SECTION A

1. A thin plastic rod is bent into a circular ring of radius R. It is uniformly

charged with charge density . The magnitude of the electric field at its
centre is :
(A) (B) Zero (C) (D)
2 0R 4 R 4 0R
0
2. Three small charged spheres X, Y and Z carrying charges + q, q and + q
respectively are placed equidistant from each other, as shown in the
figure. The spheres Y and Z are held in place. Initially X is also held in
place, but is otherwise free to move. When X is released, the path
followed by it will be :

(A) A (B) B (C) C (D) D

3. In a uniform straight wire, conduction electrons move along + x direction.
Let E and j be the electric field and current density in the wire,
respectively. Then :
(A) E and j both are along + x direction.

(B) E and j both are along x direction.

(C) E is along + x direction, but j is along x direction.

(D) E is along x direction, but j is along + x direction.

4. Two charged particles, P and Q, each having charge q but of masses m1
and m2, are accelerated through the same potential difference V. They

enter a region of magnetic field B ( v ) and describe the circular paths

m1
of radii a and b respectively. Then is equal to :
m2
2 2
a b a b
(A) (B) (C) (D)
b a b a
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5. A galvanometer of resistance G is converted into an ammeter of range
0 to I A. If the current through the galvanometer is 0.1% of I A, the
resistance of the ammeter is :
G G G G
(A) (B) (C) (D)
999 1000 1001 100·1

6. A 10 cm long wire lies along y-axis. It carries a current of 1.0 A in

^ ^
positive y-direction. A magnetic field B = (5 mT) j (8 mT) k exists in
the region. The force on the wire is :
^ ^
(A) (0·8 mN) i (B) (0·8 mN) i
^ ^
(C) (80 mN) i (D) (80 mN) i

7. The primary and secondary coils of a transformer have 500 turns and
5000 turns respectively. The primary coil is connected to an ac source of
220 V 50 Hz. The output across the secondary coil is :
(A) 220 V 50 Hz (B) 1100 V 50 Hz
(C) 2200 V 5 Hz (D) 2200 V 50 Hz

8. The first scientist who produced and observed electromagnetic waves of

wavelengths in the range 25 mm 5 mm was :
(A) J.C. Maxwell (B) H.R. Hertz
(C) J.C. Bose (D) G. Marconi

9. The waves associated with a moving electron and a moving proton have
the same wavelength . It implies that they have the same :
(A) momentum (B) angular momentum
(C) speed (D) energy

10. Two beams, A and B whose photon energies are 3·3 eV and 11·3 eV
respectively, illuminate a metallic surface (work function 2·3 eV)
successively. The ratio of maximum speed of electrons emitted due to
beam A to that due to beam B is :
1 1
(A) 3 (B) 9 (C) (D)
3 9

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11. The transition of electron that gives rise to the formation of the second
spectral line of the Balmer series in the spectrum of hydrogen atom
corresponds to :
(A) nf = 2 and ni = 3 (B) nf = 3 and ni = 4
(C) nf = 2 and ni = 4 (D) nf = 2 and ni =

12. Ge is doped with As. Due to doping,

(A) the structure of Ge lattice is distorted.
(B) the number of conduction electrons increases.
(C) the number of holes increases.
(D) the number of conduction electrons decreases.

Questions number 13 to 16 are Assertion (A) and Reason (R) type questions. Two
statements are given one labelled Assertion (A) and the other labelled Reason
(R). Select the correct answer from the codes (A), (B), (C) and (D) as given below.
(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the
correct explanation of the Assertion (A).
(B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not
the correct explanation of the Assertion (A).
(C) Assertion (A) is true, but Reason (R) is false.
(D) Assertion (A) is false and Reason (R) is also false.

13. Assertion (A) : Two long parallel wires, freely suspended and connected
in series to a battery, move apart.
Reason (R) : Two wires carrying current in opposite directions repel
each other.

14. Assertion (A) : Plane and convex mirrors cannot produce real images
under any circumstance.
Reason (R) : A virtual image cannot serve as an object to produce a
real image.

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15. Assertion (A) : The mutual inductance between two coils is maximum
when the coils are wound on each other.
Reason (R) : The flux linkage between two coils is maximum when
they are wound on each other.

16. Assertion (A) : In photoelectric effect, the kinetic energy of the emitted
photoelectrons increases with increase in the intensity of
the incident light.
Reason (R) : Photoelectric current depends on the wavelength of the
incident light.

