Assam Board Class 12 Sample Paper 2026 Physics

ASSAM BOARD

SAMPLE
PAPER
Practice Papers
Model Question Papers

Paper-1

PHYSICS (Theory)

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: Unit-I 1

  
(A) (B) Zero (C) (D)
2 0 R 4 0 R 4 0 R

2. Ten capacitors, each of capacitance 1 µF, are connected in parallel to a source of 100 V. The
total energy stored in the system is equal to: Unit-I 1

(A) 10-2 J (B) 10-3 J

(C) 0.5×10-3 J (D) 5.0×10-2 J

3. Consider the circuit shown in the figure. The potential difference between points A and B is: 1

Unit-II

A) 6 V (B) 8 V (C) 9V (D) 12 V

4. A loop carrying a current I clockwise is placed in x - y plane, in a uniform magnetic field
directed along z-axis. The tendency of the the loop will be to: Unit-III 1

(A) move along x-axis (B) move along y-axis

(C) shrink (D) expand

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 = (5mT) - (8mT) exists in the region. The force on the wire is : Unit-III 1

(A) (0.8 mN) (B) - (0.8 mN)

(C) (80 mN) (D) - (80 mN)

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: Unit-III 1

G G G G
(A)  (B)  (C)  (D) 
999 1000 1001 100.1

7. The reactance capacitor of capacitance C connected to an ac source of frequency  is ‘X’. If
the capacitance of the capacitor is doubled and the frequency of the source is tripled, the reactance
will become: Unit-IV 1
X 2 3
(A) (B) 6X (C) X (D) X
6 3 2
8. In the four regions, I, II, III and IV, the electric fields are described as: Unit-V 1

Region I : Ex = E0 sin (kz - t)

Region II : Ex = E0
Region III : Ex = E0 sin kz
Region IV : Ex = E0 cos kz
The displacement current will exist in the region :

(A) I (B) IV (C) II (D) III

9. 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 : Unit-VIII 1

(A) nf = 2 and ni = 3 (B) nf = 3 and ni = 4

(C) nf = 2 and ni = 4 (D) nf = 2 and ni = 

10. Ge is doped with As. Due to doping, Unit-IX 1

(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.

11. 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: Unit-VII 1

1 1
(A) 3 (B) 9 (C) (D)
3 9

12. The waves associated with a moving electron and a moving proton have the same wavelength
λ. It implies that they have the same : Unit-VII 1

(A) momentum (B) angular momentum

(C) speed (D) energy

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) : In photoelectric effect, the kinetic energy of the emitted photoelectrons
increases with increase in the intensity of the incident light. Unit-VII
Reason(R) : Photoelectric current depends on the wavelength of the incident light. 1
14. Assertion(A) : The mutual inductance between two coils is maximum when the coils are
wound on each other. Unit-IV
Reason(R) : The flux linkage between two coils is maximum when they are wound on each
other. 1
15. Assertion(A) : Two long parallel wires, freely suspended and connected in series to a battery,
move apart. Unit-III
Reason(R) : Two wires carrying current in opposite directions repel each other. 1
16. 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. Unit-VI 1

SECTION B

17. Find the temperature at which the resistance of a wire made of silver will be twice its
resistance at 20°C. Take 20°C as the reference temperature and temperature coefficient of
resistance of silver at 20°C = 4.0 × 10-3 K-1. Unit-II 2

18. (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. Unit-VI 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. Unit-VI 2

19. 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. Unit-VI 2

20. 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
n
expression for . Unit-VII 2
p
21. Plot a graph showing the variation of current with voltage for the material GaAs. On the
graph, mark the region where : Unit-IX 2
(a) resistance is negative, and
(b) Ohm's law is obeyed.
SECTION C

22. A cube of side 0.1 m is placed, as shown in the figure, in a region where electric field
= 500 x exists. Here x is in meters and E in NC-1. Calculate : Unit-I 3
(a) the flux passing through the cube, and
(b) the charge within the cube.

23. (a) Define 'current density'. Is it a scalar or a vector? An electric field 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 j =  , 3
 ne 2 
where  =   . Unit-II
 m 
OR
(b) What is a Wheatstone bridge? Obtain the necessary conditions under which the Wheatstone
bridge is balanced. Unit-II 3
24. A proton with kinetic energy 1.3384 × 10-14 J moving horizontally from north to south, enters
a uniform magnetic field B of 2.0 mT directed eastward. Calculate : 3
(a) the speed of the proton
(b) the magnitude of acceleration of the proton
(c) the radius of the path traced by the proton

[Take (q/m) for proton = 1.0 × 108 C/kg]
25. An inductor, a capacitor and a resistor are connected in series with an ac source v = vm sin t.
Derive an expression for the average power dissipated in the circuit. Also obtain the expression
for the resonant frequency of the circuit. Unit-IV 3

26. (a) "The wavelength of the electromagnetic wave is often correlated with the characteristic
size of the system that radiates." Give two examples to justify this statement. Unit-V
(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

27. Write the drawbacks of Rutherford's atomic model. How did Bohr remove them? Show that
different orbits in Bohr's atom are not equally spaced. Unit-VIII 3

28. (a) State any two properties of a nucleus. Unit-VIII

(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

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. Unit-VI

(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) (n  1) (2n  1)
(A) (B) (C) (D)
R R 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

P
(A) Zero (B) 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 : Unit-VI 1

(A) 6.6 D (B) 15 D

1 1
(C) D (D) D
15 80

30. Junction Diode as a Rectifier :

The process of conversion of an ac voltage into a de 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. Unit-IX

V0
(i) The root mean square value of an alternating voltage applied to a full-wave rectifier is .
2
Then the root mean square value of the rectified output voltage is : 1

V0 V0 2
(A) (B)
2 2

2V0 2 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

(b) A signal, as shown in the figure, is applied to a p-n junction diode. Identify the output across
resistance RL : Unit-IX 1

SECTION E


31. (a) (i) Derive an expression for potential energy of an electric dipole p in an external uniform

electric field . 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 x - y plane. An electric field = is switched on

in the region. Find the torque  acting on the dipole. Unit-I 5

OR

(b) (i) An electric dipole (dipole moment p = p ), 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

(ii) Two isolated metallic spheres S1 and S2 of radii 1 cm and 3 cm respectively are charged such
that both have the same charge density  109  C/m². They are placed far away from each
2

 
other and connected by a thin wire. Calculate the new charge on sphere S1. Unit-I 5

32. (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. Unit-IV

(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 : Unit-IV

(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

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 is given by

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

(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. Unit-VI

(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  ,
used in Young's double slit 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

Paper-2
PHYSICS (Theory)

SECTION-A 16 1 = 16

1. Two charges + q each are kept '2a' distance apart. A third charge - 2q is placed midway
between them. The potential energy of the system is - Unit-I 1

q2 6q 2
(A) (B)
8 0 a 8 0 a

7q 2 9q 2
(C) (D)
8 0 a 8 0 a

2. Two identical small conducting balls B1 and B2 are given 7 pC and + 4 pC charges
respectively. They are brought in contact with a third identical ball B3 and then separated. If the
final charge on each ball is 2 pC, the initial charge on B3 was Unit-I 1

(A) 2 pC (B)  3pC
(C) 5 pC (D) 15 pC

3. The quantum nature of light explains the observations on photoelectric effect as – 1
(A) there is a minimum frequency of incident radiation below which no electrons are emitted.
(B) the maximum kinetic energy of photoelectrons depends only on the frequency of incident
radiation. Unit-VII
(C) when the metal surface is illuminated, electrons are ejected from the surface after sometime.
(D) the photoelectric current is independent of the intensity of incident radiation.
4. The radius (rn) of nth orbit in Bohr model of hydrogen atom varies with n as Unit-VIII 1

1
(A) rn  n (B) rn 
n
1
(C) rn  n
2
(D) rn 
n2
5. A straight wire is kept horizontally along east-west direction. If a steady current flows in wire

from east to west, the magnetic field at a point above the wire will point towards Unit-III 1
(A) East (B) West (C) North (D) South
6. The magnetic susceptibility for a diamagnetic material is Unit-III 1
(A) small and negative (B) small and positive
(C) large and negative (D) large and positive

7. A galvanometer of resistance 100 Ω is converted into an ammeter of range (0 1 A) using a
resistance of 0.1 Ω. The ammeter will show full scale deflection for a current of about Unit-III 1
(A) 0.1 mA (B) 1 mA
(C) 10 mA (D) 0.1 A

8. A circular loop A of radius R carries a current I. Another circular loop B of radius r    is
R
 20 
placed concentrically in the plane of A. The magnetic flux linked with loop B is proportional to
Unit-IV 1

(A) R (B) R
3
(C) R 2
(D) R2
9. Figure shows the variation of inductive reactance XL of two ideal inductors of inductance L1
L1
and L2, with angular frequency . The value of is Unit-IV 1
L2

1
(A) 3 (B)
3
1
(C) 3 (D)
3

10. The phase difference between electric field and magnetic field in an electromagnetic
wave propagating along z-axis is   Unit-V    
(A) zero (B) π

(C)  (D) 
2 4

11. A coil of N turns is placed in a magnetic field such that is perpendicular to the plane of

the coil. changes with time as B = Bo cos  2 t  where T is time period. The magnitude of emf
 T 

induced in the coil will be maximum at Unit-IV 1

nT nT
(A) t = (B) t =
8 4
nT
(C) t = (D) t = nT
2
Here, n = 1, 2, 3, 4, ...

12. In Balmer series of hydrogen atom, as the wavelength of spectral lines decreases, they appear
Unit-VIII 1
(A) equally spaced and equally intense.
(B) further apart and stronger in intensity.
(C) closer together and stronger in intensity.
(D) closer together and weaker in intensity.
Note: For questions number 13 to 16, two statements are given - one labelled Assertion(A) and
the other labelled Reason(R). Select the correct answer to these questions from the codes (A),
(B), (C) and (D) as given below :
(A) If both Assertion(A) and Reason(R) are true and Reason(R) is the correct explanation of
Assertion(A).
(B) If both Assertion(A) and Reason(R) are true and Reason(R) is not the correct explanation
of Assertion(A).
(C) If Assertion(A) is true and Reason(R) is false.
(D) If both Assertion(A) and Reason(R) are false.
13. Assertion(A) : Electrons are ejected from the surface of zinc when it is irradiated by yellow
light. Unit-VII
Reason(R) : Energy associated with a photon of yellow light is more than the work function
of zinc. 1
14. Assertion(A) : The temperature coefficient of resistance is positive for metals and negative
for p-type semiconductors. Unit-II
Reason(R) : The charge carriers in metals are negatively charged, whereas the majority
charge carriers in p-type semiconductors are positively charged. 1
15. Assertion(A) : When electrons drift in a conductor, it does not mean that all free electrons in
the conductor are moving in the same direction. Unit-II
Reason(R) : The drift velocity is superposed over large random velocities of electrons. 1
16. Assertion(A): In interference and diffraction of light, light energy reduces in one region
producing a dark fringe. It increases in another region and produces a bright
fringe. Unit-VI
Reason(R) : This happens because energy is not conserved in the phenomena of interference
and diffraction. 1

SECTION – B 5  2 = 10

17. Draw the circuit diagram of a p-n junction diode in (i) forward biasing and (ii) reverse biasing.
Also draw its I-V characteristics in the two cases. Unit-IX 2

18. A proton and -particle are accelerated through different potentials V1 and V2, respectively so

that they have the same de Broglie wavelengths. Find V1 . Unit-VII 2
V2

19. A ray of light is incident normally on one face of an equilateral glass prism of refractive index
μ. When the prism is completely immersed in a transparent medium, it is observed that the
emergent ray just grazes the adjacent face. Find the refractive index of the medium.
Unit-VI 2
20. Two electric heaters have power ratings P1 and P2, at voltage V. They are connected in series
to a dc source of voltage V. Find the power consumed by the combination. Will they consume the
same power if connected in parallel across the same source? Unit-II 2
21. (a) An air bubble is trapped at point B (CB = 20 cm) in a glass sphere of radius 40 cm and
refractive index 1.5 as shown in figure. Find the nature and position of the image of the bubble as
seen by an observer at point P. Unit-VI 2

OR
(b) In normal adjustment, for a refracting telescope, the distance between objective and eye piece
lens is 1.00 m. If the magnifying power of the telescope is 19, find the focal length of the
objective and the eyepiece lens. Unit-VI 2
SECTION – C 7  3 = 21

22. (a) Differentiate between nuclear fission and fusion. 3
(b) The fission properties of 94Pu239 are very similar to those of 99U235 . How much energy (in
MeV), is released if all the atoms in 1 g of pure 94Pu239 undergo fission? The average
energy released per fission is 180 MeV. Unit-VIII
23. The electric field in a region is given by

= (10x + 4)
where x is in m and E is in N/C. Calculate the amount of work done in taking a unit charge
from Unit-I

(i) (5 m, 0) to (10 m, 0)

(ii) (5 m, 0) to (5 m, 10 m) 3

24. Draw the graph showing variation of scattered particles detected (N) with the scattering angle
() in Geiger-Marsden experiment. Write two conclusions that you can draw from this graph.
Obtain the expression for the distance of closest approach in this experiment. Unit-VIII 3
25. Find the current in branch BM in the network shown : Unit-II 3

26. A circular loop of radius 10 cm carrying current of 1.0 A lines in x-y plan. A long straight
wire lise in the same plane parallel to x- axis at a distance of 20 cm as shown in figure.

