Page 1
CBSE XII | PHYSICS
Board Paper – Solution
CBSE
Class XII Physics
Board Paper – 2016 Solution
SECTION – A
1. The frequencies of the side bands produced are
?
?
? ? ?
? ? ?
?
??
?
3
Maximum frequency: 5 kHz 2 MHz
5 10 MHz 2 MHz
0.005 2 2.005 MHz
Minimum frequency: 2 MHz 5 kHz
2 MHz 0.005 MHz
1.995 MHz
2. A particle moves along a curved path if it moves in the presence of a magnetic
field.
Now, when there is an angular projection, i.e. when the velocity of the particle is
at an angle with respect to the magnetic field, then the particle will move in a
helical path.
The vertical component (vsin ?) will be perpendicular to the field and hence will
rotate the particle in a circular path. However, the horizontal component (vcos ?)
will move the particle in a straight line path. So, the cumulative motion of the
particle is a helix.
3. The mobility of a charge carrier is defined as the drift velocity per unit electric
field.
??
?
?
?
?
? ? ?
d
d
v
E
eE
Now, v
m
Where, is the relaxation time
e
m
4. The work done in moving a charge along any circular path is zero. So, to move a
point charge Q around a circular arc of radius ‘r’ at the centre of which another
point charge ‘q’ is located, no work has to be done.
5. During fog, the light coming from an object is partly deflected by the particles of
the fog and does not reach the eye of the observer. Thus, the objects are not
seen clearly.
The phenomenon is called scattering of light.
Page 2
CBSE XII | PHYSICS
Board Paper – Solution
CBSE
Class XII Physics
Board Paper – 2016 Solution
SECTION – A
1. The frequencies of the side bands produced are
?
?
? ? ?
? ? ?
?
??
?
3
Maximum frequency: 5 kHz 2 MHz
5 10 MHz 2 MHz
0.005 2 2.005 MHz
Minimum frequency: 2 MHz 5 kHz
2 MHz 0.005 MHz
1.995 MHz
2. A particle moves along a curved path if it moves in the presence of a magnetic
field.
Now, when there is an angular projection, i.e. when the velocity of the particle is
at an angle with respect to the magnetic field, then the particle will move in a
helical path.
The vertical component (vsin ?) will be perpendicular to the field and hence will
rotate the particle in a circular path. However, the horizontal component (vcos ?)
will move the particle in a straight line path. So, the cumulative motion of the
particle is a helix.
3. The mobility of a charge carrier is defined as the drift velocity per unit electric
field.
??
?
?
?
?
? ? ?
d
d
v
E
eE
Now, v
m
Where, is the relaxation time
e
m
4. The work done in moving a charge along any circular path is zero. So, to move a
point charge Q around a circular arc of radius ‘r’ at the centre of which another
point charge ‘q’ is located, no work has to be done.
5. During fog, the light coming from an object is partly deflected by the particles of
the fog and does not reach the eye of the observer. Thus, the objects are not
seen clearly.
The phenomenon is called scattering of light.
CBSE XII | PHYSICS
Board Paper – Solution
SECTION – B
6. The H
?
line in the emission spectrum of the hydrogen atom is obtained when the
electron transition takes place between n = 2 to n = 1.
?
?
?
?
??
? ? ? ?
?
? ? ? ?
??
? ? ? ? ? ? ? ?
??
??
? ? ? ? ?
? ? ? ?
th
n
2
21
22
21
2
21
19
21
19
21
We know that the energy in n level is
13.6
E
n
13.6 13.6
EE
21
13.6
E E 13.6
2
13
E E 13.6 1 13.6 10.2 eV
44
E E 10.2 1.6 10 J
E E 16.32 10 J
Now, this difference in energ
?
?
? ? ? ?
? ?
? ? ? ?
?
? ? ? ?
21
19
21
34
15
y gives the energy of the photon emitted
E E h
EE 16.32 10
h 6.63 10
2.46 10 Hz
OR
The electron in the hydrogen atom jumps from n
2
= ? to n
1
= 1.
Now, we know that
??
??
??
??
??
?
??
??
