JEE Mains 8 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)
08/04/2019
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)
08/04/2019
Morning
PART–A : PHYSICS
1. Two particles move at right angle to each other.
Their de Broglie wavelengths are ?
1
 and ?
2
respectively. The particles suffer perfectly
inelastic collision. The de Broglie wavelength ?,
of the final particle, is given by:
(1) ?? ? ?
12
(2)
???
??
12
2
(3)
??
?? ?
12
21 1
(4)
??
?? ?
22 2
12
11 1
Answer (4)
Sol.
1
2
?
?
1
1
h
p
?
?
2
2
h
p
? ??
22
f 12
pp p
?
??
? ??
22
22
12
hh h
?
??
?? ?
22 2
12
11 1
2. In SI units, the dimensions of 
?
?
0
0
 is:
(1) AT
2
M
–1
L
–1
(2) AT
–3
ML
3/2
(3) A
–1
TML
3
(4) A
2
T
3
M
–1
L
–2
Answer (4)
Sol.
??
??
?
??
?? ??
?? ??
??
??
? ?? ??
????
1 00
0
0 00
LT
?
?
??
2
2
0
q
F
4r
?
??
?? ??
?
??
?
2
0
22
AT
[]
MLT L
?
??? ?
???
??
?
??
??
?
??
??
12134 0
0
LT A M L T
  = [M
–1
L
–2
T
3
A
2
]
3. A particle moves in one dimension from rest
under the influence of a force that varies with
the distance travelled by the particle as shown
in the figure. The kinetic energy of the particle
after it has travelled 3 m is
1
2
3
Force 
(in N)
Distance
(in ) m
1 2 3
(1) 4 J (2) 2.5 J
(3) 5 J (4) 6.5 J
Answer (4)
Sol. = Area under F–x graph
?K.E  = 
? ???? ? ?
1
W (32)(32) 22
2
= 2.5 + 4
= 6.5 J
4. Radiation coming from transitions n = 2 to n = 1
of hydrogen atoms fall on He
+
 ions in n = 1 and
n = 2 states. The possible transition of helium ions
as they absorb energy from the radiation is
(1) n = 2 ? n = 4
(2) n = 2 ? n = 5
(3) n = 2 ? n = 3
(4) n = 1 ? n = 4
Answer (1)
Sol. Energy released by hydrogen atom
??
??
??
??
1
11 3
E =13.6× = ×13.6eV
14 4
      = 10.2 eV
Also, energy absorbed by H
e
+
 ion in transition
n = 2 ? n = 4
??
??
??
??
2
11
E =13.6×4× =10.2 eV
416
So, possible transition is n = 2 ? n = 4
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)
08/04/2019
Morning
PART–A : PHYSICS
1. Two particles move at right angle to each other.
Their de Broglie wavelengths are ?
1
 and ?
2
respectively. The particles suffer perfectly
inelastic collision. The de Broglie wavelength ?,
of the final particle, is given by:
(1) ?? ? ?
12
(2)
???
??
12
2
(3)
??
?? ?
12
21 1
(4)
??
?? ?
22 2
12
11 1
Answer (4)
Sol.
1
2
?
?
1
1
h
p
?
?
2
2
h
p
? ??
22
f 12
pp p
?
??
? ??
22
22
12
hh h
?
??
?? ?
22 2
12
11 1
2. In SI units, the dimensions of 
?
?
0
0
 is:
(1) AT
2
M
–1
L
–1
(2) AT
–3
ML
3/2
(3) A
–1
TML
3
(4) A
2
T
3
M
–1
L
–2
Answer (4)
Sol.
??
??
?
??
?? ??
?? ??
??
??
? ?? ??
????
1 00
0
0 00
LT
?
?
??
2
2
0
q
F
4r
?
??
?? ??
?
??
?
2
0
22
AT
[]
MLT L
?
??? ?
???
??
?
??
??
?
??
??