Find the direction and value of current that has to be maintained in the wire so that the net
magnetic field at O is zero. Unit-III 3
27. Name the electromagnetic waves with their wavelength range which are used for Unit-V
(i) FM radio broadcast
(ii) detection of fracture in bones
(iii) treatment of muscular strain 3
28. (a) (i) Define mutual inductance. Write its SI unit. 3
(ii) Derive an expression for the mutual inductance of a system of two long coaxial
solenoids of same length l, having turns N1 and N2 and of radii r1 and r2 (> r1). Unit-IV
OR
(b) What are ferromagnetic materials? Explain ferromagnetism with the help of suitable
diagrams, using the concept of magnetic domain. Unit-IV 3
SECTION – D 24=8
Note : Questions number 29 to 30 are Case Study based questions. Read the following paragraph
and answer the questions that follow.

29. A pure semiconductor like Ge or Si, when doped with a small amount of suitable impurity,
becomes an extrinsic semiconductor. In thermal equilibrium, the electron and hole concentration
in it are related to the concentration of intrinsic charge carriers. A p-type or n-type semiconductor
can be converted into a p-n junction by doping it with suitable impurity. Two processes, diffusion
and drift take place during formation of a p-n junction. A semiconductor diode is basically a p-n

junction with metallic contacts provided at the ends for the application of an external voltage. A
p-n junction diode allows currents to pass only in one direction when it is forward biased. Due to
this property, a diode is widely used to rectify alternating voltages, in half-wave or full wave
configuration. Unit-IX 41=4
(i) When Ge is doped with pentavalent impurity, the energy required to free the weakly bound
electron from the dopant is about
(A) 0.001 eV (B) 0.01 eV
(C) 0.72 eV (D) 1.1 eV
(ii) At a given temperature, the number of intrinsic charge carriers in a semiconductor is
2.0  1010 cm3. It is doped with pentavalent impurity atoms. As a result, the number of holes in it
becomes 8  103 cm3. The number of electrons in the semiconductor is
(A) 2  1024 m3 (B) 4  1023 m3
(C) 1  1022 m3 (D) 5  1022 m3
(iii) (a) During the formation of a p-n junction 
(A) electrons diffuse from p-region into n-region and holes diffuse from n-region into p-region.
(B) both electrons and holes diffuse from n-region into p-region.
(C) electrons diffuse from n-region into p-region and holes diffuse from p-region into n-region.
(D) both electrons and holes diffuse from p-region into n-region.
OR
(iii) (b) Initially during the formation of a p-n junction 
(A) diffusion current is large and drift current is small.
(B) diffusion current is small and drift current is large.
(C) both the diffusion and the drift currents are large.
(D) both the diffusion and the drift currents are small.
(iv) An ac voltage V = 0.5 sin (100 πt) volt is applied, in turn, across a half-wave rectifier and a
full-wave rectifier. The frequency of the output voltage across them respectively will be
(A) 25 Hz, 50 Hz (B) 25 Hz, 100 Hz
(C) 50 Hz, 50 Hz (D) 50 Hz, 100 Hz
30. A lens is a transparent optical medium bounded by two surfaces; at least one of which should be
spherical. Applying the formula of image formation by a single spherical surface successively at the
two surfaces of a thin lens, a formula known as lens maker's formula and hence the basic lens formula
can be obtained. The focal length (or power) of a lens depends on the radii of its surfaces and the

refractive index of its material with respect to the surrounding medium. The refractive index of a
material depends on the wavelength of light used. Combination of lenses helps us to obtain diverging
or converging lenses of desired power and magnification. Unit-VI 41=4

(i) A thin converging lens of focal length 20 cm and a thin diverging lens of focal length 15 cm
are placed coaxially in contact. The power of the combination is

(A) 5 D (B) 5 D
6 3
3
(C) 4 D (D) D
3 2

(ii) The radii of curvature of two surfaces of a convex lens are R and 2R. If the focal length of this
4
lens is   R , the refractive index of the material of the lens is :
3
4
(A) 5 (B)
3 3

(C) 3 (D) 7
2 5
(iii) The focal length of an equiconvex lens
(A) increases when the lens is dipped in water.
(B) increases when the wavelength of incident light decreases.
(C) increases with decrease in radius of curvature of its surface.
(D) decreases when the lens is cut into two identical parts along its principal axis.
(iv) (a) A thin convex lens L of focal length 10 cm and a concave mirror M of focal length 15
cm are placed coaxially 40 cm apart as shown in figure. A beam of light coming parallel to
the principal axis is incident on the lens. The final image will be formed at a distance of

(A) 10 cm, left of lens (B) 10 cm, right of lens
(C) 20 cm, left of lens (D) 20 cm, right of lens
OR
(b) A beam of light coming parallel to the principal axis of a convex lens L1 of focal length
16 cm is incident on it. Another convex lens L2 of focal length 12 cm is placed coaxially at
a distance 40 cm from L1. The nature and distance of the final image from L2 will be

(A) real, 24 cm (B) virtual, 12 cm
(C) real, 32 cm (D) virtual, 18 cm

SECTION-E 3  5 = 15
31. (a) (i) Draw a ray diagram for the formation of the image of an object by a convex mirror.
Hence, obtain the mirror equation.
(ii) Why are multi-component lenses used for both the objective and the eyepiece in
optical instruments?
(iii) The magnification of a small object produced by a compound microscope is 200.
The focal length of the eyepiece is 2 cm and the final image is formed at infinity. Find
the magnification produced by the objective. Unit-VI 5
OR
(b) (i) Differentiate between a wavefront and a ray. Unit-VI 5
(ii) State Huygen's principle and verify laws of reflection using suitable diagram.
(iii) In Young's double slit experiment, the slits S1 and S2 are 3 mm apart and the screen
is placed 1.0 m away from the slits. It is observed that the fourth bright fringe is at a
distance of 5 mm from the second dark fringe. Find the wavelength of light used.
32. (a) (i) A dielectric slab of dielectric constant 'K' and thickness 't' is inserted between plates
of a parallel plate capacitor of plate separation d and plate area A. Obtain an expression
for its capacitance.
(ii) Two capacitors of different capacitances are connected first (1) in series and then
(2) in parallel across a de source of 100 V. If the total energy stored in the combination
in the two cases are 40 mJ and 250 mJ respectively, find the capacitance of the
capacitors. Unit-I 5
OR

(b) (i) Using Gauss's law, show that the electric field at a point due to a uniformly
charged infinite plane sheet is given by where symbols have their usual
meanings.

(ii) Electric field in a region is given by

where E is in N/C and x is in meters.
A cube of side 10 cm is placed in the region as shown in figure.

Calculate (1) the electric flux through the cube. and (2) the net charge enclosed by the
cube. Unit-I 5
33. (a) (i) Mention the factors on which the resonant frequency of a series LCR circuit
depends. Plot a graph showing variation of impedance of a series LCR circuit with the
frequency of the applied a.c. source.
(ii) With the help of a suitable diagram, explain the working of a step-up transformer.
(iii) Write two causes of energy loss in a real transformer. Unit-IV 5
OR

(b) (i) With the help of a diagram, briefly explain the construction and working of ac
generator.
(ii) An electron is revolving around a proton in an orbit of radius r with a speed v. Obtain
expression for magnetic moment associated with the electron. Unit-IV 5

Paper-3
PHYSICS (Theory)
SECTION A
1. Two charged particles P and Q, having the same charge but different masses mp and mQ, start

from rest and travel equal distances in a uniform electric field in time tp and tQ respectively.
 
Neglecting the effect of gravity, the ratio  t p  is: Unit-I 1
t 
 Q

(A) mP (B) mQ
mQ mP

(C) mP (D) mQ
mQ mP

2. Electrons drift with speed vd in a conductor with potential difference V across its ends. If V is
reduced to  V  , their drift speed will become : Unit-II 1
2

Vd
(A)
2

(B) Vd
(C) 2 Vd
(D) 4 Vd
3. A wire of length 4.4 m is bent round in the shape of a circular loop and carries a current of 1.0
A. The magnetic moment of the loop will be : Unit-III 1

(A) 0.7 Am2 (B) 1.54 Am2
(C) 2.10 Am2 (D) 3.5 Am2

4. A circular coil of radius 10 cm is placed in a magnetic field = (1.0 + 0.5 ) mT such that
the outward unit vector normal to the surface of the coil is (0.6 + 0.8 ). The magnetic flux
linked with the coil is: Unit-IV 1

(A) 0.314 µWb (B) 3.14 μWb
(C) 31.4 µWb (D) 1.256 µWb
5. Which of the following quantity/quantities remains same in primary and secondary coils of an
ideal transformer ? Unit-IV

Current, Voltage, Power, Magnetic flux
(A ) Current only (B) Voltage only
(C) Power only (D) Magnetic flux and Power both

6. A resistor and an ideal inductor are connected in series to a 100√2 V, 50 Hz ac source. When a
voltmeter is connected across the resistor or the inductor, it shows the same reading. The reading
of the voltmeter is : Unit-IV 1

(A) 100 2V (B) 100 V

(C) 50 2V (D) 50 V

7. Electromagnetic waves with wavelength 10 nm are called : Unit-V 1
(A) Infrared waves (B) Ultraviolet rays
(C) Gamma rays (D) X-rays
8. The work function for a photosensitive surface is 3.315 eV. The cut-off wavelength for
photoemission of electrons from this surface is : Unit-VIII 1
(A) 150 nm (B) 200 nm
(C) 375 nm (D) 500 nm
9. Energy levels A, B and C of an atom correspond to increasing values of energy i.e. EA < EB <
EC. Let λ1, λ2 and λ3 be the wavelengths of radiation corresponding to the transitions C to B, B to
A and C to A, respectively. The correct relation between λ1, λ2 and λ3 is : Unit-VIII 1

1 1 1
(A) λ12 + λ22 = λ32 (B)  
1 2 3

(C) λ1 + λ2 + λ3 = 0 (D) λ1 + λ2 = λ3
10. An alpha particle approaches a gold nucleus in Geiger-Marsden experiment with kinetic
energy K. It momentarily stops at a distance d from the nucleus and reverses its direction. Then d
is proportional to: Unit-VIII 1

(A) 1 (B)
K

1
(C) (D) K
K

11. An n-type semiconducting Si is obtained by doping intrinsic Si with : Unit-IX 1
(A) Al (B) B
(C) P (D) In
12. When a p-n junction diode is subjected to reverse biasing: Unit-IX 1

(A) the barrier height decreases and the depletion region widens

(B) the barrier height increases and the depletion region widens.
(C) the barrier height decreases and the depletion region shrinks.
(D) the barrier height increases and the depletion region shrinks.

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) : Photoelectric current increases with an increase in intensity of incident

radiation, for a given frequency of incident radiation and the accelerating

potential. Unit-VII

Reason (R) : Increase in the intensity of incident radiation results in an increase in the

number of photoelectrons emitted per second and hence an increase in the

photocurrent. 1

14. Assertion (A) : Lenz's law is a consequence of the law of conservation of energy. Unit-IV

Reason (R) : There is no power loss in an ideal inductor. 1

15. Assertion (A) : An electron and a proton enter with the same momentum in a magnetic field
such that  . Then both describe a circular path of the same radius.

Reason (R) : The radius of the circular path described by the charged particle (charge q,

mass m) moving in the magnetic field is given by r = mv Unit-III 1
qB

16. Assertion (A) : The magnifying power of a compound microscope is negative. Unit-VI

Reason (R) : The final image formed is erect with respect to the object. 1

SECTION B

17. Define resistivity of a conductor. How does the resistivity of a conductor depend upon the
following: Unit-III 2

(a) Number density of free electrons in the conductor (n)

(b) Their relaxation time ()

18. (a) Two waves, each of amplitude 'a' and frequency '' emanating from two coherent sources
of light superpose at a point. If the phase difference between the two waves is , obtain an
expression for the resultant intensity at that point. Unit-VI 2

OR
(b) What is the effect on the interference pattern in Young's double-slit experiment when (i) the
source slit is moved closer to the plane of the slits, and (ii) the separation between the two slits is
increased ? Justify your answers. Unit-VI 2
19. A convex lens (n = 1.52) has a focal length of 15.0 cm in air. Find its focal length when it is
immersed in liquid of refractive index 1.65. What will be the nature of the lens? Unit-VI 2
20. The carbon isotope 126C has a nuclear mass of 12.000000 u. Calculate the binding energy of
its nucleus. Unit-VIII
Given mp = 1.007825 u; mn = 1.008665 u. 2
21. How does the energy gap of an an intrinsic semiconductor effectively change when doped
with a (a) trivalent impurity, and (b) pentavalent impurity? Justify your answer in each case.
Unit-IX 2
SECTION C

22. The figure shows a circuit with three ideal batteries. Find the magnitude and direction of
currents in the branches AG, BF and CD. Unit-II 3

23. (a) On what factors does the speed of an electromagnetic wave in a medium depend?

(b) How is an electromagnetic wave produced? Unit-V

(c) Sketch a schematic diagram depicting the electric and magnetic fields for an electromagnetic
wave propagating along z-axis. 3

24. A 100-turn coil of radius 1.6 cm and resistance 5.0  is co-axial with a solenoid of 250
turns/cm and radius 1.8 cm. The solenoid current drops from 1.5 A to zero in 25 ms. Calculate the
current induced in the coil in this duration. (Take π² = 10) Unit-IV 3

25. (a) Two long, straight, parallel conductors carry steady currents in opposite directions.