? ? ? ? ? ?
??
??
??
? ? ? ? ? ? ?
?
? ? ?
22
12
77
8 10
7
o
1 1 1
R
nn
1 1 1
1.097 10 1.097 10
1
1
9.116 10 m 911.6 10 m
1.097 10
911.6 A
Page 3
CBSE XII | PHYSICS
Board Paper – Solution
CBSE
Class XII Physics
Board Paper – 2016 Solution
SECTION – A
1. The frequencies of the side bands produced are
?
?
? ? ?
? ? ?
?
??
?
3
Maximum frequency: 5 kHz 2 MHz
5 10 MHz 2 MHz
0.005 2 2.005 MHz
Minimum frequency: 2 MHz 5 kHz
2 MHz 0.005 MHz
1.995 MHz
2. A particle moves along a curved path if it moves in the presence of a magnetic
field.
Now, when there is an angular projection, i.e. when the velocity of the particle is
at an angle with respect to the magnetic field, then the particle will move in a
helical path.
The vertical component (vsin ?) will be perpendicular to the field and hence will
rotate the particle in a circular path. However, the horizontal component (vcos ?)
will move the particle in a straight line path. So, the cumulative motion of the
particle is a helix.
3. The mobility of a charge carrier is defined as the drift velocity per unit electric
field.
??
?
?
?
?
? ? ?
d
d
v
E
eE
Now, v
m
Where, is the relaxation time
e
m
4. The work done in moving a charge along any circular path is zero. So, to move a
point charge Q around a circular arc of radius ‘r’ at the centre of which another
point charge ‘q’ is located, no work has to be done.
5. During fog, the light coming from an object is partly deflected by the particles of
the fog and does not reach the eye of the observer. Thus, the objects are not
seen clearly.
The phenomenon is called scattering of light.
CBSE XII | PHYSICS
Board Paper – Solution
SECTION – B
6. The H
?
line in the emission spectrum of the hydrogen atom is obtained when the
electron transition takes place between n = 2 to n = 1.
?
?
?
?
??
? ? ? ?
?
? ? ? ?
??
? ? ? ? ? ? ? ?
??
??
? ? ? ? ?
? ? ? ?
th
n
2
21
22
21
2
21
19
21
19
21
We know that the energy in n level is
13.6
E
n
13.6 13.6
EE
21
13.6
E E 13.6
2
13
E E 13.6 1 13.6 10.2 eV
44
E E 10.2 1.6 10 J
E E 16.32 10 J
Now, this difference in energ
?
?
? ? ? ?
? ?
? ? ? ?
?
? ? ? ?
21
19
21
34
15
y gives the energy of the photon emitted
E E h
EE 16.32 10
h 6.63 10
2.46 10 Hz
OR
The electron in the hydrogen atom jumps from n
2
= ? to n
1
= 1.
Now, we know that
??
??
??
??
??
?
??
??
? ? ? ? ? ?
??
??
??
? ? ? ? ? ? ?
?
? ? ?
22
12
77
8 10
7
o
1 1 1
R
nn
1 1 1
1.097 10 1.097 10
1
1
9.116 10 m 911.6 10 m
1.097 10
911.6 A
CBSE XII | PHYSICS
Board Paper – Solution
7. The drift speed is
?
d
I
v
neA
Now, we know that the current is given from Ohm’s law as
??
?
?
??
??
??
??
? ? ?
? ? ?
? ? ? ? ? ?
? ? ? ? ?
d
d
d
d
28 19 4
5
V
I
R
V
v
RneA
V
RA
nev
V RA
nev l l
RA
Now, resistivity is given as
l
V
nev l
5
8 10 1.6 10 2.5 10 0.1
1.56 10 m
8.
(i) The de Broglie wavelength is related to the accelerating potential as
?
??
? ? ? ?
?
?
??
? ? ?
??
?
? ? ? ?
?
??
? ? ? ?
p
pp
p
p p p p
p
h
2meV
h
2m e V
h
And,
2m e V
2m e V m e
h
h
2m e V m e
Now, mass and charge of particle is greater than that of proton.
for the same potential difference.
