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 0R 4 0R

2. A charged sphere of radius r has surface charge density . The electric

field on its surface is E. If the radius of the sphere is doubled, keeping
charge density the same, the ratio of the electric field on the old sphere to
that on the new sphere will be :
1 1
(A) 1 (B) (C) (D) 4
2 4

3. A student is asked to connect four cells, each of emf E and internal

resistance r, in series. But she/he connects one cell wrongly in series with
the other cells. The equivalent emf and the equivalent internal resistance
of the combination will be :
(A) 4E and 2r (B) 4E and 3r
(C) 3E and 4r (D) 2E and 4r

4. A piece of wire bent in the form of a circular loop A carries a current I.

The wire is then bent into a circular loop B of two turns and carries the
same current. The ratio of magnetic fields at the centre of loop A to that
of loop B will be :
1
(A) (B) 16
16
1
(C) 4 (D)
4

5. 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

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6. 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

7. A conducting circular loop is placed in a uniform magnetic field

B = 50 mT with its plane perpendicular to the magnetic field. The radius
1
of the loop is made to shrink at a constant rate of 1 mm s . At the
instant the radius of the loop is 4 cm, the induced emf in the loop is :
(A) V (B) 2 V
(C) 4 V (D) 8 V

8. The electric and magnetic fields of electromagnetic waves are :

(A) In the same phase and perpendicular to each other.
(B) In the same phase and not perpendicular to each other.
(C) Not in the same phase but are perpendicular to each other.
(D) Neither in the same phase nor perpendicular to each other.

9. 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

10. 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

11. 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.
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12. 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 =

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) : 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.

14. 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.

15. 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.

16. 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.
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 SECTION B

17. Two batteries of emfs 6 V and 3 V and internal resistances 0·8 and
0·2 respectively are connected in series to an external resistance R, as
shown in figure. Find the value of R so that the potential difference
across the 6 V battery be zero. 2

18. 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

19. (a) Monochromatic light of frequency 5·0 1014 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

20. 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

21. How does the conductivity of an intrinsic semiconductor vary with

temperature ? Explain. Show the variation in a plot. 2

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 SECTION C

22. Three point charges Q1, Q2 and Q3 are located in x y plane at points
( d, 0), (0, 0) and (d, 0) respectively. Q1 and Q3 are identical and Q2 is
positive. What will be the nature and value of Q1 so that the potential
energy of the system is zero ? 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

1
24. A bar magnet of magnetic moment 2·5 JT lies aligned with the
direction of a uniform magnetic field of 0·32 T.
(a) Find the amount of work done to turn the magnet so as to align its
magnetic moment (i) normal to the field direction, and (ii) opposite
to the field direction.
(b) What is the torque on the magnet in above cases (i) and (ii) ? 3

25. Consider the arrangement of two coils P and Q shown in the figure. When
current in coil P is switched on or switched off, a current flows in coil Q.
(a) Explain the phenomenon involved in it.
(b) Mention two factors on which the current produced in coil Q
depends.
(c) Give the direction of current in coil Q when there is a current in
the coil P and (i) R is increased, and (ii) R is decreased. 3

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26. Write the drawbacks
them 3

27. (a)
Give two
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

28. (a) Write two characteristic properties of nuclear force.

(b) Draw a plot of potential energy of a pair of nucleons as a function

of their separation. Write two important conclusions that can be
drawn from the plot. 3

SECTION D

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

29. 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.

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 (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.

(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

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 (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)

30. 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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 SECTION E

31. (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
(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)
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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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 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.

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 (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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