Explain the nature of the force of interaction between them. Obtain an expression for the
magnitude of the force between the two conductors. Hence define one ampere. Unit-III 3

OR

(b) Obtain an expression for the torque acting on a current carrying loop in a uniform

magnetic field . Draw the necessary diagram. Unit-III 3

26. Using Bohr's postulates, derive the expression for the radius of the nth orbit of an electron in a
hydrogen atom. Also find the numerical value of Bohr's radius a0. Unit-VIII 3

27. de Broglie wavelength λ as a function of 1 , for two particles of masses m1 and m2 are
K
shown in the figure. Here, K is the energy of the moving particles. Unit-VII

(a) What does the slope of a line represent ?

(b) Which of the two particles is heavier?

(c) Is this graph also valid for a photon ? Justify your answer in each case. 3

28. With the help of a circuit diagram, explain the working of a p-n junction diode as a full wave
rectifier. Draw its input and output waveforms. Unit-IX 3

SECTION D

Case Study Based Questions

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

29. When the terminals of a cell are connected to a conductor of resistance R, an electric current
flows through the circuit. The electrolyte of the cell also offers some resistance in the path of the
current, like the conductor. This resistance offered by the electrolyte is called internal resistance
of the cell (r). It depends upon the nature of the electrolyte, the area of the electrodes immersed in
the electrolyte and the temperature. Due to internal resistance, a part of the energy supplied by the
cell is wasted in the form of heat.

When no current is drawn from the cell, the potential difference between the two electrodes in
known as emf of the cell (ε). With a current drawn from the cell, the potential difference between
the two electrodes is termed as terminal potential difference (V).

(i) Choose the incorrect statement : Unit-II 1

(A) The potential difference (V) between the two terminals of a cell in a closed circuit is
always less than its emf (  ), during discharge of the cell.

(B) The internal resistance of a cell decreases with the decrease in temperature of the
electrolyte.

(C) When current is drawn from the cell then V = ε – Ir.

(D) The graph between potential difference between the two terminals of the cell (V) and
the current (I) through it is a straight line with a negative slope.

(ii) Two cells of emfs 2.0 V and 6.0 V and internal resistances 0.1  and 0.4 Ω respectively, are
connected in parallel. The equivalent emf of the combination will be: Unit-II 1

(A) 2.0 V (B) 2.8 V
(C) 6.0 V (D) 8.0 V
(iii) Dipped in the solution, the electrode exchanges charges with the electrolyte. The positive
electrode develops a potential V+ (V+ > 0), and the negative electrode develops a potential - (V_)
(V_  0), relative to the electrolyte adjacent to it. When no current is drawn from the cell then: 1

(A) ε = V+ + V_ > 0 (B) ε = V+ - V_ > 0

(C) ε = V+ + V_ < 0 (D) ε = V+ + V_ = 0

(iv) (a) Five identical cells, each of emf 2 V and internal resistance 0.1  are connected in
parallel. This combination in turn is connected to an external resistor of 9.98  . The current
flowing through the resistor is : Unit-II 1

(A) 0.05 A (B) 0.1 A

(C) 0.15 A (D) 0.2 A

OR

(b) Potential difference across a cell in the open circuit is 6 V. It becomes 4 V when a current of 2
A is drawn from it. The internal resistance of the cell is: Unit-II 1

(A) 1.0 Ω (B) 1.5 Ω

(C) 2.0 Ω (D) 2.5 Ω

30. When a ray of light propagates from a denser medium to a rarer medium, it bends away from
the normal. When the incident angle is increased, the refracted ray deviates more from the
normal. For a particular angle of incidence in the denser medium, the refracted ray just grazes the
interface of the two surfaces. This angle of incidence is called the critical angle for the pair of

media involved.

(i) For a ray incident at the critical angle, the angle of reflection is : Unit- VI 1

(A) 0° (B) < 90°
(C) > 90° (D) 90°

(ii) A ray of light of wavelength 600 nm is incident in water  n = 4  on the water-air interface at
 3
an angle less than the critical angle. The wavelength associated with the refracted ray is: 1

(A) 400 nm (B) 450 nm

(C) 600 nm (D) 800 nm

(iii) (a) The interface AB between the two media A and B is shown in the figure. In the denser
medium A, the incident ray PQ makes an angle of 30° with the horizontal. The refracted ray is
parallel to the interface. The refractive index of medium B w.r.t. medium A is: Unit- VI 1

3 5
(A) (B)
2 2
4
(B) (D) 2
3 3

OR

(b) Two media A and B are separated by a plane boundary. The speed of light in medium A and B
is 2  108 ms-1 and 2.5  108 ms-1 respectively. The critical angle for a ray of light going from
medium A to medium B is: Unit- VI 1
1 1 4
(A) sin 1 (B) sin
2 5
1 3 1 2
(C) sin (D) sin
5 5
(iv) The figure shows the path of a light ray through a triangular prism. In this phenomenon, the
angle  is given by: Unit- VI 1

1
(A) sin 1 n 2  1
2
(B) sin (n -1)
 1   1 
(C) sin 1   (D) sin 1  2 

 n -1 
2
 (n -1) 
SECTION E
31. (a) (i) Obtain an expression for the electric potential due to a small dipole of dipole moment

, at a point from its centre, for much larger distances compared to the size of the dipole.

(ii) Three point charges q, 2q and nq are placed at the vertices of an equilateral triangle. If the
potential energy of the system is zero, find the value of n. Unit-I 5
OR
(b) (i) State Gauss's Law in electrostatics. Apply this to obtain the electric field at a point near
a uniformly charged infinite plane sheet.
(ii) Two long straight wires 1 and 2 are kept as shown in the figure. The linear charge density of
the two wires are λ1 = 10 µC/m and λ2 = - 20 µC/m. Find the net force experienced by an
electron held at point P. Unit-I 5

32. (a) (i) A particle of mass m and charge q is moving with velocity in a magnetic field as
shown in the figure. Show that it follows a helical path. Hence, obtain its frequency of revolution.

(ii) In a hydrogen atom, the electron moves in an orbit of radius 2Å making 8×1014 revolutions per
second. Find the magnetic moment associated with the orbital motion of the electron. Unit-III 5
OR
(b) (i) What is current sensitivity of a galvanometer? Show how the current sensitivity of a
galvanometer may be increased. "Increasing the current sensitivity of a galvanometer may not
necessarily increase its voltage sensitivity." Explain. Unit-III
(ii) A moving coil galvanometer has a resistance 15  and takes 20 mA to produce full scale

deflection. How can this galvanometer be converted into a voltmeter of range 0 to 100 V ?
Unit-III 5
33. (a) (i) Give any two differences between the interference pattern obtained in Young's double-
slit experiment and a diffraction pattern due to a single slit. Unit-VI

(ii) Draw an intensity distribution graph in case of a double-slit interference pattern.

(iii) In Young's double-slit experiment using monochromatic light of wavelength λ, the intensity
of light at a point on the screen, where path difference is λ, is K units. Find the intensity of light at

a point on the screen where the path difference is . 5

OR

(b) (i) Draw a labelled ray diagram of a compound microscope showing image formation at least
distance of distinct vision. Derive an expression for its magnifying power.

(ii) A telescope consists of two lenses of focal length 100 cm and 5 cm. Find the magnifying
power when the final image is formed at infinity. Unit-VI 5

Paper-4
PHYSICS (Theory)
SECTION A
1. Consider a group of charges q1, q2, q3 such that ∑q ≠ 0. Then equipotentials at a large distance,
due to this group are approximately: Unit-I 1

(A) Plane (B) Spherical surface

(C) Paraboloidal surface (D) Ellipsoidal surface

2. A proton is taken from point P1 to point P2, both located in an electric field. The potentials at
points P1 and P2 are -5 V and +5 V respectively. Assuming that kinetic energies of the proton at
points P1 and P2 are zero, the work done on the proton is: Unit-I 1

(A) -1.6 × 10-18 J (B) 1.6 × 10-18 J

(C) Zero (D) 0.8 × 10-18 J

3. A 2.0 cm segment of wire, carrying 5.0 A current in positive y-direction lies along y-axis, as
shown in the figure. The magnetic field at a point (3 m, 4 m, 0) due to this segment (part of a
circuit) is : Unit-I 1

(A) (0.12 nT) (B) - (0.10 nT)

(C) - (0.24 nT) (D) (0.24 nT)
4. A circular loop of wire, carrying a current 'I' is lying in xy-plane with its centre coinciding with
the origin. It is subjected to a uniform magnetic field pointing along + z-axis. The loop will: 1

(A) move along x-axis (B) move along - y-axis
(C) move along z-axis (D) remain stationary Unit-III

5. A current carrying circular loop of magnetic moment is suspended in a vertical plane in an
external magnetic field such that its plane is normal to . The work done in rotating this loop
by 45° about an axis perpendicular to is closest to: Unit-III 1

(A) - 0.3MB (B) 0.3 MB
(C) - 1.7MB (D) 1.7 MB

6. The current in a coil of 15 mH increases uniformly from zero to 4 A in 0.004 s. The emf
induced in the coil will be: Unit-IV 1

(A) 22 .5 V (B) 17.5 V

(C) 15.0 V (D) 12.5 V

7. Consider a solenoid of length l and area of cross-section A with fixed number of turns. The
self-inductance of the solenoid will increase if: Unit-IV 1

(A) both l and A are increased
(B) l is decreased and A is increased
(C) l is increased and A is decreased
(D) both l and A are decreased
8. Which one of the following has the highest frequency? Unit-V 1

(A) Infrared rays (B) Gamma rays

(C) Radio waves (D) Microwaves

9. A proton and an alpha particle having equal velocities approach a target nucleus. They come
momentarily to rest and then reverse their directions. The ratio of the distance of closest approach
of the proton to that of the alpha particle will be: Unit-VIII 1

(A) 1 (B) 2
2

(C) 1 (D) 4
4

10. Which one of the following is the correct graph between the maximum kinetic energy (Km) of
the emitted photoelectrons and the frequency of incident radiation (v) for a given photosensitive
surface? Unit-VII 1

11. An electron makes a transition from n = 2 level to n = 1 level in the Bohr model of a hydrogen
atom. Its period of revolution: Unit-VIII 1

(A) increases by 87.5%
(B) decreases by 87.5%
(C) increases by 43.75%
(D) decreases by 43.75%
12. Si is doped with a pentavalent element. The energy required to set the additional electron free
is about: Unit-IX 1

(A) 0.01 eV (B) 0.05 eV

(C) 0.72 eV (D) 1.1 eV

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) : In a semiconductor, the electrons in the conduction band have lesser energy
than those in the valence band. Unit-IX
Reason(R): Donor energy level is just above the valence band in a semiconductor. 1
14. Assertion(A): Photoelectric effect demonstrates the particle nature of light. Unit-IX
Reason(R): Photoelectric current is proportional to frequency of incident radiation. 1

15. Assertion(A): A proton and an electron enter a uniform magnetic field with the same

momentum such that is perpendicular to . They describe circular paths
of the same radius. Unit-III

Reason (R) : In a magnetic field, orbital radius r is equal to p .
qB

16. Assertion(A: A convex lens, when immersed in a liquid, disappears. Unit-VI
Reason(R): The refractive indices of material of the lens and the liquid are equal. 1

SECTION B

17. (a) What is meant by 'relaxation time' of free electrons in a conductor? Show that the
ml
resistance of a conductor can be expressed by R = 2 , where symbols have their usual
ne  A
meanings. Unit-II 2

OR
(b) Draw the circuit diagram of a Wheatstone bridge. Obtain the condition when no current flows
through the galvanometer in it. Unit-II 2

18. The magnifying power of an astronomical telescope is 24. In normal adjustment, distance
between its two lenses is 150 cm. Find the focal Length of the objective lens. Unit-VI 2

19. Explain the following: Unit-VI 2

(a) For a simple microscope, the angular size of the object equals the angular size of the image.
Yet it offers magnification.

(b) Both plane and convex mirrors produce virtual images of objects. Can they produce real
images under some circumstances?

20. The minimum intensity of white light that our eyes can perceive is about 0.1 nWm-2. Calculate
the number of photons of this light entering our pupil (area 0.4 cm²) per second. Unit-VII 2

(Take average wavelength of white light = 500 nm and Planck's constant = 6.6 × 10-34 Js)

21. Suppose a pure Si crystal has 5 × 1028 atoms m-3. It is doped by 1 ppm concentration of boron.
Calculate the concentration of holes and electrons, given that ni = 1.5 × 1016 m-3. Is the doped
crystal n-type or p-type? Unit-IX 2

SECTION C

22. Determine the current in branches AB, AC and BC of the network shown in figure.

Unit-II 3

23. Two long straight parallel conductors carrying currents, exert a force on each other. Why?
Derive an expression for the force per unit length between two long straight parallel conductors
carrying currents in opposite directions. Explain the nature of the force between these conductors.
Unit-III 3

24. A sinusoidal voltage is applied to an electric circuit containing a circuit element 'X' in which

the current leads the voltage by . Unit-IV 3
2

(a) Identify the circuit element 'X' in the circuit.
(b) Write the formula for its reactance.
(c) Show graphically the variation of this reactance with frequency of ac voltage.
(d) Explain the behaviour of this element when it is used in (i) an ac circuit, and (ii) a de circuit.
25. The electric field in an electromagnetic wave in vacuum is given by : Unit-V 3

= (6.3 N/C) [cos (1.5 rad/m) y + (4.5 x 108 rad/s) t]

(a) Find the wavelength and frequency of the wave.

