ˆ s
5
??
??
?
??
??
(2)
ˆˆ
3i 4j
ˆ s
5
??
?
?
??
??
(3)
ˆ ˆ
4k 3j
ˆ s
5
??
??
?
??
??
(4)
ˆ ˆ
4j 3k
ˆ s
5
??
?
?
??
??
Answer (1)
Sol. ????
0
EEsin(t 6y 8z)
ˆˆ ˆˆ
8k 6j 4k 3j
ˆ s
10 5
??
??
??
??
??
10. A sample of an ideal gas is taken through the
cyclic process abca as shown in the figure. The
change in the internal energy of the gas along
the path ca is –180 J. The gas absorbs 250 J of
heat along the path ab and 60 J along the path
bc. The work done by the gas along the path
abc is :
P
a b
c
V
(1) 130 J (2) 100 J
(3) 140 J (4) 120 J
Answer (1)
Sol. For the process (c – a), ?U
ca
 = – 180 J
For process (b – c) ? Isochoric (W
bc
 = 0)
??U = 60 J
Heat absorbs along (a – b), Q
ab
 = 250 J
Also ?? ?U
cycle
 = 0
??U
ab
 = 120 J
So W
a ? b
 = 130 J
Total work done from (a ? b ? c)
= W
ab
 + W
bc
 = 130 J
11. At 40°C, a brass wire of 1 mm radius is hung
from the ceiling. A small mass, M is hung from
the free end of the wire. When the wire is cooled
down from 40°C to 20°C it regains its original
length of 0.2 m. The value of M is close to :
(Coefficient of linear expansion and Young's
modulus of brass are 10
–5
/°C and 10
11
 N/m
2
,
respectively ; g = 10 ms
–2
)
(1) 0.5 kg (2) 0.9 kg
(3) 1.5 kg (4) 9 kg
Answer (Bonus)
Sol.
Mgl
Y
Al
?
?
??l
Mechanical
 = 
Mgl
AY
?l
Thermal
 = 
lT l 20 ?? ? ? ?
Mgl
20 l
AY
??
5611
20 10 1 10 10
M6.28kg
10
??
??????
??
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)
12/04/2019
Morning
PART–A : PHYSICS
1. The value of numerical aperture of the
objective lens of a microscope is 1.25. If light
of wavelength 5000 Å is used, the minimum
separation between two points, to be seen as
distinct, will be :
(1) 0.24 ?m (2) 0.38 ?m
(3) 0.48 ?m (4) 0.12 ?m
Answer (1)
Sol.
min
1.22
D
?
??
D
1.25
2f
?
10
min
1.22 f 1.22 5000 10
d
D2.50
?
?? ?
??
 