12134 0
0
LT A M L T
  = [M
–1
L
–2
T
3
A
2
]
3. A particle moves in one dimension from rest
under the influence of a force that varies with
the distance travelled by the particle as shown
in the figure. The kinetic energy of the particle
after it has travelled 3 m is
1
2
3
Force 
(in N)
Distance
(in ) m
1 2 3
(1) 4 J (2) 2.5 J
(3) 5 J (4) 6.5 J
Answer (4)
Sol. = Area under F–x graph
?K.E  = 
? ???? ? ?
1
W (32)(32) 22
2
= 2.5 + 4
= 6.5 J
4. Radiation coming from transitions n = 2 to n = 1
of hydrogen atoms fall on He
+
 ions in n = 1 and
n = 2 states. The possible transition of helium ions
as they absorb energy from the radiation is
(1) n = 2 ? n = 4
(2) n = 2 ? n = 5
(3) n = 2 ? n = 3
(4) n = 1 ? n = 4
Answer (1)
Sol. Energy released by hydrogen atom
??
??
??
??
1
11 3
E =13.6× = ×13.6eV
14 4
      = 10.2 eV
Also, energy absorbed by H
e
+
 ion in transition
n = 2 ? n = 4
??
??
??
??
2
11
E =13.6×4× =10.2 eV
416
So, possible transition is n = 2 ? n = 4
5. Water from a pipe is coming at a rate of
100 liters per minute. If the radius of the pipe
is 5 cm, the Reynolds number for the flow is of
the order of : (density of water = 1000 kg/m
3
,
coefficient of viscosity of water  = 1 mPa s)
(1) 10
2
(2) 10
4
(3) 10
3
(4) 10
6
Answer (2)
Sol. Flow rate of water (Q) = 100 lit/min
?
?
?
???
3
33
100 10 5
10 m
60 3
? Velocity of flow (v) = 
?
?
?
?
?? ? ?
3
22
Q510
A 3 (510 )
??
??
10 2
m/s
15 3
= 0.2 m/s
? Reynold number (R
e
) 
?
?
?
Dv
?
?? ?
?
?
2
2
(10 10 ) 1000
3
1
  2 × 10
4
Order of R
e
 = 10
4
6. In figure, the optical fiber is l = 2 m long and
has a diameter of d = 20 ?m. If a ray of light is
incident on one end of the fiber at angle
?
1
 = 40°, the number of reflections it makes
before emerging from the other end is close to:
(refractive index of fiber is 1.31 and
sin 40° = 0.64)
?
2
40°
d
(1) 66000 (2) 55000
(3) 45000 (4) 57000
Answer (4)
Sol. 1 × sin 40° = 1.31 sin ?
? ?? ??? 
0.64
sin 30
1.31
?l = 20 ?m × cot ?
?
?
?
?? ?
6
2
N
20 10 cot
  
?
??
?
6
210
57735
20 3
? N 57000
7. A 200 ? resistor has a certain color code. If
one replaces the red color by green in the
code, the new resistance will be:
(1) 400 ?
(2) 500 ?
(3) 300 ?
(4) 100 ?
Answer (2)
Sol. 200 ? = Red + Black + Brown
Green ? 5
So, Green + Black + Brown  ? 500 ?
8. A 20 Henry inductor coil is connected to a
10 ohm resistance in series as shown in figure.
The time at which rate of dissipation of energy
(Joule’s heat) across resistance is equal to the
rate at which magnetic energy is stored in the
inductor, is:
i
10 ??
20 H E
(1)
2
ln2
(2) 2 ln2
(3) ln2
(4)
1
ln2
2
Answer (2)
Sol. P
R
 = i
2
 × R
P
B
 = V × i
? P
L
 = Vi – i
2
R
? Vi – i
2
R = i
2
R
? i = 
??
??
?? ?
t/
VV
and i 1 e
2R R
?
??
??
??
t/
VV
1e
2R R
? ?? ? ?
20
tln(2) ln(2) 2ln(2)
10
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)
08/04/2019
Morning
PART–A : PHYSICS
1. Two particles move at right angle to each other.
Their de Broglie wavelengths are ?