(b) What is the amplitude of the magnetic field of the wave?

(c) Write an expression for the magnetic field of this wave.

26. State Bohr's first and second postulates. Use them to derive an expression for the radius of the
nth orbit in a hydrogen atom. Unit-VIII 3

27. (a) Define atomic mass unit (u).

(b) Calculate the energy required to separate a deuteron into its constituent parts (a proton and a
neutron). Given: Unit-VIII 3

m(D) = 2.014102 u

mH = 1.007825 u

mn = 1.008665 u

28. (a) Draw the circuit diagrams for obtaining the V  I characteristics of a p-n junction diode.
Explain briefly the salient features of the V  I characteristics in (i) forward biasing, and (ii)
reverse biasing. Unit-IX 3
OR

(b) On the basis of energy band diagrams, distinguish between (i) an insulator, (ii) a
semiconductor, and (iii) a conductor.

SECTION D

Case Study Based Questions

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

29. The figure shows four pairs of parallel identical conducting plates, separated by the same
distance 2.0 cm and arranged perpendicular to x-axis. The electric potential of each plate is

mentioned. The electric field 2 between a pair of plates is uniform and normal to the plates.

(i) For which pair of the plates is the electric field along ? Unit-I 1

(A) I (B) II

(C) III (D) IV

(ii) An electron is released midway between the plates of pair IV. It will : 1

(A) move along at constant speed

(B) move along  at constant speed

(C) accelerate along

(D) accelerate along 

(iii) Let Vo be the potential at the left plate of any set, taken to be at x = 0 m. Then potential V at
any point (0 ≤ x ≤ 2 cm) between the plates of that set can be expressed as: 1

(A) V = Vo + x (B) V = Vo +  x2

(C) V = Vo + x1/2 (D) V = Vo +  x3/2
where  is a constant, positive or negative.

(iv) (a) Let E1, E2, E3 and E4 be the magnitudes of the electric field between the pairs of plates, I,
II, III and IV respectively. Then : 1
(A) E1 > E2 > E3 > E4 (B) E3 > E4 > E1 > E2
(C) E4 > E3 > E2 > E1 (D) E2 > E3 > E4 > E1
OR
(b) An electron is projected from the right plate of set I directly towards its left plate. It just comes
to rest at the plate. The speed with which it was projected is about: 1
11
(Take (e/m) =1.76 × 10 C/kg)
(A) 1.3 × 105 m/s (B) 2.6 × 106 m/s

(C) 6.5 × 105 m/s (D) 5.2 × 107 m/s

30. Diffraction and interference are closely related phenomena that occur together. Diffraction is
the phenomenon of bending of light around the edges of the obstacle, while interference is the
combination of waves that results in a new wave pattern. In order to get interference, there must

be at least two waves that are diffracting. So while diffraction can occur without interference,
interference cannot occur without diffraction.
Two slits of width 2 m each in an opaque material are separated by a distance of 6 m.
Monochromatic light of wavelength 450 nm is incident normally on the slits. One finds a
combined interference and diffraction pattern on the screen. Unit-VI
(i) The number of peaks of the interference fringes formed within the central peak of the
envelope of the diffraction pattern will be : 1
(A) 2 (B) 3
(C) 4 (D) 6
(ii) The number of peaks of the interference formed if the slit width is doubled while
keeping the distance between the slits same will be : 1
(A) 1 (B) 2
(C) 3 (D) 4
(iii) (a) If instead of 450 nm light, another light of wavelength 680 nm is used, number of
peaks of the interference formed in the central peak of the envelope of the diffraction
pattern will be: 1
(A) 2 (B) 4
(C) 6 (D) 9
OR
(b) Consider the diffraction of light by a single slit described in this case study. The first
minimum falls at an angle  equal to: 1
(A) sin (0.12)
1
(B) sin (0.225)
(C) sin (0.32) (D) sin (0.45)
4
(iv) The number of bright fringes formed due to interference on 1 m of screen placed at m
3
away from the slits is : 1
(A) 2 (B) 3
(C) 6 (D) 10

SECTION E
31. (a) (i) Obtain the expression for the capacitance of a parallel plate capacitor with a dielectric
medium between its plates.
(ii) A charge of 6 µC is given to a hollow metallic sphere of radius 0.2 m. Find the
potential at (i) the surface and (ii) the centre of the sphere. Unit-I 5
OR
(b) (i) A charge + Q is placed on a thin conducting spherical shell of radius R. Use Gauss's
theorem to derive an expression for the electric field at a point lying (i) inside and (ii)
outside the shell. Unit-I
(ii) Show that the electric field for same charge density (σ) is twice in case of a conducting
plate or surface than in a non conducting sheet. 5

32. (a) (i) (1) What is meant by current sensitivity of a galvanometer? Mention the factors on
which it depends. Unit-III

(2) A galvanometer of resistance G is converted into a voltmeter of range (0 V)
by using a resistance R. Find the resistance, in terms of R and G, required to
convert it into a voltmeter of range  0   .
V
 2
(ii) The magnetic flux through a coil of resistance 5 Ω increases with time as :
 = (2.0 t³ + 5.0 t² + 6.0 t) mWb Unit-IV
Find the magnitude of induced current through the coil at t = 2s. 5
OR
(b) (i) A rectangular coil of N turns and area of cross-section A is rotated at a steady angular
speed in  uniform magnetic field. Obtain an expression for the emf induced in the coil at
any instant of time.
(ii) Two coplanar and concentric circular loops L1 and L2 are placed coaxially with their
centres coinciding. The radii of L1 and L2 are 1 cm and 100 cm respectively. Calculate the
mutual inductance of the loops. (Take π² = 10) Unit-IV 5
33. (a) (i) Trace the path of a ray of light showing refraction through a triangular prism and hence
obtain an expression for angle of deviation () in terms of A, i and e, where symbols have their
usual meanings. Draw a graph showing the variation of angle of deviation with the angle of
incidence.

(ii) In the figure, a ray of light is incident on a transparent liquid contained in a thin glass box at
an angle of 45° with its one face. The emergent ray passes along the face AB. Find the refractive
index of the liquid. Unit-VI 5

OR
(b) (i) The displacement of two light waves, each of amplitude 'a' and frequency , emanating
from two coherent sources of light, are given by y1 = a cos t and y 2 = a cos (t + ).  is the
phase difference between the two waves. These light waves superpose at a point. Obtain the
expression for the resultant intensity at that point. Unit-VI
(ii) In Young's double slit experiment, find the ratio of intensities at two points on a screen when
waves emanating from two slits reaching these points have path differences (i) and  (ii)  .

5
6 12

Paper-5

PHYSICS (Theory)

SECTION A

1. A battery supplies 0.9 A current through a 2 Ω resistor and 0.3 A current through a 7 Ω
resistor when connected one by one. The internal resistance of the battery is: Unit-II 1
(A) 2 Ω (Β) 1.2 Ω
(C) 1 Ω (D) 0.5 Ω
2. A particle of mass m and charge q describes a circular path of radius R in a magnetic field. If
its mass and charge were 2 m and q respectively, the radius of its path would be 1
2
(A) R (B) R Unit-III
4 2
(C) 2 R (D) 4 R
3. Which of the following pairs is that of paramagnetic materials? Unit-III 1
(A) Copper and Aluminium (B) Sodium and Calcium
(C) Lead and Iron (D) Nickel and Cobalt
4. A galvanometer of resistance 50 Ω is converted into a voltmeter of range (0
2V) using a resistor of 1.0 k Ω. If it is to be converted into a voltmeter of range (0-10 V),
the resistance required will be Unit-III 1
(A) 4.8 Κ Ω (Β) 5.0 Κ Ω
(C) 5.2 Κ Ω (D) 5.4 Κ Ω
5. Two coils are placed near each other. When the current in one coil is changed at the rate of 5
A/s, an emf of 2 mV is induced in the other. The mutual inductance of the two coils is 1
(A) 0.4 mH (B) 2.5 mH Unit-IV
(C) 10mH (D) 2.5 H
6. The electromagnetic waves used to purify water are Unit-V 1
(A) Infrared rays (B) Ultraviolet rays
(C) X-rays (D) Gamma rays
7. The focal lengths of the objective and the eyepiece of a compound microscope are 1 cm and
2 cm respectively. If the tube length of the microscope is 10 cm, the magnification obtained
by the microscope for most suitable viewing by relaxed eye is: Unit-VI 1
(A) 250 (B) 200
(C) 150 (D) 125
8. The variation of the stopping potential (V0) with the frequency (v) of the incident radiation
for four metals A, B, C and D is shown in the figure. For the same frequency of incident
radiation producing photo-electrons in all metals, the kinetic energy of photo-electrons will
be maximum for metal Unit-VII 1

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

9. The energy of an electron in the ground state of hydrogen atom is 13.6 eV. The kinetic and
potential energy of the electron in the first excited state will be Unit-VII 1
(A) 13.6 eV, 27.2 eV (B) 6.8 eV, 13.6 eV
(C) 3.4 eV, 6.8 eV (D) 6.8 eV, 3.4 eV
10. A Young's double-slit experimental set up is kept in a medium of refractive index  4 
3
Which maximum in this case will coincide with the 6th maximum obtained if the medium is
replaced by air? Unit-VI 1
th th
(A) 4 (B) 6
th
(C) 8 (D) 10th
11. The potential energy between two nucleons inside a nucleus is minimum at a distance of
about Unit-VIII 1
(A) 0.8 fm (B) 1.6 fm
(C) 2.0 fm (D) 2.8 fm
12. A pure Si crystal having 5  10 atoms m3 is dopped with 1 ppm concentration of
28

antimony. If the concentration of holes in the doped crystal is found to be 4.5  109 m3, the
concentration (in m-³) of intrinsic charge carriers in Si crystal is about Unit-IX 1
(A) 1.2  10 15
(B) 1.5  10 16

(C) 3.0  10 15
(D) 2.0  1016
For Questions 13 to 16, two statements are given - one labelled Assertion(A) and other labelled
Reason(R). Select the correct answer to these questions from the options as given below.
(A) If both Assertion(A) and Reason(R) are true and Reason(R) is correct explanation of
Assertion(A).
(B) If both Assertion(A) and Reason(R) are true and Reason(R) is not the correct explanation
of Assertion(A).
(C) If Assertion(A) is true but Reason(R) is false.
(D) If both Assertion(A) and Reason(R) are false.

13. Assertion(A): Equal amount of positive and negative charges are distributed uniformly on
two halves of a thin circular ring as shown in figure. The resultant electric field
at the centre O of the ring is along OC. Unit-I
Reason (R): It is so because the net potential at O is not zero. 1

14. Assertion(A) : The energy of a charged particle moving in a magnetic field does not change.
Reason (R) : It is because the work done by the magnetic force on the charge moving in a
magnetic field is zero. Unit-III 1

15. Assertion(A): In a Young's double-slit experiment, interference pattern is not observed
when two coherent sources are infinitely close to each other. Unit-VI 1
Reason(R): The fringe width is proportional to the separation between the two sources.
16. Assertion(A): An alpha particle is moving towards a gold nucleus. The impact parameter is
maximum for the scattering angle of 180°. Unit-VIII
Reason(R): The impact parameter in an alpha particle scattering experiment does not
depend upon the atomic number of the target nucleus. 1
SECTION -B
17. (a) Four point charges of 1 µC, 2 µC, 1 µC and 2 µC are placed at the corners A, B, C and
D respectively, of a square of side 30 cm. Find the net force acting on a charge of 4 µC
placed at the centre of the square. Unit-I 2
OR
17. (b) Three point charges, 1 pC each, are kept at the vertices of an equilateral triangle of side 10
cm. Find the net electric field at the centroid of triangle. Unit-I 2
18. Derive an expression for magnetic force acting on a straight conductor of length L
carrying current I in an external magnetic field . Is it valid when the conductor is in zig-
zag form? Justify. Unit-III 2
19. A telescope has an objective lens of focal length 150 cm and an eyepiece of focal length 5
cm. Calculate its magnifying power in normal adjustment and the distance of the image
formed by the objective. Unit-VI 2
20. (a) Two energy levels of an electron in hydrogen atom are separated by 2.55 eV. Find the
wavelength of radiation emitted when the electron makes transition from the higher energy
level to the lower energy level.
(b) In which series of hydrogen spectrum this line shall fall? Unit-VIII 2
11
21. The earth revolves around the sun in an orbit of radius 1.5 × 10 m with orbital speed 30
km/s. Find the quantum number that characterises its revolution using Bohr's model in this
case (mass of earth = 6.0 × 1024 kg). Unit-VIII 2
SECTION - C
22. (a) Write Einstein's photoelectric equation. How did Millikan prove the validity of this
equation?
(b) Explain the existence of threshold frequency of incident radiation for photoelectric
emission from a given surface. Unit-VII 3
23. (a) Define the term 'electric flux' and write its dimensions.
(b) A plane surface, in shape of a square of side 1 cm is placed in an electric
such that the unit vector normal to the surface is given by . Find the
electric flux through the surface. Unit-I 3
24. (a) (i) State Lenz's Law. In a closed circuit, the induced current opposes the change in magnetic
flux that produced it as per the law of conservation of energy. Justify.
(ii) A metal rod of length 2 m is rotated with a frequency 60 rev/s about an axis passing
through its centre and perpendicular to its length. A uniform magnetic field of 2T

perpendicular to its plane of rotation is switched-on in the region. Calculate the e.m.f.
induced between the centre and the end of the rod. Unit-IV 3
OR
24.(b) (i) State and explain Ampere's circuital law.