 
= 0.24 ?m
2. A circular disc of radius b has a hole of radius
a at its centre (see figure). If the mass per unit
area of the disc varies as 
0
,
r
? ??
??
??
 then the
radius of gyration of the disc about its axis
passing through the centre is :
(1)
ab
2
?
(2)
22
ab ab
2
??
(3)
ab
3
?
(4)
22
ab ab
3
??
Answer (4)
Sol. ?
00
2 rdr dm
rr
??
?? ? ? ?
? m = ?
0
2 ? (b – a)
b
233 0
0
a
2
I2rdr (ba )
3
??
?? ? ? ?
?
?
2233 0
0
2
mk I 2 (b a)k (b a )
3
??
? ? ?? ? ? ?
?
22 2
1
k(b aba)
3
?? ?
?
33
1(ba )
k
3b a
?
?
?
3. A shell is fired from a fixed artillery gun with
an initial speed u such that it hits the target on
the ground at a distance R from it. If
t
1
 and t
2
 are the values of the time taken by it
to hit the target in two possible ways, the
product  t
1
t
2
 is :
(1)
R
2g
(2)
2R
g
(3)
R
g
(4)
R
4g
Answer (2)
Sol. For same horizontal range.
2
1
usin2
R
g
?
??? ?
?
2
 = (90 – ?)
so12
2usin 2ucos
tandt
gg
??
??
?
2
12
2
u4sin cos
tt
g
??
?
?
2
12
2
2u sin2 2R
tt
g g
?
??
4. The resistive network shown below is
connected to a D.C. source of 16 V. The power
consumed by the network is 4 Watt. The value
of R is :
(1) 8 ? (2) 1 ?
(3) 16 ? (4) 6 ?
Answer (1)
Sol. R
eq
 = 2R + R + 4R + R = 8R
2
eq
v1616
P4watt
R8R
?
? ? ?
16 16
RR8
48
?
? ? ??
?
5. In a double slit experiment, when a thin film of
thickness t having refractive index ? is
introduced in front of one of the slits, the
maximum at the centre of the fringe pattern
shifts by one fringe width. The value of t is
( ? is the wavelength of the light used) :
(1)
2
( 1)
?
??
(2)
2( 1)
?
??
(3)
(21)
?
??
(4)
( 1)
?
??
Answer (4)
Sol. ?t – t = ?
? t( ? – 1) = ?
?
t
( 1)
?
?
??
6. A galvanometer of resistance 100 ? has 50
divisions on its scale and has sensitivity of
20 ?A/division. It is to be converted to a
voltmeter with three ranges, of 0-2 V, 0-10 V
and 0-20 V. The appropriate circuit to do so is :
(1)
(2)
(3)
(4)
Answer (1)
Sol. For R
1
? I
g
 = 10
–3
 A
? 10
–3
(R
1
 + 100) = 2 V ? R
1
 = 1900 ?
For R
2
10
–3
(R
1
 + R
2
 + 100) = 10 V
? R
1
 + R
2
2
 = 8000 ?
For R
3
10
–3
(R
1
 + R
2
 + R
3
 + 100) = 20 V
? R
1
 + R
2
 + R
3
 + 100 = 20 × 1000
? R
3
 = 10000 ?
7. A point dipole 
0
ˆ pp x ??

 is kept at the origin.
The potential and electric field due to this
dipole on the y-axis at a distance d are,
respectively : (Take V = 0 at infinity)
(1)
23
00
|p| p
,
4d 4d ?? ??

(2)
23
00
|p| p
,
4d 4d
?
?? ??

(3)
3
0
p
0,
4d
?
??

(4)
3
0
p
0,
4d ??

Answer (3)
Sol.
2
3
p
EK 3cos 1
r
???


?? = ?/2  (0, d, 0)
?
3
kp
E
d
?
?


 + 100 = 10000
? R
JEE (MAIN)-2019 (Online) Phase-2
8. A magnetic compass needle oscillates
30 times per minute at a place where the dip
is 45°, and 40 times per minute where the dip
is 30°. If B
1
 and B
2
 are respectively the total
magnetic field due to the earth at the two
places, then the ratio B
1
/B
2
 is best given by :
(1) 2.2 (2) 0.7
(3) 3.6 (4) 1.8
Answer (2)
Sol. T
1
 = 2 sec., T
2
 = 3/2
For place (1), 
1
1
H1
B
BBcos45
2
???
For place (2), 
2
2
H2
B3
BBcos30
2
???
?
H
I
T2
MB
?? ?
2
1
H
1
2H
B
T
TB
?
2
1
B3 2 44
92B
? ?
? ?
1
2
B 69
B216
?
?
?
1
2
B
0.68 0.7.
B
? ??
9. An electromagnetic wave is represented by
the electric field
????