1
 and ?
2
respectively. The particles suffer perfectly
inelastic collision. The de Broglie wavelength ?,
of the final particle, is given by:
(1) ?? ? ?
12
(2)
???
??
12
2
(3)
??
?? ?
12
21 1
(4)
??
?? ?
22 2
12
11 1
Answer (4)
Sol.
1
2
?
?
1
1
h
p
?
?
2
2
h
p
? ??
22
f 12
pp p
?
??
? ??
22
22
12
hh h
?
??
?? ?
22 2
12
11 1
2. In SI units, the dimensions of 
?
?
0
0
 is:
(1) AT
2
M
–1
L
–1
(2) AT
–3
ML
3/2
(3) A
–1
TML
3
(4) A
2
T
3
M
–1
L
–2
Answer (4)
Sol.
??
??
?
??
?? ??
?? ??
??
??
? ?? ??
????
1 00
0
0 00
LT
?
?
??
2
2
0
q
F
4r
?
??
?? ??
?
??
?
2
0
22
AT
[]
MLT L
?
??? ?
???
??
?
??
??
?
??
??
12134 0
0
LT A M L T
  = [M
–1
L
–2
T
3
A
2
]
3. A particle moves in one dimension from rest
under the influence of a force that varies with
the distance travelled by the particle as shown
in the figure. The kinetic energy of the particle
after it has travelled 3 m is
1
2
3
Force 
(in N)
Distance
(in ) m
1 2 3
(1) 4 J (2) 2.5 J
(3) 5 J (4) 6.5 J
Answer (4)
Sol. = Area under F–x graph
?K.E  = 
? ???? ? ?
1
W (32)(32) 22
2
= 2.5 + 4
= 6.5 J
4. Radiation coming from transitions n = 2 to n = 1
of hydrogen atoms fall on He
+
 ions in n = 1 and
n = 2 states. The possible transition of helium ions
as they absorb energy from the radiation is
(1) n = 2 ? n = 4
(2) n = 2 ? n = 5
(3) n = 2 ? n = 3
(4) n = 1 ? n = 4
Answer (1)
Sol. Energy released by hydrogen atom
??
??
??
??
1
11 3
E =13.6× = ×13.6eV
14 4
      = 10.2 eV
Also, energy absorbed by H
e
+
 ion in transition
n = 2 ? n = 4
??
??
??
??
2
11
E =13.6×4× =10.2 eV
416
So, possible transition is n = 2 ? n = 4
5. Water from a pipe is coming at a rate of
100 liters per minute. If the radius of the pipe
is 5 cm, the Reynolds number for the flow is of
the order of : (density of water = 1000 kg/m
3
,
coefficient of viscosity of water  = 1 mPa s)
(1) 10
2
(2) 10
4
(3) 10
3
(4) 10
6
Answer (2)
Sol. Flow rate of water (Q) = 100 lit/min
?
?
?
???
3
33
100 10 5
10 m
60 3
? Velocity of flow (v) = 
?
?
?
?
?? ? ?
3
22
Q510
A 3 (510 )
??
??
10 2
m/s
15 3
= 0.2 m/s
? Reynold number (R
e
) 
?
?
?
Dv
?
?? ?
?
?
2
2
(10 10 ) 1000
3
1
  2 × 10
4
Order of R
e
 = 10
4
6. In figure, the optical fiber is l = 2 m long and
has a diameter of d = 20 ?m. If a ray of light is
incident on one end of the fiber at angle
?
1
 = 40°, the number of reflections it makes
before emerging from the other end is close to:
(refractive index of fiber is 1.31 and
sin 40° = 0.64)
?
2
40°
d
(1) 66000 (2) 55000
(3) 45000 (4) 57000
Answer (4)
Sol. 1 × sin 40° = 1.31 sin ?
? ?? ??? 
0.64
sin 30
1.31
?l = 20 ?m × cot ?
?
?
?