(ii) Two long straight parallel wires separated by 20 cm, carry 5 A and 10 A current
respectively, in the same direction. Find the magnitude and direction of the net magnetic
field at a point midway between them. Unit-III 3
25. An electron moving with a velocity enters a
region of uniform magnetic field . Find the radius of the circular path
described by it. While rotating; does the electron trace a linear path too? If so, calculate
the linear distance covered by it during the period of one revolution. Unit-III 3
26 (a) Name the parts of the electromagnetic spectrum which are (i) also known as 'heat waves'
and (ii) absorbed by ozone layer in the atmosphere. Unit-V
(b) Write briefly one method each, of the production and detection of these radiations. 3
27.(a) Explain the characteristics of a p-n junction diode that makes it suitable for its use as a
rectifier. Unit-IX
(b) With the help of a circuit diagram, explain the working of a full wave rectifier. 3
28. Explain the following, giving reasons: Unit-IX 3
(a) A doped semiconductor is electrically neutral.
(b) In a p-n junction under equilibrium, there is no net current.
(c) In a diode, the reverse current is practically not dependent on the applied voltage.
SECTION – D
29. Dielectrics play an important role in design of capacitors. The molecules of a dielectric
may be polar or non-polar. When a dielectric slab is placed in an external electric field,
opposite charges appear on the two surfaces of the slab perpendicular to electric field. Due
to this an electric field is established inside the dielectric. Unit-I
The capacitance of a capacitor is determined by the dielectric constant of the material that
fills the space between the plates. Consequently, the energy storage capacity of a capacitor
is also affected. Like resistors. capacitors can also be arranged in series and/or parallel.
(i) Which of the following is a polar molecule? 1
(A) O2 (B) H2
(C) N2 (D) HCl
(ii) Which of the following statements about dielectrics is correct? 1
(A) A polar dielectric has a net dipole moment in absence of an external electric field
which gets modified due to the induced dipoles.
(B) The net dipole moments of induced dipoles is along the direction of the applied
electric field.
(C) Dielectrics contain free charges.
(D) The electric field produced due to induced surface charges inside a dielectric is
along the external electric field.
(iii) When a dielectric slab is inserted between the plates of an isolated charged capacitor,
the energy stored in it: 1
(A) increases and the electric field inside it also increases.
(B) decreases and the electric field also decreases.

(C) decreases and the electric field increases.
(D) increases and the electric field decreases.
(iv) (a) An air-filled capacitor with plate area A and plate separation d has capacitance
C0. A slab of dielectric constant K, area A and thickness D is inserted between
5
the plates. The capacitance of the capacitor will become 1

(B) 
K+5 
(A) 
4K 
C0 C0
 5k+1  4 
 K+4 
(C) 
5K 
C0 (D)  C0
 4k+1  4K 
OR
(iv) (b) Two capacitors of capacitances 2 C0 and 6 C0 are first connected in series and
then in parallel across the same battery. The ratio of energies stored in series
combination to that in parallel is 1
1 1
(A) (B)
4 6
2 3
(C) (D)
15 16
30. A prism is an optical medium bounded by three refracting plane surfaces. A ray of light
suffers successive refractions on passing through its two surfaces and deviates by a certain
angle from its original path. The refractive index of the material of the prism is given by
 A+ m  A
  sin   / sin . If the angle of incidence on the second surface is greater than an
 2  2
angle called critical angle, the ray will not be refracted from the second surface and is
totally internally reflected. Unit-VI
(i) The critical angle for glass is , and that for water is 2. The critical angle for glass-water
surface would be (given ag = 1.5, aw = 1.33) 1
(A) less than 2 (B) between 1 and 2
(C) greater than 2 (D) less than 1
(ii) When a ray of light of wavelength  and frequency  is refracted into a denser medium 1
(A)  and v both increase.
(B) increases but v is unchanged.
(C)  decreases but v is unchanged.
(D) and v both decrease.
(iii) (a) The critical angle for a ray of light passing from glass to water is minimum for 1
(A) red colour (B) blue colour
(C) yellow colour (D) violet colour
OR
(iii) (b) Three beams of red, yellow and violet colours are passed through a prism, one by one
under the same condition. When the prism is in the position of minimum deviation, the
angles of refraction from the second surface are rR, rY and rV respectively. Then 1
(A) rV <rY <rR (B) rY <rR < rV
(C) rR < rY < rV (D) rR = rY = rV
(iv) A ray of light is incident normally on a prism ABC of refractive index 2 , as shown in
figure. After it strikes face AC, it will 1

(A) go straight undeviated
(B) just graze along the face AC
(C) refract and go out of the prism
(D) undergo total internal reflection
SECTION - E
31. (a) (i) Draw equipotential surfaces for an electric dipole.
(ii) Two point charges q1 and q2 are located at , and respectively in an external

electric field . Obtain an expression for the potential energy of the system.

(iii) The dipole moment of a molecule is 1030 Cm. It is placed in an electric field

of 105 V/m such that its axis is along the electric field. The direction of is
suddenly changed by 60° at an instant. Find the change in the potential energy of
the dipole, at that instant. Unit-I 5
OR
31. (b) (i) A thin spherical shell of radius R has a uniform surface charge density . Using
Gauss' law, deduce an expression for electric field (i) outside and (ii) inside the
shell.
(ii) Two long straight thin wires AB and CD have linear charge densities 10 µC/m and
20 µC/m, respectively. They are kept parallel to each other at a distance 1 m.
Find magnitude and direction of the net electric field at a point midway between
them. Unit-I 5
32. (a ) (i) You are given three circuit elements X, Y and Z. They are connected one by one
across a given ac source. It is found that V and I are in phase for element X. V
leads I by    for element Y while I leads V    by for element Z. Identify
4 4
elements X, Y and Z. Unit-IV
(ii) Establish the expression for impedance of circuit when elements X, Y and Z are
connected in series to an ac source. Show the variation of current in the circuit
with the frequency of the applied ac source.
(iii) In a series LCR circuit, obtain the conditions under which (i) impedance is
minimum and (ii) wattless current flows in the circuit. 5
OR
32. (b) (i) Describe the construction and working of a transformer and hence obtain the
 
relation for  vs  in terms of number of turns of primary and secondary.
 vp 
 
(ii) Discuss four main causes of energy loss in a real transformer. Unit-IV 5
33. (a) (i) A plane light wave propagating from a rarer into a denser medium, is incident at an
angle i on the surface separating two media. Using Huygen's principle, draw the
refracted wave and hence verify Snell's law of refraction. Unit-VI

(ii) In a Young's double slit experiment, the slits are separated by 0.30 mm and the
screen is kept 1.5 m away. The wavelength of light used is 600 nm. Calculate the
distance between the central bright fringe and the 4th dark fringe. 5
OR
33. (b) (i) Discuss briefly diffraction of light from a single slit and draw the shape of the
diffraction pattern.

(ii) An object is placed between the pole and the focus of a concave mirror. Using
mirror formula, prove mathematically that it produces a virtual and an enlarged
image. Unit-VI 5

Paper-6

SECTION A

Note : Selected the most appropriate option from those given below each question :

1. A cell of emf (E) and internal resistance r is connected across a variable external
resistance R. The graph of terminal potential difference V as a function of R is – Unit - II

(a) (b) (c) (d) 1
2. A uniform wire of resistance 2R is bent in the form of a circle. The effective resistance
between the ends of any diameter of the circle is: Unit - II 1

𝑅 𝑅
(a) 2R (b) R (c) (d)
2 4

3. A current I flows through a long straight conductor which is bent into a circular loop of
radius R in the middle as shown in the figure. Unit – III

The magnitude of the net magnetic field at point O will be

(a) Zero (b) (c) (d)
1
4. A circular loop of radius r, carrying a current I lies in y-z plane with its centre at the origin.
The net magnetic flux through the loop is : Unit - IV 1
(a) directly proportional to r (b) zero
(c) inversely proportional to r (d) directly proportional to I

5. The kinetic energy of a proton and that of an 𝛼 - particle are 4eV and 1eV, respectively.
The ratio of the de-Broglie wavelengths associated with them, will be Unit – VII 1
(a) 2:1 (b) 1:1 (c) 1:2 (d) 4:1

6. A photocell connected in an electrical circuit is placed at a distance ‘d’ from a source of
light. As a result, current I flows in the circuit. What will be the current in the circuit when
the distance is reduced to ‘d/2’ ? Unit - VII 1

(a) I (b) 2I (c) 4I (d) I/2.

7. A current of 10A is flowing from east to west in a long straight wire kept on a horizontal
table. The magnetic field developed at a distance of 10 cm due north on the table is : 1

(a) 2×10-5T, acting downwards (b) 2×10-5T, acting upwards Unit - III
(c) 4×10-5T, acting downwards (b) 4×10-5T, acting upwards

8. When a wave undergoes reflection at an interface from rarer to denser medium, adhoc
change in its phase is : Unit - VI 1

𝜋 𝜋
(a) (b) 0 (c) 𝜋 (d) 4
2

9. Paschen series of atomic spectrum of hydrogen gas lies in : Unit - VIII 1
(a) Infrared region (b) Ultraviolet region
(c)Visible region (d) Partly in ultraviolet and partly in visible region

10. In the 𝜶- particle scattering experiment, the shape of the trajectory of the scattered 𝜶-
particles depend upon : Unit - VIII 1

(a) only on impact parameter.

(b) only on the source of 𝜶- particles.

(c) both impact parameter and source of 𝜶- particles.

(d) impact parameter and the screen material of the detector.

Note : Find in the blanks with appropriate answer :

11. Torqure acting on an electric dipole in an electric field is maximum when the angle
between the electric field and the dipole moment is ________ Unit - I 1
12. A proton released from rest in an electric field, will start moving towards a region of
_______ potential in the field. Unit – I 1

Note : Answer the following

13. The work done in moving a charged particle between two points in an uniform electric
field, does not depend on the path followed by the particle. Why? Unit - I 1

14. An A.C. source with variable frequency is connected to a parallel plate capacitor. How
will the displacement current be affected with the decrease in frequency of the source ?
Unit – V 1
15. An astronomical telescope may be a refracting type or a reflecting type. Which of the two
produces image of better quality ? Justify your answer. Unit - VI 1
16. Can a slab of p-type semi-conductor be physically joined to another n-type semiconductor
slab to form p-n junction ? Justify your answer. Unit - IX 1

OR

In a p-n junction diode the forward bias resistance is low as compared to the reverse bias
resistance. Give reason. Unit - IX 1

SECTION B

17. Find the total charge stored in the network of capacitors connected between A and B as
shown in figure : Unit-I 2

Unit - I

18. A wire of length Lo has a resistance Ro. It is gradually stretched till its length
becomes 2Lo. Unit – II 2

(a) Plot a graph showing variation of its resistance R with its length ι during
stretching.
(b) What will be its resistance when its length becomes 2Lo ?

19. A resistor R and an inductor L are connected in series to a source of voltage V = V o sin
𝜔𝑡. The voltage is found to lead current in phase by 𝜋/4. If the inductor is replaced by a
capacitor C, the voltage lags behind current in phase by /4 . When L, C and R are
connected in series with the same source, Unit - IV 2

Find the :

i. average power dissipated and

ii. instantaneous current in the circuit.

20. Light of same wavelength is incident on three photo-sensitive surfaces A, B and C. The
following observations are recorded. Unit - VII 2

i. From surface A, photo electrons are not emitted.

ii. From surface B, photo electrons are just emitted.
iii. From surface C, photo electrons with some kinetic energy are emitted. Compare
the threshold frequencies of the three surfaces and justify your answer.

OR

If the frequency of light incident on the cathode of a photo-cell is increased, how will the
following be affected ? Justify your answer. Unit – VII 2

(i) Energy of the photo electrons.
(ii) Photo current.

21. Briefly explain how a potential barrier is set up across a p-n junction as a result of
diffusion and drift of the charge carriers. Unit - IX 2

22. (a) Explain the formation of energy bands formed in a crystalline solids. Unit - IX

(b) Draw the energy band diagrams of (i) a metal and (ii) semiconductor. 2

SECTION C

23. A hollow conducting sphere of inner radius r1 and outer radius r2 has a charge Q on its
surface. A point charge –q is also placed at the centre of the sphere.

(a) What is the surface charge density on the (i) inner and (ii) outer surface of the
sphere ?

(b) Use Gauss’ law of electrostatics to obtain the expression for the electric field at a
point lying outside the sphere. Unit - I 3

OR

(a) An infinitely long thin straight wire has a uniform linear charge density 𝜆. Obtain
the expression for the electric field (E) at a point lying at a distance 𝓍 from the
wire, using Gauss’ law.

(b) Show graphically the variation of this electric field E as a function of distance 𝓍
from the wire. Unit - I 3

24. (a) Differentiate between self inductance and mutual inductance. Unit – IV 3

(b) The mutual inductance of two coaxial coils is 2H. The current in one coil is
changed uniformly from zero to 0.5A in 100 ms. Find the :

(i) change in magnetic flux through the other coil.

(ii) emf induced in the other coil during the change.

25. Explain with the help of a diagram, the working of a step-down transformer. Why is a
laminated iron core used in a transformer ? Unit - IV 3

26. Name the electro-magnetic waves with their frequency range, produced in 3
(a) some radioactive decay Unit - V
(b) sparks during electric welding
(c) TV remote.