SECTION B

17. A uniform wire of length L and area of cross-section A has resistance R.

The wire is uniformly stretched so that its length increases by 25%.
Calculate the percentage increase in the resistance of the wire. 2

18. An object is placed 30 cm in front of a concave mirror of radius of

curvature 40 cm. Find the (i) position of the image formed and
(ii) magnification of the image. 2

19. Consider a neutron (mass m) of kinetic energy E and a photon of the

same energy. Let n and p be the de Broglie wavelength of neutron and

the wavelength of photon respectively. Obtain an expression for n . 2

p

14
20. (a) Monochromatic light of frequency 5·0 10 Hz passes from air
into a medium of refractive index 1·5. Find the wavelength of the
light (i) reflected, and (ii) refracted at the interface of the two
media. 2
OR
(b) A plano-convex lens of focal length 16 cm is made of a material of
refractive index 1.4. Calculate the radius of the curved surface of
the lens. 2

21.
role in the formation of p-n junction. 2
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 SECTION C

22. An air-filled parallel plate capacitor with plate separation 1 mm has a

capacitance of 20 pF. It is charged to 4.0 C. Calculate the amount of
work done to pull its plates to a separation of 5 mm. Assume the charge
on the plates remains the same. 3

23. (a) Define current density. Is it a scalar or a vector ? An electric field

E is maintained in a metallic conductor. If n be the number of
electrons (mass m, charge e) per unit volume in the conductor
and its relaxation time, show that the current density
ne 2
j = E , where = . 3
m
OR
(b) What is a Wheatstone bridge ? Obtain the necessary conditions
under which the Wheatstone bridge is balanced. 3

24. A circular coil with cross-sectional area 0.2 cm2 carries a current of 4 A.
It is kept in a uniform magnetic field of magnitude 0.5 T normal to the
plane of the coil. Calculate :
(a) the net force on the coil.
(b) the torque on the coil.
(c) the average force on each electron in the coil due to the
magnetic field. The free electron density in the material of the coil
is 1028 m 3. 3

25. (a) Draw the graphs showing the variation of the following with the
frequency of ac source in a circuit :
(i) Resistance
(ii) Capacitive reactance
(iii) Inductive reactance
(b) Can the voltage drop across the inductor or the capacitor in a
series LCR circuit be greater than the applied voltage of the ac
source ? Justify your answer. 3

11-55/1/3 13 P.T.O.
26. (a) State any two properties of a nucleus.

(b) Why is the density of a nucleus much more than that of an atom ?

(c) Show that the density of the nuclear matter is the same for all
nuclei. 3

27. State the three postulates of B

A hydrogen atom de-excites from level n to level (n 1). Show that,
v , for
n3
large values of n, where is a constant. This result exactly agrees with
that obtained from classical physics
theory. 3

28. (a)

examples to justify this statement.

(b) (i) Long distance radio broadcasts use short-wave bands. Why ?
(ii) Optical and radio telescopes are built on the ground, but
X-ray astronomy is possible only from satellites orbiting the
Earth. Why ? 3

SECTION D

Questions number 29 and 30 are case study-based questions. Read the following
paragraphs and answer the questions that follow.

29. A lens is a transparent medium bounded by two surfaces, with one or

both surfaces being spherical. The focal length of a lens is determined by
the radii of curvature of its two surfaces and the refractive index of its
medium with respect to that of the surrounding medium. The power of a
lens is reciprocal of its focal length. If a number of lenses are kept in
contact, the power of the combination is the algebraic sum of the powers
of the individual lenses.

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 (i) A double-convex lens, with each face having same radius of
curvature R, is made of glass of refractive index n. Its power is : 1
2 (n 1) (2n 1)
(A) (B)
R R
(n 1) (2n 1)
(C) (D)
2R 2R
(ii) A double-convex lens of power P, with each face having same
radius of curvature, is cut into two equal parts perpendicular to its
principal axis. The power of one part of the lens will be : 1
P
(A) 2P (B) P (C) 4P (D)
2
(iii) The above two parts are kept in contact with each other as shown
in the figure. The power of the combination will be : 1

P P
(A) (B) P (C) 2P (D)
2 4
(iv) (a) A double-convex lens of power P, with each face having same
radius of curvature, is cut along its principal axis. The two
parts are arranged as shown in the figure. The power of the
combination will be : 1

(A) Zero (B) P

P
(C) 2P (D)
2
OR
(b) Two convex lenses of focal lengths 60 cm and 20 cm are held
coaxially in contact with each other. The power of the
combination is : 1
(A) 6·6 D (B) 15 D
1 1
(C) D (D) D
15 80