?? ?
6
2
N
20 10 cot
  
?
??
?
6
210
57735
20 3
? N 57000
7. A 200 ? resistor has a certain color code. If
one replaces the red color by green in the
code, the new resistance will be:
(1) 400 ?
(2) 500 ?
(3) 300 ?
(4) 100 ?
Answer (2)
Sol. 200 ? = Red + Black + Brown
Green ? 5
So, Green + Black + Brown  ? 500 ?
8. A 20 Henry inductor coil is connected to a
10 ohm resistance in series as shown in figure.
The time at which rate of dissipation of energy
(Joule’s heat) across resistance is equal to the
rate at which magnetic energy is stored in the
inductor, is:
i
10 ??
20 H E
(1)
2
ln2
(2) 2 ln2
(3) ln2
(4)
1
ln2
2
Answer (2)
Sol. P
R
 = i
2
 × R
P
B
 = V × i
? P
L
 = Vi – i
2
R
? Vi – i
2
R = i
2
R
? i = 
??
??
?? ?
t/
VV
and i 1 e
2R R
?
??
??
??
t/
VV
1e
2R R
? ?? ? ?
20
tln(2) ln(2) 2ln(2)
10
9. Four particles A, B, C and D with masses
m
A
 = m, m
B
 = 2m, m
C
 = 3m and m
D
 = 4m are at
the corners of a square. They have
accelerations of equal magnitude with
directions as shown. The acceleration of the
centre of mass of the particles is :
(1) Zero (2) ??
?
ˆˆ
ai j
(3) ??
?
a
ˆˆ
i j
5
(4) ??
?
a
ˆˆ
i j
5
Answer (4)
Sol.
?? ? ? ? ? ?
?
?? ?
CM
ˆˆ ˆ ˆ
(2m)aj 3m ai ma( i) 4m a(j)
a
2m 3m 4m m
 
?
???
ˆˆ
2ai 2aj a
ˆˆ
(i j)
10 5
10. A plane electromagnetic wave travels in free
space along the x-direction. The electric field
component of the wave at a particular point of
space and time is E = 6 Vm
–1
 along y-direction.
Its corresponding magnetic field component, B
would be :
(1) 2 × 10
–8
 T along y-direction
(2) 6 × 10
–8
 T along z-direction
(3) 2 × 10
–8
 T along z-direction
(4) 6 × 10
–8
 T along x-direction
Answer (3)
Sol.
?
?? ? ?
?
8 0
0
8
E 6
B210T
c 310
Propagation direction = ?
ˆˆ
EB
??
ˆˆ ˆ
ijB
? ?
ˆ ˆ
Bk
11. Voltage rating of a parallel plate capacitor is
500 V. Its dielectric can withstand a maximum
electric field of 10
6
 V/m. The plate area is
10
–4
 m
2
. What is the dielectric constant if the
capacitance is 15 pF?
(given ?
0
 = 8.86 × 10
–12
 C
2
/Nm
2
)
(1) 3.8 (2) 4.5
(3) 8.5 (4) 6.2
Answer (3)
Sol.
?
?
0
kA
C
d
?
V
E
d
??
?
?? ? ?
??
12 4 6
12
k8.86 10 10 10
15 10
500
k = 8.5
12. The wavelength of the carrier waves in a
modern optical fiber communication network is
close to :
(1) 600 nm (2) 900 nm
(3) 1500 nm (4) 2400 nm
Answer (3)
Sol. Fact Based
Wavelength of carrier waves in modern optical
fiber communication is most widely used near
about 1500 nm.
13. A steel wire having a radius of 2.0 mm,
carrying a load of 4 kg, is hanging from a
ceiling. Given that g = 3.1 ? ms
–2
, what will be
the tensile stress that would be developed in
the wire?
(1) 4.8 × 10
6 
Nm
–2
(2) 3.1 × 10
6 
Nm
–2
(3) 5.2 × 10
6 
Nm
–2
(4) 6.2 × 10
6 
Nm
–2
Answer (2)
Sol.