27. Two coherent light waves of intensity 5× 10-2Wm-2 each super-impose and produce the
interference pattern on a screen. At a point where the path difference between the waves is
𝜆
, 𝜆 being wavelength of the wave, find the Unit - VI 3
6

(a) phase difference between the waves.
(b) resultant intensity at the point.
(c) resultant intensity in terms of the intensity at the maximum.

28. Two objects P and 𝑄 when placed at different positions in front of a concave mirror of
focal length 20 cm, form real images of equal size. Size of object P is three times size of
object Q. If the distance of P is 50 cm from the mirror, find the distance of Q from the
mirror. Unit - VI 3

SECTION D

29. (a) Show that a current carrying solenoid behaves like a small bar magnet. Obtain
the expression for the magnetic field at an external point lying on its axis. Unit - III

(b) A steady current of 2A flows through a circular coil having 5 turns of radius 7 cm.
The coil lies in X-Y plane with its centre at the origin. Find the magnitude and
direction of the magnetic dipole moment of the coil. 5

OR

(a) Derive the expression for the force acting between two long parallel current
carrying conductors. Hence, define 1 A current.
(b) A bar magnet of dipole moment 3 Am2 rests with its centre on a frictionless pivot.
A force F is applied at right angles to the axis of the magnet, 10 cm from the pivot.
It is observed that an external magnetic field of 0.25 T is required to hold the
magnet in equilibrium at an angle of 30o with the field. Unit – III 5

Calculate the value of F.

How will the equilibrium be effected if F is withdrawn ?

36. (a) Draw the ray diagram showing refraction of ray of light through a glass prism.
Derive the expression for the refractive index 𝜇 of the material of prism in terms
of the angle of prism A and angle of minimum deviation 𝛿𝑚 . Unit – VI 5

(b) A ray of light PQ enters an isosceles right angled prism ABC of refractive index
1.5 as shown in figure.

(i) Trace the path of the ray through the prism.
(ii) What will be the effect on the path of the ray if the refractive index of the
prism is 1·4 ?

OR

(a) Two thin lenses are placed coaxially in contact. Obtain the expression for the focal
length of this combination in terms of the focal lengths of the two lenses.
(b) A converging lens of refractive index 1.5 has a power of 10 D. When it is
completely immersed in a liquid, it behaves as a diverging lens of focal length 50
cm. Find the refractive index of the liquid. Unit - VI 5

OR

(a) State the postulates of Bohr’s model of hydrogen atom and derive the expression
for Bohr radius.
(b) Find the ratio of the longest and the shortest wavelengths amongst the spectral
lines of Balmer series in the spectrum of hydrogen atom. Unit – VIII 5

Paper-7

SECTION A

Note : Selected the most appropriate option from those given below each question :

1. If a positive charge is displaced against the electric field in which it was situated, then 1
(A) work will be done by the electric field on the charge. Unit- I
(B) the intensity of the electric field decreases.
(C) energy of the system will decrease.
(D) energy will be provided by external source displacing the charge.
2. The electric flux emerging out from 1 C charge is Unit- I 1

(A)

(B)

(C)

(D)

3. Two capacitors of capacitances C1 and C2 are connected in parallel. If a charge Q is given to
the combination, the ratio of the charge on capacitor C1 to the charge on C2 will be Unit- I 1
(A) c1 (B) c1
c2 c2

c2 c2
(C) (D)
c1 c1
4. The electrical resistance of a conductor Unit- II 1
(A) varies directly proportional to its area of cross-section.
(B) decreases with increase in its temperature.
(C) decreases with increase in its conductivity.
(D) is independent of its shape but depends only on its volume.
5. m2V-1S-1 is the SI unit of which of the following ? Unit- II 1

(A) drift velocity (B) mobility
(C) resistivity (D) Potential gradient
𝑉
6. The element of a heater is rated (P,V). If it is connected across a source of voltage 2 , then
the power consumed by it will be Unit- II 1

(A) P (B) 2P

𝑃 𝑃
(C) (D)
2 4

7. In Bohr’s model of hydrogen atom, the total energy of the electron in nth discrete orbit is
proportional to Unit- VIII 1
1
(A) n (B) 𝑛

1
(C) n2. (D)
n2
8. A region has a uniform magnetic field in it. A proton enters into the region with velocity
making an angle of 45∘ with the direction of the magnetic field. In this region the proton
will move on a path having the shape of a Unit- III 1
(A) straight line. (B) circle.
(C) spiral. (D) helix.

9. An isosceles right angled current carrying loop PQR is placed in a uniform magnetic field
→ pointing along PR. If the magnetic force acting on the arm PQ is F, then the magnetic
𝐁
force which acts on the arm QR will be Unit- III 1

(A) F (B) √2
(C) √2𝐹 (D) –F

Note : Find in the blanks with appropriate answer :

10. The shape of the wavefront originating from a line source is ________ Unit- VI 1

11. The refractive index of the material of a converging lens is 1.5. If air is replaced by a medium
of reflective index 1.6, then the lens will now behave as a ____ lens. Unit- III 1

12. In young’s double slit experiment, the separation between the two slits is halved. The new
fringe width will be ________ times its initial value. Unit- VI 1

13. In photoelectric effect, the number of emitted photoelectrons is proportional to _________
to incident light. Unit- VII 1

OR

Light of frequency v is incident on a photosensitive surface of threshold frequency v0 (v > v0).
The value of kinetic energy of the emitted photoelectrons will be _______ Unit- VII 1

Note : Answer the following

14. An ac is passed through a series LCR circuit. What is the impedance of the circuit at
resonance ? Unit- IV 1
15. Two identical coils, one of copper and the other of aluminium are rotated with the same
angular speed in an external magnetic field. In which of the two coils will the induced
current be more ? Unit- IV 1

𝜋
16. In an AC circuit, the applied voltage and following current are E=E0 sin I=I0sin (ωt + )
2
respectively. What is the average power consumed in one cycle in this circuit Unit-IV 1
17. Mention the contribution of Indian physicist J.C. Bose in the production of
electromagnetic waves. Unit- V 1
16 20
18. Write one use of the electromagnetic waves of frequency range from 10 Hz to 10 Hz.
Unit- V 1
19. Explain briefly the fact that electromagnetic waves carry energy. Unit- V 1

SECTION B

20. Two identical bars, one of paramagnetic material and other of diamagnetic material are
kept in a uniform external magnetic field parallel to it. Draw diagrammatically the
modifications in the magnetic field pattern in each case. Unit- III 2
21. Two coplanar and concentric coils 1 and 2 have respectively the number of turns N1and N2
and radii r1 and r2 (r2>>r1) Deduce the expression for mutual inductance of this system.
Unit- IV 2
22. How does an oscillating charge radiate an electromagnetic wave ? Give the relation between
the frequency of radiated wave and the frequency of oscillating charge. Unit- V 2
23. A converging lens of focal length f1 is placed coaxially in contact with a diverging lens of
focal length f2 (f1 > f2) . Determine the power and nature of the combination in terms
of f1 and f2. Unit- VI 2
24. Define the terms (a) threshold frequency, and (b) stopping potential. How were these
terms incorporated in Einstein’s photoelectric equation ? Unit- VII 2
25. A hydrogen atom is in its third excited state. Unit- VIII 2

(a) How many spectral lines can be emitted by it before coming to the ground state? Show
these transitions in the energy level diagram.
(b) In which of the above transitions will the spectral line of shortest wavelength be
emitted?

SECTION C

26. (a) Differentiate between the random velocity and the drift velocity of electrons in an
electrical conductor. Give their order of magnitudes.

(b) A conductor of uniform cross-sectional area is connected across a dc source of variable
voltage. Draw a graph showing variation of drift velocity of electrons (vd ) as a function of
current density (J) in it. Unit- II 3

27. A series LCR ac circuit has L = 2·0 H, C = 32 𝜇F and R = 10 . Unit- IV 3

(a) At what angular frequency of ac will it resonate ?

(b) Calculate the Q value of the circuit.

OR

5
An ideal inductor of 𝜋 H inductance is connected to a 200 V, 50 Hz ac supply. Unit- IV

(a) Calculate the rms and peak value of current in the inductor.

(b) What is the phase difference between current through the inductor and the applied
voltage? How will it change if a small resistance is connected in series with this
inductor in the circuit? 3

28. (a) Using the necessary ray diagram, derive the mirror formula for a concave mirror.

(b) In the magnified image of a measuring scale (with equidistant markings) lying
along the principal axis of a concave mirror, the markings are not equidistant.
Explain. Unit- VI 3

29. (a) The density of the nuclear matter is tremendously larger than the physical density
of the material. Explain.

(b) The nuclear forces are not coulomb forces between nucleons. Explain.

(c) Draw a plot of the potential energy between a pair of nucleons as a function of
distance between them inside a nucleus. Unit- VIII 3

30. What do you mean by wave nature of an electron ? How was quantisation of angular
momentum of the orbiting electron in Bohr’s model of hydrogen atom explained by de
Broglie hypothesis ? Unit- VIII 3
31. (a) Why is an intrinsic semiconductor deliberately converted into an extrinsic
semiconductor by adding impurity atoms ?

(b) Explain briefly the two processes that occur in p-n junction region to create a
potential barrier. Unit- IX 3

SECTION D

32. (a) An electric dipole of dipole moment is placed in a uniform electric field at
an angle with it. Derive the expression for torque ( ) acting on it. Find the
orientation of the dipole relative to the electric field for which torque on it is
(i) maximum, and (ii) half of maximum.

(b) Two point charges q1  1 C and q2  4  C are placed 2 m apart in air. At what
distance from q1 along the line joining the two charges, will the net electric field be
zero ? Unit- I 5

OR

(a) Derive an expression for the energy stored in a parallel plate capacitor of
capacitance C when charged up to voltage V. How is this energy stored in the
capacitor ?
(b) A capacitor of capacitance is charged by connecting a battery of negligible
internal resistance and emf 10 V across it. Calculate the amount of charge supplied by
the battery in charging the capacitor fully. Unit-I 5

33. (a) Derive the expression for the force acting per unit length between two long
straight parallel current carrying conductors. Hence define one ampere.

(b) Two long parallel straight conductors are placed 12 cm apart in air. They carry
equal currents of 3 A each. Find the magnitude and direction of the magnetic field
at a point midway between them (drawing a figure) when the currents in them flow
in opposite directions. Unit-III 5

OR

𝑉
(b) To convert a given galvanometer into a voltmeter of ranges 2 V, V and 2 volt,
resistances R1, R2 and R3 ohm respectively, are required to be connected in series with
the galvanometer. Obtain the relationship between R1, R2 and R3. Unit-III 2

34. (a) Briefly describe the Young’s double slit experiment of interference of light. Drive
the expression for fringe width in the pattern.

(b) Monochromatic light of wavelength 588 nm is incident from air to water interface.
Find the wavelength and speed of the refracted light. The refractive index of water
4
is 3 . Unit-VI 5

Paper-8

SECTION A

Note : Selected the most appropriate option from those given below each question :

1. A cell of internal resistance r connected across an external resistance R can supply
maximum current when Unit- II 1
(A) R = r (B) R > r
𝑟
(C) R = 2 (D) R = 0
2. In a current carrying conductor, the ratio of the electric field and the current density at a
point is called Unit- II 1
(A) Resistivity (B) Conductivity
(C) Resistance (D) Mobility
3. An electron is released from rest in a region of uniform electric and magnetic field acting
parallel to each other. The electron will Unit- III 1
(A) Move in a straight line. (B) Move in a circle.
(C) Remain stationary. (D) Move in a helical path.
4. Above Curie temperature, a Unit- III 1
(A) ferromagnetic material becomes diamagnetic.
(B) ferromagnetic material becomes paramagnetic.
(C) paramagnetic material becomes ferromagnetic.
(D) paramagnetic material becomes diamagnetic.
5. Displacement current exists only when Unit- V 1
(A) electric field is changing. (B) Magnetic field is changing.
(C) electric field is not changing. (D) Magnetic field is not changing .
6. Electromagnetic waves used as a diagnostic tool in medicine are Unit- V 1
(A) X-rays. (B) Ultraviolet rays.
(C) Infrared radiation. (D) Ultrasonic waves.
7. At equilibrium, in a p-n junction diode the net current is Unit- IX 1
(A) due to diffusion of majority charge carries.
(B) due to drift of minority charge carriers.
(C) zero as diffusion and drift currents are equal and opposite.
(D) zero as no charge carriers cross the junction.
8. In an n-type semiconductor, the donor energy level lies Unit- IX 1
(A) at the centre of the energy gap. (B) just below the conduction band.
(C) just above the valance band. (D) in the conduction band.
9. When two nuclei (A< 10) fuse together to form a heavier nucleus, the Unit- VIII 1
(A) binding energy per nucleon increases.
(B) binding energy per nucleon decreases.

(C) binding energy per nucleon does not change.
(D) Total binding energy decreases.