(ii) The kinetic energy is related to accelerating potential as
??
??
?
?
??
?
??
?
pp
pp
p
K.E. eV
K.E. e V
And, K.E. e V
K.E. e
K.E. e
Since, the charge on proton is less than that on alpha particle,
K.E. K.E. for the same potential difference.
Page 4
CBSE XII | PHYSICS
Board Paper – Solution
CBSE
Class XII Physics
Board Paper – 2016 Solution
SECTION – A
1. The frequencies of the side bands produced are
?
?
? ? ?
? ? ?
?
??
?
3
Maximum frequency: 5 kHz 2 MHz
5 10 MHz 2 MHz
0.005 2 2.005 MHz
Minimum frequency: 2 MHz 5 kHz
2 MHz 0.005 MHz
1.995 MHz
2. A particle moves along a curved path if it moves in the presence of a magnetic
field.
Now, when there is an angular projection, i.e. when the velocity of the particle is
at an angle with respect to the magnetic field, then the particle will move in a
helical path.
The vertical component (vsin ?) will be perpendicular to the field and hence will
rotate the particle in a circular path. However, the horizontal component (vcos ?)
will move the particle in a straight line path. So, the cumulative motion of the
particle is a helix.
3. The mobility of a charge carrier is defined as the drift velocity per unit electric
field.
??
?
?
?
?
? ? ?
d
d
v
E
eE
Now, v
m
Where, is the relaxation time
e
m
4. The work done in moving a charge along any circular path is zero. So, to move a
point charge Q around a circular arc of radius ‘r’ at the centre of which another
point charge ‘q’ is located, no work has to be done.
5. During fog, the light coming from an object is partly deflected by the particles of
the fog and does not reach the eye of the observer. Thus, the objects are not
seen clearly.
The phenomenon is called scattering of light.
CBSE XII | PHYSICS
Board Paper – Solution
SECTION – B
6. The H
?
line in the emission spectrum of the hydrogen atom is obtained when the
electron transition takes place between n = 2 to n = 1.
?
?
?
?
??
? ? ? ?
?
? ? ? ?
??
? ? ? ? ? ? ? ?
??
??
? ? ? ? ?
? ? ? ?
th
n
2
21
22
21
2
21
19
21
19
21
We know that the energy in n level is
13.6
E
n
13.6 13.6
EE
21
13.6
E E 13.6
2
13
E E 13.6 1 13.6 10.2 eV
44
E E 10.2 1.6 10 J
E E 16.32 10 J
Now, this difference in energ
?
?
? ? ? ?
? ?
? ? ? ?
?
? ? ? ?
21
19
21
34
15
y gives the energy of the photon emitted
E E h
EE 16.32 10
h 6.63 10
2.46 10 Hz
OR
The electron in the hydrogen atom jumps from n
2
= ? to n
1
= 1.
Now, we know that
??
??
??
??
??
?
??
??
? ? ? ? ? ?
??
??
??
? ? ? ? ? ? ?
?
? ? ?
22
12
77
8 10
7
o
1 1 1
R
nn
1 1 1
1.097 10 1.097 10
1
1
9.116 10 m 911.6 10 m
1.097 10
911.6 A
CBSE XII | PHYSICS
Board Paper – Solution
7. The drift speed is
?
d
I
v
neA
Now, we know that the current is given from Ohm’s law as
??
?
?
??
??
??
??
? ? ?
? ? ?
? ? ? ? ? ?
? ? ? ? ?
d
d
d
d
28 19 4
5
V
I
R
V
v
RneA
V
RA
nev
V RA
nev l l
RA
Now, resistivity is given as
l
V
nev l
5
8 10 1.6 10 2.5 10 0.1
1.56 10 m
8.
(i) The de Broglie wavelength is related to the accelerating potential as
?
??
? ? ? ?
?
?
??
? ? ?
??
?
? ? ? ?
?
??
? ? ? ?
p
pp
p
p p p p
p
h
2meV
h
2m e V
h
And,
2m e V
2m e V m e
h
h
2m e V m e
Now, mass and charge of particle is greater than that of proton.
for the same potential difference.