?
??
?? ? ?
?? ?
62
32
F43.1
Stress 3.1 10 N/m
A (2 10 )
14. A thin circular plate of mass M and radius R
has its density varying as ?(r) = ?
0
 r with ?
0
 as
constant and r is the distance from its center.
The moment of inertia of the circular plate
about an axis perpendicular to the plate and
passing through its edge is I = a MR
2
. The value
of the coefficient a is
(1)
3
2
(2)
1
2
(3)
3
5
(4)
8
5
Answer (4)
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)
08/04/2019
Morning
PART–A : PHYSICS
1. Two particles move at right angle to each other.
Their de Broglie wavelengths are ?
1
 and ?
2
respectively. The particles suffer perfectly
inelastic collision. The de Broglie wavelength ?,
of the final particle, is given by:
(1) ?? ? ?
12
(2)
???
??
12
2
(3)
??
?? ?
12
21 1
(4)
??
?? ?
22 2
12
11 1
Answer (4)
Sol.
1
2
?
?
1
1
h
p
?
?
2
2
h
p
? ??
22
f 12
pp p
?
??
? ??
22
22
12
hh h
?
??
?? ?
22 2
12
11 1
2. In SI units, the dimensions of 
?
?
0
0
 is:
(1) AT
2
M
–1
L
–1
(2) AT
–3
ML
3/2
(3) A
–1
TML
3
(4) A
2
T
3
M
–1
L
–2
Answer (4)
Sol.
??
??
?
??
?? ??
?? ??
??
??
? ?? ??
????
1 00
0
0 00
LT
?
?
??
2
2
0
q
F
4r
?
??
?? ??
?
??
?
2
0
22
AT
[]
MLT L
?
??? ?
???
??
?
??
??
?
??
??
12134 0
0
LT A M L T
  = [M
–1
L
–2
T
3
A
2
]
3. A particle moves in one dimension from rest
under the influence of a force that varies with
the distance travelled by the particle as shown
in the figure. The kinetic energy of the particle
after it has travelled 3 m is
1
2
3
Force 
(in N)
Distance
(in ) m
1 2 3
(1) 4 J (2) 2.5 J
(3) 5 J (4) 6.5 J
Answer (4)
Sol. = Area under F–x graph
?K.E  = 
? ???? ? ?
1
W (32)(32) 22
2
= 2.5 + 4
= 6.5 J
4. Radiation coming from transitions n = 2 to n = 1
of hydrogen atoms fall on He
+
 ions in n = 1 and
n = 2 states. The possible transition of helium ions
as they absorb energy from the radiation is
(1) n = 2 ? n = 4
(2) n = 2 ? n = 5
(3) n = 2 ? n = 3
(4) n = 1 ? n = 4
Answer (1)
Sol. Energy released by hydrogen atom
??
??
??
??
1
11 3
E =13.6× = ×13.6eV
14 4
      = 10.2 eV
Also, energy absorbed by H
e
+
 ion in transition
n = 2 ? n = 4
??
??
??
??
2
11
E =13.6×4× =10.2 eV
416
So, possible transition is n = 2 ? n = 4
5. Water from a pipe is coming at a rate of
100 liters per minute. If the radius of the pipe
is 5 cm, the Reynolds number for the flow is of
the order of : (density of water = 1000 kg/m
3
,
coefficient of viscosity of water  = 1 mPa s)
(1) 10
2
(2) 10
4
(3) 10
3
(4) 10
6
Answer (2)
Sol. Flow rate of water (Q) = 100 lit/min
?
?
?
???
3
33
100 10 5
10 m
60 3
? Velocity of flow (v) = 
?
?
?
?
?? ? ?
3
22
Q510
A 3 (510 )
??
??
10 2
m/s
15 3
= 0.2 m/s
? Reynold number (R
e
) 
?
?
?
Dv
?
?? ?
?
?