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30. Junction Diode as a Rectifier :
The process of conversion of an ac voltage into a dc voltage is called
rectification and the device which performs this conversion is called a
rectifier. The characteristics of a p-n junction diode reveal that when a
p-n junction diode is forward biased, it offers a low resistance and when it
is reverse biased, it offers a high resistance. Hence, a p-n junction diode
conducts only when it is forward biased. This property of a p-n junction
diode makes it suitable for its use as a rectifier.
Thus, when an ac voltage is applied across a p-n junction, it conducts
only during those alternate half cycles for which it is forward biased. A
rectifier which rectifies only half cycle of an ac voltage is called a
half-wave rectifier and one that rectifies both the half cycles is known as
a full-wave rectifier.
(i) The root mean square value of an alternating voltage applied to a
V
full-wave rectifier is 0 . Then the root mean square value of the
2
rectified output voltage is : 1
V0 V02
(A) (B)
2 2
2 V0 V0
(C) (D)
2 2 2

(ii) In a full-wave rectifier, the current in each of the diodes flows for : 1
(A) Complete cycle of the input signal
(B) Half cycle of the input signal
(C) Less than half cycle of the input signal
(D) Only for the positive half cycle of the input signal
(iii) In a full-wave rectifier : 1
(A) Both diodes are forward biased at the same time.
(B) Both diodes are reverse biased at the same time.
(C) One is forward biased and the other is reverse biased at the
same time.
(D) Both are forward biased in the first half of the cycle and
reverse biased in the second half of the cycle.
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 (iv) (a) An alternating voltage of frequency of 50 Hz is applied to a
half-wave rectifier. Then the ripple frequency of the output
will be : 1
(A) 100 Hz (B) 50 Hz
(C) 25 Hz (D) 150 Hz
OR

(b) A signal, as shown in the figure, is applied to a p-n junction

diode. Identify the output across resistance RL : 1

(A)

(B)

(C)

(D)

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 SECTION E

31. (a) (i) A resistor and a capacitor are connected in series to an ac

source v = vm sin t. Derive an expression for the impedance
of the circuit.

(ii) When does an inductor act as a conductor in a circuit ? Give

reason for it.

(iii) An electric lamp is designed to operate at 110 V dc and

11 A current. If the lamp is operated on 220 V, 50 Hz
ac source with a coil in series, then find the inductance of
the coil. 5

OR

(b) (i) Draw a labelled diagram of a step-up transformer and

describe its working principle. Explain any three causes for
energy losses in a real transformer.

(ii) A step-up transformer converts a low voltage into high

voltage. Does it violate the principle of conservation of
energy ? Explain.

(iii) A step-up transformer has 200 and 3000 turns in its

primary and secondary coils respectively. The input voltage
given to the primary coil is 90 V. Calculate :

(1) The output voltage across the secondary coil

(2) The current in the primary coil if the current in the

secondary coil is 2·0 A. 5

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32. (a) (i) Derive an expression for potential energy of an electric
dipole p in an external uniform electric field E . When is
the potential energy of the dipole (1) maximum, and
(2) minimum ?

(ii) An electric dipole consists of point charges 1·0 pC and

+ 1·0 pC located at (0, 0) and (3 mm, 4 mm) respectively in
1000 V ^
x y plane. An electric field E = i is switched on
m
in the region. Find the torque acting on the dipole. 5

OR
^
(b) (i) An electric dipole (dipole moment p = p i ), consisting of
charges q and q, separated by distance 2a, is placed along
the x-axis, with its centre at the origin. Show that the
potential V, due to this dipole, at a point x, (x >> a) is equal
^
1 p. i
to . .
4 2
0 x

(ii) Two isolated metallic spheres S1 and S2 of radii 1 cm and

3 cm respectively are charged such that both have the same
2
charge density 10 9 C / m2 . They are placed far away

from each other and connected by a thin wire. Calculate the

new charge on sphere S1. 5

33. (a) (i) A ray of light passes through a triangular prism. Show
graphically, how the angle of deviation varies with the angle
of incidence ? Hence define the angle of minimum deviation.
(ii) A ray of light is incident normally on a refracting face of a
prism of prism angle A and suffers a deviation of angle .
Prove that the refractive index n of the material of the prism
sin ( A )
is given by n .
sin A

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 (iii) The refractive index of the material of a prism is 2 . If the
refracting angle of the prism is 60 , find the

(1) Angle of minimum deviation, and

(2) Angle of incidence. 5

OR

(b) (i) State Huygens principle. A plane wave is incident at an

angle i on a reflecting surface. Construct the corresponding
reflected wavefront. Using this diagram, prove that the
angle of reflection is equal to the angle of incidence.

(ii) What are the coherent sources of light ? Can two

independent sodium lamps act like coherent sources ?
Explain.

(iii) A beam of light consisting of a known wavelength 520 nm

and an unknown wavelength
experiment produces two interference patterns such that the
fourth bright fringe of unknown wavelength coincides with
the fifth bright fringe of known wavelength. Find the value
of . 5

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