(ii) The kinetic energy is related to accelerating potential as
??
??
?
?
??
?
??
?
pp
pp
p
K.E. eV
K.E. e V
And, K.E. e V
K.E. e
K.E. e
Since, the charge on proton is less than that on alpha particle,
K.E. K.E. for the same potential difference.
CBSE XII | PHYSICS
Board Paper – Solution
9. The angle of the prism is A = 60 ?. It is also given that AQ = AR.
Therefore, the angles opposite to these two sides are also equal.
? ? ?
? ? ? ? ? ? ?
? ? ? ? ? ?
? ? ? ? ? ? ? ? ?
? ? ? ?
12
12
AQR ARQ
Now, for a triangle
A AQR ARQ 180
AQR ARQ 60
r r 30 ( AQO ARO 90 )
r r 60
When r
1
and r
2
are equal, we have i = e.
Now, according to Snell’s law,
??
? ? ? ? ?
? ? ?
1
1
sini
sinr
3
sini sinr 3 sin30
2
i 60
Now, the angle of deviation ? is
? ? ? ?
? ? ? ? ?
? ? ? ?
i e A
60 60 60
60
10. The baseband signal is not transmitted directly because
(i) Its higher wavelength (low frequency) will require the size of the antenna or
aerial used for transmission to be very high.
(ii) For linear antenna (length l), the power radiated is proportional to
??
??
?
??
2
1
, and
hence, the effective power radiated by a long wavelength baseband signal would
be small.
Page 5
CBSE XII | PHYSICS
Board Paper – Solution
CBSE
Class XII Physics
Board Paper – 2016 Solution
SECTION – A
1. The frequencies of the side bands produced are
?
?
? ? ?
? ? ?
?
??
?
3
Maximum frequency: 5 kHz 2 MHz
5 10 MHz 2 MHz
0.005 2 2.005 MHz
Minimum frequency: 2 MHz 5 kHz
2 MHz 0.005 MHz
1.995 MHz
2. A particle moves along a curved path if it moves in the presence of a magnetic
field.
Now, when there is an angular projection, i.e. when the velocity of the particle is
at an angle with respect to the magnetic field, then the particle will move in a
helical path.
The vertical component (vsin ?) will be perpendicular to the field and hence will
rotate the particle in a circular path. However, the horizontal component (vcos ?)
will move the particle in a straight line path. So, the cumulative motion of the
particle is a helix.
3. The mobility of a charge carrier is defined as the drift velocity per unit electric
field.
??
?
?
?
?
? ? ?
d
d
v
E
eE
Now, v
m
Where, is the relaxation time
e
m
4. The work done in moving a charge along any circular path is zero. So, to move a
point charge Q around a circular arc of radius ‘r’ at the centre of which another
point charge ‘q’ is located, no work has to be done.
5. During fog, the light coming from an object is partly deflected by the particles of
the fog and does not reach the eye of the observer. Thus, the objects are not
seen clearly.
The phenomenon is called scattering of light.
CBSE XII | PHYSICS
Board Paper – Solution
SECTION – B
6. The H
?
line in the emission spectrum of the hydrogen atom is obtained when the
electron transition takes place between n = 2 to n = 1.
?
?
?
?
??
? ? ? ?
?
? ? ? ?
??
? ? ? ? ? ? ? ?
??
??
? ? ? ? ?
? ? ? ?
th
n
2
21
22
21
2
21
19
21
19
21
We know that the energy in n level is
13.6
E
n
13.6 13.6
EE
21
13.6
E E 13.6
2
13
E E 13.6 1 13.6 10.2 eV
44
E E 10.2 1.6 10 J
E E 16.32 10 J
Now, this difference in energ
?
?
? ? ? ?
? ?
? ? ? ?
?
? ? ? ?
21
19
21
34
15
y gives the energy of the photon emitted
E E h
EE 16.32 10
h 6.63 10
2.46 10 Hz
OR
The electron in the hydrogen atom jumps from n
2
= ? to n
1
= 1.
Now, we know that
??
??
??
??
??
?
??
??