Fill in the blanks with appropriate answer:

10. If the electric flux entering and leaving a closed surface within the surface is 1 and  2
respectively, the net electric charge enclosed within the surface is ____. Unit - I 1

11. In young’s double slit experiment, the path difference between two interfering waves at a
5𝜆
point on the screen is 2 , 𝜆 being wavelength of the light used. The ____ dark fringe will
lie at this point. Unit- VI 1
OR
If one of the slits in Young’s double slit experiment is fully closed, the new pattern has
_______ central maximum in angular size. Unit- IV 1

Note : Answering the following :

12. What is the impedance of a capacitor of capacitance C in an ac circuit using source of
frequency n Hz ? Unit- IV 1

OR

What is the value of impedance of a resonant series LCR circuit? Unit- IV 1

13. A conducting rod of length ᶩ is kept parallel to a uniform magnetic field B. It is moved
along the magnetic field with a velocity → . What is the value of emf induced in the
𝑣
conductor ? Unit- IV 1
14. Draw the graph showing variation of the value of the induced emf as a function of rate of
change of current flowing through an ideal inductor. Unit- IV 1
-19
15. What is the wavelength of a photon of energy 3.3 × 10 J? Unit- VII 1
16. Define the term ‘threshold frequency’ in photoelectric emission. Unit- VII 1

SECTION B

17. Define the term ‘mobility’ of charge carriers in a current carrying conductor. Obtain the
relation for mobility in terms of relaxation time. Unit- II 2

OR

Define the term ‘drift velocity’ of electrons in a current carrying conductor. Obtain the
relationship between the current density and the drift velocity of electrons. Unit- II 2
18. An ammeter of resistance 0·8 Ω can measure a current upto 1·0 A. Find the value of shunt
resistance required to convert this ammeter to measure a current upto 5·0A. Unit- III 2
19. (a) Explain the term ‘sharpness of resonance’ in ac circuit. Unit- IV 2
(b) In series LCR circuit, VL = VC ≠ VR. What is the value of power factor for this circuit?

OR

An ac source of emf V =V0 sin 𝜔t is connected to a capacitor of capacitance C. Deduce

the expression for the current (I) flowing in it. Plot the graph of (i) V vs. 𝜔t, and (ii) I vs.
𝜔t. Unit- IV 2
20. Which of the following electromagnetic waves has (a) minimum wavelength, and (b)
minimum frequency ? Write one use of each of these two waves. Unit- V 2
Infrared waves, Microwaves, 𝛾- rays and X –rays.

21. An object is kept 20 cm in front of a concave mirror or radius of curvature 60 cm. Find the
nature and position of the image formed. Unit- VI 2

22. In Geiger-Marsden scattering experiment, the trajectory of ɑ- particles in Coulomb’s field
of a heavy nucleus is shown in the figure. Unit- VIII 2

(a) What do ‘b’ and ‘𝜃’ represent in the figure?
(b) What will be the value of ‘b’ for (i) 𝜃 = 00, and (ii) 𝜃 = 1800?

23. Draw V-I characteristics of a p-n junction diode. Explain, why the current under reverse
bias is almost independent of the applied voltage up to the critical voltage. Unit- IX 2

SECTION C


24. Two small identical electric dipoles AB and CD, each of dipole moment p are kept at an
angle of to each other in an external electric field pointing along the x-axis as
shown in the figure. Find the Unit- I 3

(a) dipole moment of the arrangement, and

(b) magnitude and direction of the net torque acting on it.

OR

In the figure given below, find the

(a) equivalent capacitance of the network between points A and B.

Given : C1 = C5 = 8𝜇F, C2 = C3 = C4 = 4𝜇F

(b) maximum charge supplied by the battery, and

(c) total energy stored in the network. 3

25. (a) Derive the condition of balance for Wheatstone bridge. 1½

26. The figure shows the graphical variation of the reactance of a capacitor with frequency of ac
source. Unit- IV 3

(a) Find the capacitance of the capacitor.

(b) An ideal inductor has the same reactance at 10 Hz frequency as the capacitor has at the
same frequency. Find the value of inductance of the inductor.

(c) Draw the graph showing the variation of the reactance of this inductor with frequency.
27. What is the difference in the construction of an astronomical telescope and a compound
microscope? The focal lengths of the objective and eyepiece of a compound microscope
are 1·25 cm and 5·0 cm, respectively. Find the position of the object relative to the
objective in order to obtain an angular magnification of 30 when the final image is formed
at the near point. Unit- VI 3
28. The maximum kinetic energy of the photoelectrons emitted is doubled when the
wavelength of light incident on the photosensitive surface changes from λ1 to λ2. Deduce

expressions for the threshold wavelength and work function for the metal surface in terms
of λ1 and λ2. Unit- VII 3

SECTION D

29. (a) Use Gauss’s law to show that due to a uniformly charged spherical shell of radius
R, the electric field at any point situated outside the shell at a distance 𝑟 from its
centre is equal to the electric field at the same point, when the entire charge on the
shell were concentrated at its centre. Also plot the graph showing the variation of
electric field with 𝑟 for and .

(b) Two point charges of + 1 𝜇C, and + 4 𝜇C are kept 30 cm apart. How far from the
+ 1 𝜇C charge on the line joining the two charges, will the net electric field be
zero? Unit- I 5

OR

(a) Two point charges q1 and q2 are kept r distance apart in a uniform external electric
field . Find the amount of work done in assembling this system of charges.
(b) A cube of side 20 cm is kept in a region as shown in the figure. An electric field
exists in the region such that the potential at a point is given by V = 10x +5,
where V is in volt and x is in m. Unit- I 5

Find the
(i) electric field , and

(ii) total electric flux through the cube.

30. (a) A circular loop of radius R carries a current I. Obtain an expression for the
magnetic field at a point on its axis at a distance 𝑥 from its centre.

(a) Obtain the expression for the deflecting torque acting on the current carrying
rectangular coil of a galvanometer in a uniform magnetic field. Why is a radial
magnetic field employed in the moving coil galvanometer ? Unit- III 5

31. (a) Derive lens maker’s formula for a biconvex lens.

(b) A point object is placed at a distance of 12 cm on the principal axis of a convex

lens of focal length 10 cm. A convex mirror is placed coaxially on the other side of
the lens at a distance of 10 cm. If the final image coincides with the object, sketch
the ray diagram and find the focal length of the convex mirror. Unit- VI 5

OR

(a) What is a wavefront ? How does it propagate ? Using Huygens’ principle, explain
reflection of a plane wavefront from a surface and verify the laws of reflection.
(b) A parallel beam of light of wavelength 500 nm falls on a narrow slit and the
resulting diffraction pattern is obtained on a screen 1 m away. If the first minimum
is formed at a distance of 2.5 mm from the centre of the screen, find the (i) width
of the slit, and (ii) distance of first secondary maximum from the centre of the
screen. Unit- VI 5

Paper-9

SECTION A

Note : Selected the most appropriate option from those given below each question :

1. If the net electric flux through a closed surface is zero, then we can infer Unit- I 1
(A) Not net charge is enclosed by the surface.
(B) Uniform electric field exists within the surface.
(C) Electric potential varies from point to point inside the surface.
(D) Charges is preset inside the surface.
2. An electric dipole consisting of charges + q and – q separated by a distance L is in stable
equilibrium in a uniform electric field E. The electrostatic potential energy of the dipole is 1
(A) qLE (B) zero Unit- I
(C) –qLE, (D) –2qEL
3. Two resistors R1 and R2 of 4 Ω and 6 Ω are connected in parallel across a battery. The
ratio of power dissipated in them, P1 : P2 will be Unit- II 1
(A) 4 : 9 (B) 3 : 2
(C) 9 : 4 (D) 2 : 3
4. The magnetic dipole moment of a current carrying coil does not depend upon Unit- III 1
(A) Number of turns of the coil. (B) Cross-sectional area of the coil.
(C) Current flowing in the coil. (D) Material of the turns of the coil.
5. Large aperture of the objective lens in an astronomical telescope Unit- VI 1
(A) Increases the resolving power of the telescope.
(B) Decreases the brightness of the images.
(C) Increases the size of the image.
(D) Decreases the length of the telescope.
6. A biconvex lens of glass having refractive index 1.47 is immersed in a liquid. It becomes
invisible and behaves as a plane glass plate. The refractive index of the liquid is Unit- VI 1
(A) 1.47 (B) 1.62
(C) 1.33 (D) 1.51
7. For a glass prism, the angle of minimum deviation will be smallest for the light of Unit- VI 1
(A) Red colour. (B) Blue colour
(C) Yellow colour. (D) Green colour
8. Which of the following statements is not correct according to Rutherford model ? 1
(A) Most of the space inside an atom is empty. Unit- VIII
(B) The electrons revolve around the nucleus under the influence of coulomb force
acting on them.
(C) Most part of the mass of the atom and its positive charge are concentrated at its
centre.

(D) The stability of atom was established by the model.

9. Photons of energies 1 eV and 2 eV are successively incident on a metallic surface of work
function 0.5 eV. The ratio of kinetic energy of most energetic photoelectrons in the two
cases will be Unit- VII 1

(A) 1 : 2 (B) 1 : 1

(C) 1 : 3 (D) 1 : 4

Note : Fill in the blanks with appropriate answer :

10. The number of turns of a solenoid are double without changing its length and area of cross-
section. The self-inductance of the solenoid will become ___________ times. Unit- IV 1

11. According to Bohr’s atomic model, the circumference of the electron orbit is always an
_________ multiple of de Broglie wavelength. Unit- VIII 1

12. A ray of light on passing through an equilateral glass prism, suffers a minimum deviation
equal to the angle of the prism. The value of refractive index of the material of the prism is
_______________. Unit- VI 1

Note : Answer the following :

13. Write the mathematical form of Ampere-Maxwell circuital law. Unit- V 1

14. How does an increase in doping concentration affect the width of depletion layer of a p-n
junction diode ? Unit- IX 1

15. The nuclear radius of is 3.6 fermi. Find the nuclear radius of . Unit- VIII 1

16. A proton and an electron have equal speeds. Find the ration of de Broglie wavelengths
associated with them. Unit- VII 1

17. The variation of the stopping potential (Vo) with frequency (v) of the light incident on two
different photosensitive surfaces M1 and M2 is shown in the figure. Identify the surface
which has greater value of the work function. Unit- VII 1

SECTION B

18. The space between the plates of a parallel plate capacitor is completely filled in two ways.
In the first case, it is filled with a slab of dielectric constant K. In the second case, it is
filled with two slabs of equal thickness and dielectric constants K1 and K2 respectively as
shown in the figure. The capacitance of the capacitor is same in the two cases. Obtain the
relationship between K, K1 and K2 . Unit- I 2

19. Define wave front of a travelling wave. Using Huygens principle, obtain the law of refraction
at a plane interface when light passes from a denser to rarer medium. Unit- VI 2
1 1 1
20. Using lens maker’s formula, derive the thin lens formula 𝑓 = 𝑣 − 𝑢 for a biconvex lens.
Unit- VI 2

21. Two long straight parallel wires A and B separated by a distance d. carry equal current I
flowing in same direction as shown in the figure. Unit- III 2

(a) Find the magnetic field at a point P situated between them at a distance x from one
wire.
(b) Show graphically the variation of the magnetic field with distance x for 0 <x<d.

22. Using Bohr’s atomic model, derive the expression for the radius of nth orbit of the
revolving electron in a hydrogen atom. Unit- VIII 2

OR

(a) Write two main observations of photoelectric effect experiment which could only be
explained by Einstein’s photoelectric equation.
(b) Draw a graph showing variation of photocurrent with the anode potential of a
photocell. Unit- VII 2

23. Explain the terms ‘depletion layer’ and ‘potential barrier’ in a p-n junction diode. How are
the (a) width of depletion layer, and (b) value of potential barrier affected when the p-n
junction is forward biased ? Unit- IX 2

SECTION C

24. (a) Two cells of emf E1 and E2 have their internal resistances r1 and r2, respectively.
Deduce an expression for the equivalent emf and internal resistance of their
parallel combination when connected across and external resistance R. Assume
that the two cells are supporting each other. Unit- II

(b) In case the two cells are identical, each of emf E=5V and internal resistance r =2Ω,
calculate the voltage across the external resistance R = 10Ω. 3

25. (a) Write an expression of magnetic moment associated with a current (I) carrying
circular coil of radius r having N turns. Unit- III

(b) Consider the above mentioned coil placed in YZ plane with its centre at the origin.
Derive expression for the value of magnetic field due to it at point (x,0,0). 3

OR

(a) Define current sensitivity of a galvanometer. Write its expression.

(b) A galvanometer has resistance G and shows full scale deflection for current Ig.

(i) How can it be converted into an ammeter to measure current up to I0 (I0 > Ig)?

(ii) What is the effective resistance of this ammeter ? Unit- III 3

26. A resistance R and a capacitor C are connected in series to a source V=V0 Sin 𝜔t.

Find :

(a) The peak value of the voltage across the (i) resistance and (ii) capacitor.
(b) The phase difference between the applied voltage and current. Which of them is
ahead ? Unit- III 3

27. What is the effect on the interference fringes in Young’s double slit experiment due to
each of the following operations? Justify your answers. Unit- VI 3

(a) The screen is moved away from the plane of the slits.
(b) The separation between slits is increased.
(c) The source slit moved closer to the plane of double slit.

28. (a) Write the expression for the speed of light in a material medium of relative
permittivity  r and relative magnetic permeability 𝜇 r .

(b) Write the wavelength range and name of the electromagnetic waves which are
used in (i) radar systems for aircraft navigation, and (ii) Earth satellites to observe
the growth of the crops. Unit- V 3

27. The nucleus , initially at rest, decays into by emitting an 𝛼- particle.

The binding energies per nucleon energies per nucleon of the parent nucleus, the daughter
nucleus and 𝛼- particle are 7.8 MeV, 7.835 MeV and 7.07 Mev, respectively. Assuming
the daughter nucleus to be formed in the unexcited state and neglecting its share in the
energy of the reaction, find the speed of the emitted 𝛼- particle. (Mass of 𝛼- particle =
6.68 ×10-27 kg). Unit- VIII 3

SECTION D

28. (a) Using gauss law, drive expression for electric field due to a spherical shell of
uniform charge distribution σ and radius R at a point lying at a distance x from

the centre of shell, such that Unit- I

(i) 0 < x < R, and

(ii) x < R.