0
ˆ EEnsin[ t (6y 8z)]. Taking unit vectors in
x, y and z directions to be 
ˆ ˆˆ
i, j,k, the direction
of propogation ˆ s, is:
(1)
ˆ ˆ
3j 4k
ˆ s
5
??
??
?
??
??
(2)
ˆˆ
3i 4j
ˆ s
5
??
?
?
??
??
(3)
ˆ ˆ
4k 3j
ˆ s
5
??
??
?
??
??
(4)
ˆ ˆ
4j 3k
ˆ s
5
??
?
?
??
??
Answer (1)
Sol. ????
0
EEsin(t 6y 8z)
ˆˆ ˆˆ
8k 6j 4k 3j
ˆ s
10 5
??
??
??
??
??
10. A sample of an ideal gas is taken through the
cyclic process abca as shown in the figure. The
change in the internal energy of the gas along
the path ca is –180 J. The gas absorbs 250 J of
heat along the path ab and 60 J along the path
bc. The work done by the gas along the path
abc is :
P
a b
c
V
(1) 130 J (2) 100 J
(3) 140 J (4) 120 J
Answer (1)
Sol. For the process (c – a), ?U
ca
 = – 180 J
For process (b – c) ? Isochoric (W
bc
 = 0)
??U = 60 J
Heat absorbs along (a – b), Q
ab
 = 250 J
Also ?? ?U
cycle
 = 0
??U
ab
 = 120 J
So W
a ? b
 = 130 J
Total work done from (a ? b ? c)
= W
ab
 + W
bc
 = 130 J
11. At 40°C, a brass wire of 1 mm radius is hung
from the ceiling. A small mass, M is hung from
the free end of the wire. When the wire is cooled
down from 40°C to 20°C it regains its original
length of 0.2 m. The value of M is close to :
(Coefficient of linear expansion and Young's
modulus of brass are 10
–5
/°C and 10
11
 N/m
2
,
respectively ; g = 10 ms
–2
)
(1) 0.5 kg (2) 0.9 kg
(3) 1.5 kg (4) 9 kg
Answer (Bonus)
Sol.
Mgl
Y
Al
?
?
??l
Mechanical
 = 
Mgl
AY
?l
Thermal
 = 
lT l 20 ?? ? ? ?
Mgl
20 l
AY
??
5611
20 10 1 10 10
M6.28kg
10
??
??????
??
12. A thin ring of 10 cm radius carries a uniformly
distributed charge. The ring rotates at a
constant angular speed of 40 ? rad s
–1
 about its
axis, perpendicular to its plane. If the magnetic
field at its centre is 3.8 × 10
–9
 T , then the charge
carried by the ring is close to ( ?
0
 = 4 ? × 10
–7
 N/A
2
).
(1) 4 × 10
–5
 C (2) 3 × 10
–5
 C
(3) 7 × 10
–6
 C (4) 2 × 10
–6
 C
Answer (2)
Sol.
0
i q
Band i
2a 2
? ?
??
?
?
0
q
B
2a 2
? ?
??
?
7
5
10 40
B qq 310 C
0.1
?
?
?
???? ? ??
13. An excited He
+
 ion emits two photons in
succession, with wavelengths 108.5 nm and
30.4 nm, in making a transition to ground
state. The quantum number n, corresponding
to its initial excited state is (for photon of
wavelength ?, energy 
1240eV
E
(innm)
?
?
):
(1) n = 5 (2) n = 7
(3) n = 4 (4) n = 6
Answer (1)
Sol. ? ??
2
0
n
2
EZ
E–
n
Let it start from n to m and from m to ground.
Then ?? ?
2
hc 1
13.6 4 1
30.4nm
m
? ?? ? ?
22
11
10.7498 0.25
mm
? m = 2, and now 
?
??
?? ?
??
? ??
9 2
hc 11
13.6 4
4
108.5 10 n
n ? 5.
14. The figure shows a square loop L of side 5 cm
which is connected to a network of
resistances. The whole setup is moving towards
right with a constant speed of 1 cm s
–1
. At some
instant, a part of L is in a uniform magnetic
field of 1 T, perpendicular to the plane of the
loop. If the resistance of L is 1.7 ?, the current
in the loop at that instant will be close to:
L
5 cm
v = 1 cm/sec
1 ?
A
2 ?
C
D
B
1 ?
2 ?
B
3 ?
(1) 170 ?A (2) 60 ?A
(3) 150 ?A (4) 115 ?A
Answer (1)
Sol. VBl = iR
eq
eq
4
R1.73
3
??? ? ? ?
??
??
??
22
eq
(BLV)(1)(510 ) 10
i
R3
4
5
10 A
3
?
??  1.7 × 10
–4
 A
= 170 ?A
15. A uniform rod of length l is being rotated in a
horizontal plane with a constant angular
speed about an axis passing through one of its
ends. If the tension generated in the rod due
to rotation is T(x) at a distance x from the axis,
then which of the following graphs depicts it
most closely?
(1)
T(x)
l
x
(2)
T(x)
l
x
(3)
T(x)
l
x
(4)
T(x)
l
x
Answer (3)
Sol.
x
T
x
? ?
2
222
x
MM Lx
T(Lx) (Lx) x
L2L 2
? ?
?? ?? ? ?