2
2
(10 10 ) 1000
3
1
  2 × 10
4
Order of R
e
 = 10
4
6. In figure, the optical fiber is l = 2 m long and
has a diameter of d = 20 ?m. If a ray of light is
incident on one end of the fiber at angle
?
1
 = 40°, the number of reflections it makes
before emerging from the other end is close to:
(refractive index of fiber is 1.31 and
sin 40° = 0.64)
?
2
40°
d
(1) 66000 (2) 55000
(3) 45000 (4) 57000
Answer (4)
Sol. 1 × sin 40° = 1.31 sin ?
? ?? ??? 
0.64
sin 30
1.31
?l = 20 ?m × cot ?
?
?
?
?? ?
6
2
N
20 10 cot
  
?
??
?
6
210
57735
20 3
? N 57000
7. A 200 ? resistor has a certain color code. If
one replaces the red color by green in the
code, the new resistance will be:
(1) 400 ?
(2) 500 ?
(3) 300 ?
(4) 100 ?
Answer (2)
Sol. 200 ? = Red + Black + Brown
Green ? 5
So, Green + Black + Brown  ? 500 ?
8. A 20 Henry inductor coil is connected to a
10 ohm resistance in series as shown in figure.
The time at which rate of dissipation of energy
(Joule’s heat) across resistance is equal to the
rate at which magnetic energy is stored in the
inductor, is:
i
10 ??
20 H E
(1)
2
ln2
(2) 2 ln2
(3) ln2
(4)
1
ln2
2
Answer (2)
Sol. P
R
 = i
2
 × R
P
B
 = V × i
? P
L
 = Vi – i
2
R
? Vi – i
2
R = i
2
R
? i = 
??
??
?? ?
t/
VV
and i 1 e
2R R
?
??
??
??
t/
VV
1e
2R R
? ?? ? ?
20
tln(2) ln(2) 2ln(2)
10
9. Four particles A, B, C and D with masses
m
A
 = m, m
B
 = 2m, m
C
 = 3m and m
D
 = 4m are at
the corners of a square. They have
accelerations of equal magnitude with
directions as shown. The acceleration of the
centre of mass of the particles is :
(1) Zero (2) ??
?
ˆˆ
ai j
(3) ??
?
a
ˆˆ
i j
5
(4) ??
?
a
ˆˆ
i j
5
Answer (4)
Sol.
?? ? ? ? ? ?
?
?? ?
CM
ˆˆ ˆ ˆ
(2m)aj 3m ai ma( i) 4m a(j)
a
2m 3m 4m m
 
?
???
ˆˆ
2ai 2aj a
ˆˆ
(i j)
10 5
10. A plane electromagnetic wave travels in free
space along the x-direction. The electric field
component of the wave at a particular point of
space and time is E = 6 Vm
–1
 along y-direction.
Its corresponding magnetic field component, B
would be :
(1) 2 × 10
–8
 T along y-direction
(2) 6 × 10
–8
 T along z-direction
(3) 2 × 10
–8
 T along z-direction
(4) 6 × 10
–8
 T along x-direction
Answer (3)
Sol.
?
?? ? ?
?
8 0
0
8
E 6
B210T
c 310
Propagation direction = ?
ˆˆ
EB
??
ˆˆ ˆ
ijB
? ?
ˆ ˆ
Bk
11. Voltage rating of a parallel plate capacitor is
500 V. Its dielectric can withstand a maximum
electric field of 10
6
 V/m. The plate area is
10
–4
 m
2
. What is the dielectric constant if the
capacitance is 15 pF?
(given ?
0
 = 8.86 × 10
–12
 C
2
/Nm
2
)
(1) 3.8 (2) 4.5
(3) 8.5 (4) 6.2
Answer (3)
Sol.
?
?
0
kA
C
d
?
V
E
d
??
?
?? ? ?
??
12 4 6
12
k8.86 10 10 10
15 10
500
k = 8.5
12. The wavelength of the carrier waves in a
modern optical fiber communication network is
close to :
(1) 600 nm (2) 900 nm
(3) 1500 nm (4) 2400 nm
Answer (3)
Sol. Fact Based
Wavelength of carrier waves in modern optical
fiber communication is most widely used near
about 1500 nm.