? ? ? ? ? ?
??
??
??
? ? ? ? ? ? ?
?
? ? ?
22
12
77
8 10
7
o
1 1 1
R
nn
1 1 1
1.097 10 1.097 10
1
1
9.116 10 m 911.6 10 m
1.097 10
911.6 A
CBSE XII | PHYSICS
Board Paper – Solution
7. The drift speed is
?
d
I
v
neA
Now, we know that the current is given from Ohm’s law as
??
?
?
??
??
??
??
? ? ?
? ? ?
? ? ? ? ? ?
? ? ? ? ?
d
d
d
d
28 19 4
5
V
I
R
V
v
RneA
V
RA
nev
V RA
nev l l
RA
Now, resistivity is given as
l
V
nev l
5
8 10 1.6 10 2.5 10 0.1
1.56 10 m
8.
(i) The de Broglie wavelength is related to the accelerating potential as
?
??
? ? ? ?
?
?
??
? ? ?
??
?
? ? ? ?
?
??
? ? ? ?
p
pp
p
p p p p
p
h
2meV
h
2m e V
h
And,
2m e V
2m e V m e
h
h
2m e V m e
Now, mass and charge of particle is greater than that of proton.
for the same potential difference.
(ii) The kinetic energy is related to accelerating potential as
??
??
?
?
??
?
??
?
pp
pp
p
K.E. eV
K.E. e V
And, K.E. e V
K.E. e
K.E. e
Since, the charge on proton is less than that on alpha particle,
K.E. K.E. for the same potential difference.
CBSE XII | PHYSICS
Board Paper – Solution
9. The angle of the prism is A = 60 ?. It is also given that AQ = AR.
Therefore, the angles opposite to these two sides are also equal.
? ? ?
? ? ? ? ? ? ?
? ? ? ? ? ?
? ? ? ? ? ? ? ? ?
? ? ? ?
12
12
AQR ARQ
Now, for a triangle
A AQR ARQ 180
AQR ARQ 60
r r 30 ( AQO ARO 90 )
r r 60
When r
1
and r
2
are equal, we have i = e.
Now, according to Snell’s law,
??
? ? ? ? ?
? ? ?
1
1
sini
sinr
3
sini sinr 3 sin30
2
i 60
Now, the angle of deviation ? is
? ? ? ?
? ? ? ? ?
? ? ? ?
i e A
60 60 60
60
10. The baseband signal is not transmitted directly because
(i) Its higher wavelength (low frequency) will require the size of the antenna or
aerial used for transmission to be very high.
(ii) For linear antenna (length l), the power radiated is proportional to
??
??
?
??
2
1
, and
hence, the effective power radiated by a long wavelength baseband signal would
be small.
CBSE XII | PHYSICS
Board Paper – Solution
SECTION – C
11.
(i) The distance between the object and the screen (image) is 100 cm.
Now, for the first position of the lens:
?
??
? ? ? ? ?
? ? ?
uu
v 100 u
1 1 1 1 1
...... (1)
f 100 u u 100 u u
Now, for the second position of the lens:
? ?
??
? ? ?
? ? ? ? ?
? ? ? ??
u u 20
v 100 u 20
1 1 1 1 1
...... (2)
f 80 u 80 u u 20 u 20
Therefore, from equations (1) and (2), we get
? ? ? ? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
? ? ?
? ? ?
? ? ? ?
? ? ?
? ? ? ? ?
??
? ? ?
??
??
? ? ?
? ? ? ? ?
? ? ? ? ?
??
??
? ? ? ? ? ?
22
1 1 1 1
100 u u 80 u u 20
1 1 1 1
100 u 80 u u 20 u
80 u 100 u u u 20
100 u 80 u u u 20
20 20
100 u 80 u u u 20
u u 20 100 u 80 u
u 20u 8000 180u u
200u 8000
u 40 cm
v 100 u 100 40 60 cm
Therefore, from the lens for
? ? ? ? ? ?
?
?
? ? ?
??
mula
1 1 1 1 1 1 1
f v u 60 40 60 40
1 2 3 5
f 120 120
f 24 cm
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