13. A steel wire having a radius of 2.0 mm,
carrying a load of 4 kg, is hanging from a
ceiling. Given that g = 3.1 ? ms
–2
, what will be
the tensile stress that would be developed in
the wire?
(1) 4.8 × 10
6 
Nm
–2
(2) 3.1 × 10
6 
Nm
–2
(3) 5.2 × 10
6 
Nm
–2
(4) 6.2 × 10
6 
Nm
–2
Answer (2)
Sol.
?
??
?? ? ?
?? ?
62
32
F43.1
Stress 3.1 10 N/m
A (2 10 )
14. A thin circular plate of mass M and radius R
has its density varying as ?(r) = ?
0
 r with ?
0
 as
constant and r is the distance from its center.
The moment of inertia of the circular plate
about an axis perpendicular to the plate and
passing through its edge is I = a MR
2
. The value
of the coefficient a is
(1)
3
2
(2)
1
2
(3)
3
5
(4)
8
5
Answer (4)
Sol.
??
?? ? ? ?
?
R 3
0
0
0
2R
Mr2rdr
3
??
?? ? ? ? ?
?
R 5
2 0
C0
0
2R
Ir2rdrr
5
?? ??
?? ? ? ?? ? ?
??
??
5
25 0
C0
16 R 11
II MR 2 R
35 15
??
??? ?
??
??
32 2
0
82 8
RR MR
53 5
15. An alternating voltage v(t) = 220  sin 100 ?t volt
is applied to a purely resistive load of 50 ?. The
time taken for the current to rise from half of
the peak value to the peak value is
(1) 2.2 ms (2) 7.2 ms
(3) 5 ms (4) 3.3 ms
Answer (4)
Sol. I = I
m
 sin(100 ?t)
???
m
m1
I
Isin(100t)
2
?
?
??
1
100 t
6
? ?
1
1
ts
600
?
??
?
21
Ts
100 50
? ?? ? ? ? ? ?
req 1
T1 1 2 1
tt s3.3ms
4 200 600 600 300
16. Four identical particles of mass M are located
at the corners of a square of side ‘a’. What
should be their speed if each of them revolves
under the influence of others’ gravitational field
in a circular orbit circumscribing the square?
a
(1)
GM
1.41
a
(2)
GM
1.16
a
(3)
GM
1.21
a
(4)
GM
1.35
a
Answer (2)
Sol.
??
?? ?
22
22
aGM GM
r,F 2
a2a 2
a
a
?
??
??
??
??
??
??
??
22
2
Mv GM 1
2
a 2 a
2
?
??
??
??
??
2
GM 1
v1
a
22
?
??
?? ?
??
??
GM 1 GM
v 1 1.16
aa
22
17. The bob of a simple pendulum has mass 2 g
and a charge of 5.0 ?C. It is at rest in a uniform
horizontal electric field of intensity 2000 V/m.
At equilibrium, the angle that the pendulum
makes with the vertical is
(take g = 10 m/s
2
)
(1) tan
–1
 (0.2) (2) tan
–1
 (5.0)
(3) tan
–1
 (2.0) (4) tan
–1
 (0.5)
Answer (4)
Sol. Tcos ? = mg
mg
?
qE
? ?
T
Tsin ? = qE
??
qE
tan
mg
?
?
??
?? ?
??
6
3
510 2000 1
tan
2 210 10
?
?
??
??
??
1
1
tan
2
18.
A
B
LL
A wire of length 2L, is made by joining two
wires A and B of same length but different radii
r and 2r and made of the same material. It is
vibrating at a frequency such that the joint of
the two wires forms a node. If the number of
antinodes in wire A is p and that in B is q then
the ratio p : q is
(1) 4 : 9 (2) 1 : 2
(3) 3 : 5 (4) 1 : 4
Answer (2)