(b) An electric field is uniform and acts long + X direction in the region of positive x.
It is also uniform with the same magnitude but acts is –x direction in the region of
negative x. The value of the field is E = 200 N/C for x > 0 and E = −200 N/C for
x < 0. A right circular cylinder of length 20 cm and radius 5 cm has its centre at the
origin and its axis along the x-axis so that one flat face is at x = + 10 cm and the
other is at x = − 10 cm.

Find :

(i) The net outward flux through the cylinder.
(ii) The net charge present inside the cylinder. 5

OR

(a) Find the expression for the potential energy of a system of two point charges q 1
and q2 located at → and → , respectively in an external electrical filed⃗⃗⃗⃗𝐸
𝑟1 𝑟2

(b) Draw equipotential surfaces due to an isolated point charge (−q) and depict the
electric field lines.

(c) Three point charges +1 𝜇C, −1 𝜇C and + 2 𝜇C are initially infinite distance apart.
Calculate the work done in assembling these charges at the vertices of an
equilateral triangle of side 10 cm. Unit- I 5

29. (a) Derive the expression for the torque acting on the rectangular current carrying
coil of a galvanometer. Why is the magnetic field made radial ?

(b) An 𝛼- particle is accelerated through a potential difference of 10 kV and moves
along x- axis. It enters in a region of uniform magnetic field B = 2 × 10-3 T acting
along y- axis. Find the radius of its path. (Take mass of 𝛼-particle = 6.4 × 10-27
Kg). Unit- III 5

OR

(a) With the help of a labeled diagram, explain the working of step-up transformer.
Give reasons to explain the following : Unit- IV 5
(i) The core of the transformer is laminated.
(ii) Thick copper wire is used in windings.
(b) A conducting rod PQ of length 20 cm and resistance 0.1 Ω rests on two smooth
parallel rails of negligible resistance AA′ and CC′. It can slide on the rails and the
arrangement is positioned between the poles of a permanent magnet producing
uniform magnetic field B = 0·4 T. The rails, the rod and the magnetic field are in
three mutually perpendicular direction as shown in the figure. If the ends A and C
of the rails are short circuited, find the

(i) External force required to move the rod with uniform velocity v = 10cm/s,
and
(ii) Power required to do so.

30. (a) An astronomical telescope has an objective lens of focal length 20 m and eyepiece of focal
length 1 cm. Unit- VI 3

(i) Find the angular magnification of the telescope.

(ii) If this telescope is used to view the Moon, find the diameter of the image
formed by the objective lens. Given the diameter of the Moon is 3·8 × 108 m.

31. (a) An object is placed in front of a concave mirror. It is observed that a virtual image
is formed. Draw the ray diagram to show the image formation and hence derive the
1 1 1
mirror equation 𝑓 = 𝑢 + 𝑣.
(c) An object is placed 30 cm in front of a plano-convex lens with its spherical surface
of radius of curvature 20 cm. It the refractive index of the material of the lens is
1.5, find the position and nature of the image formed. Unit- VI 5

Paper-10
SECTION-A
1. What is meant by doping of an intrinsic semiconductor? Name the two types of atoms used
for doping of Ge/Si. Unit-IX 2
2. (a) (i) Distinguish between isotopes and isobars. 2
(ii) Two nuclei have different mass numbers A1 and A2. Are the ……
necessarily the isotopes of the same element? Explain. Unit-VIII 2
OR
(b) (i) Name the factors on which photoelectric emission from a surface depends.
(ii) Define the term threshold frequency’ for a photosensitive material. Unit-VII 2
3. Explain the formation of the barrier potential in a p-n function. Unit-IX 2

SECTION-B
4. State Bohr's postulate to explain stable orbits in a hydrogen atom. Prove that the speed with
which the electron revolves in nth orbit is proportional to (1/n). Unit-VIII 3
5. A narrow beam of protons, each having 4.1 MeV energy is approaching a sheet of lead
(Z=82), Calculate: Unit-VIII
(i) the speed of a proton in the beam, and
(ii) the distance of its closest approach 3
6. In a diffraction pattern due to a single slit, how will the angular width of central maximum
change, if Unit-VII
(i) Orange light is used in place of green light.
(ii) the screen is moved closer to the slit,
(iii) the slit width is decreased? 3
Justify your answer in each case,
7. (a) Write two necessary conditions for total internal reflection.
(b) Two prisms ABC and DBC are arranged as shown in figure.

The critical angles for the two prisms with respect to air are 41.1o and 45o respectively. Trace
the path of the ray through the combination. Unit-VI 3
OR

(a) An object is placed in front of a converging lens. Obtain the conditions under
which the magnification produced by the lens is (i) negative and (ii) positive
(b) A point object is placed at O in front of a glass sphere as shown in figure.
Show the formation of image by the sphere. Unit-VI

8. An electron is accelerated from rest through a potential difference of 100 V.
Find: Unit-VII
(i) the wavelength associated with
(ii) the momentum of and
(iii) the velocity required by, the electron. 3
9. In a Young's double slit experiment using light of wavelength 600 nm, the slit separation is
0.8 mm and the screen is kept 1.6 m from the plane of the slits.
Calculate: Unit-VI
(i) the fringe width
(ii)the distance of (a) third minimum and (b) fifth maximum, from the central maximum. 3
10. (a) Electromagnetic waves of wavelengths λ1, λ2 and λ3 are used in radar systems, in water
purifiers and in remote switches of TV, respectively. Unit-V 3
(i) Identify the electromagnetic waves, and
(ii) Write one source of each of them.
OR
(b) (i) State two conditions for two light sources to be coherent.
(ii) Give two points of difference between an interference pattern due to a double - slit and a
diffraction pattern due to a single slit. Unit-VI 3

SECTION-C
CASE STUDY
11. A compound microscope consists of two converging lenses. One of them, of smaller aperture
and smaller focal length is called objective and the other of slightly larger aperture and
slightly larger focal length is called eye-piece. Both the lenses are fitted in a tube with an
arrangement to vary the distance between them. A tiny object is placed in front of the
objective at a distance slightly greater than its focal length. The objective produces the image
of the object which acts as an object for the eye-piece. The eye piece, in turn produces the
final magnified image. Unit-VI 1×5=5
I. In a compound microscope the images formed by the objective and the eye-piece are
respectively.
(A) virtual, real
(B) real, virtual
(C) virtual, virtual
(D) real, real
II. The magnification due to a compound microscope does not depend upon

(A) the aperture of the objective and the eye-piece
(B) the focal length of the objective and the eye-piece
(C) the length of the tube
(D) the colour of the light used

III. Which of the following is not correct in the context of a compound microscope?
(A) Both the lenses are of short focal lengths.
(B) The magnifying power increases by decreasing the focal lengths of the two
lenses.
(C) The distance between the two lenses is more than (fo+fe).
(D) The microscope can be used as a telescope by interchanging the two lenses.
IV. A compound microscope consists of an objective of 10X and an eye-piece of 20X. The
magnification due to the microscope would be
(A) 2 (B) 10
(C) 30 (D) 200
V. The focal lengths of objective and eye-piece of a compound microscope are 1.2 cm and 3.0 cm
respectively. The object is placed at a distance of 1.25 cm from the objective. If the final
image is formed at infinity, the magnifying power of the microscope would be
(A) 100 (B) 150
(C) 200 (D) 250

Paper-11
SECTION A
1. How is the forward biasing different from the reverse biasing in a p-n junction diode? Name
one device, each which works under forward and reverse biasing. Unit-IX 2
2. (a) Define the terms 'distance of closest approach and impact parameter'.
OR
(b) Explain briefly any two features of photoelectric effect. Unit-VIII 2
3. How are (a) n-type semiconductor, and (b) p-type semiconductor obtained from an intrinsic
semiconductor? Name the majority charge carriers in each of the semiconductors. Unit-IX 2

SECTION B
4. A hydrogen atom has only one electron yet its spectrum has many lines. Explain. Name the
spectral series which lies in the visible region of electromagnetic spectrum. Mention the
conditions under which the spectral line in this series will have (a) maximum, and (b)
minimum wavelengths. Unit-IX 3
5. (a) State Bohr's second postulate for hydrogen atom.
(b) The ground state energy of a hydrogen atom is -13.6 eV. Find its kinetic energy and
potential energy in the ground and the second excited states. Unit-VIII 3
6. A ray of light passes through an equilateral triangular prism and suffers minimum deviation
of 30o. Calculate: Unit-VI
(a) the refractive index of the material of the prism.
(b) the angle at which the ray is incident on the prism. 3
7. (a) (i) Two independent monochromatic sources of light cannot constitute coherent sources.
Explain.
(ii) Two waves represented by
y1 = a1 cos  t, and
y2 = a2 cos  t
produce an interference pattern in Young's double slit experiment. If the ratio of intensities at
maximum and at minimum is 25:9, then calculate the ratio of intensities of light waves from
the Sources. Unit-VI 3
OR
(b) (i) What is meant by total internal reflection of light? Write the two necessary conditions for
total internal reflection to occur.
(ii) Calculate the speed of light in a medium for which the critical angle with respect to air is
45°. Unit-VI 3
8. A beam of light of wavelength 500 nm is incident on a photosensitive surface. If the
threshold wavelength for the surface is 663 nm, then calculate: Unit-VII 3
(a) the work function for the surface, and
(b) the maximum kinetic energy (in eV) of the photoelectrons.
9. Answer the following: Unit-VI 3

(a) A convex lens produces a real image of an object. If the upper half of the lens is
covered with a black paper, then how will the image be affected?
(b) The time difference between the apparent sunrise and the actual sunrise is about 2
minutes. Explain.
(c) Modern telescopes use a concave mirror rather than a lens for the objective.
Why?

10. (a) (i) Write the wavelength range of the following electromagnetic radiation: Unit-V 3
Gamma: rays, Microwaves and Ultraviolet rays
(ii) Write one use each of the above mentioned radiation.
OR
(i) State Huygens' principle. How did Huygens explain the absence of secondary wavelets in
the backward direction?
(ii) What is the shape of a wavefront emanating from (I) a point source, and (II) a linear
source? Unit-VI 3
SECTION C
11. When light passes through a narrow aperture or falls on an obstacle of very small dimensions,
it bends into the shadow region. The bending of light waves around the corners and edges of
the obstacles as well as aperture is called diffraction of light. For prominent diffraction effect,
the size of the aperture or obstacle must be comparable to the wavelength of the light used. If
we place a screen in front of the slit, a broad central maxima and a few alternate dark and
bright bands of successively decreasing intensities on either sides of central bright band are
obtained on the screen. Unit-VI 5×1=5
(a) Light of wavelength ‘λ’ falls normally on a slit of width ‘a’. The diffraction due to the slit will
be most prominently observed when:
(i) a = 5λ (ii) a = 100λ
(iii) a = 10 λ
3
(iv) a = 105λ
(b) When monochromatic light is replaced by white light, then:
(i) the diffraction pattern disappears.
(ii) the diffraction band becomes circular.
(iii) a white band is formed at the centre and coloured bands are formed at both its
sides.
(iv) only a white band is formed at the centre.
(c) If in a diffraction experiment, the width of the slit is slightly increased, then the central
maximum of the diffraction pattern becomes:
(i) broader and brighter.
(ii) broader and fainter.
(ii) narrow and brighter.
(iv) narrow and fainter.
(d) If a convex lens of focal length 'f' is placed very close to the slit of width 'a' and the screen is
kept at the focus of the lens, the size of the central maximum in the diffraction pattern will
be:
f 2f
(i) (ii)
a a
f f
(iii) (iv)
2a 4a
(e) A parallel beam of light of wavelength 500 nm falls on a narrow slit. The diffraction pattern is

observed on a screen 1 m away. The first minimum is at a distance of 2.5 mm from the centre
of the screen. The width of the slit is:
(i) 0.16 mm (ii) 0.20 mm
(iii) 0.40 mm (iv) 0.60 mm

Paper-12
SECTION A
1. With the help of a circuit diagram, explain briefly how a p-n junction diode works as a half-
wave rectifier. Unit-IX 2
2. (a) What results do you expect if  -particle scattering experiment is repeated using a
thin sheet of hydrogen in place of a gold foil? Explain. (Hydrogen is a solid at
temperature below 14K). Unit-VIII 2
OR
(b) Why it is the frequency and not the intensity of light source that determines
whether emission of photoelectrons will occur or not? Explain. Unit-VII 2

SECTION B
3. Draw a graph showing the variation of number of particles scattered (N) with the scattering
angle  in Geiger-Marsden experiment. Why only a small fraction of the particles are
scattered at  >90o ? Mention two limitations of Rutherford nuclear model of an atom. 3
Unit-VIII
4. (i) Draw V-I characteristics of a p-n Junction diode. Unit-IX 3
(ii) Differentiate between the threshold voltage and the breakdown voltage for a
diode.
(iii) Write the property of a junction diode which makes it suitable for rectification
of ac voltages.
5. In a fission event of 238
92 U by fast moving neutrons, no neutrons are emitted and final

products, after the beta decay of the primary fragments, are 140 99
58 Ce and 44 Ru . Calculate Q for

this process. Neglect the masses of electrons/positrons emitted during the intermediate steps.
Given: m  U  = 238.05079u; m  Ce  = 139.90543u;
238
92
140
58

m  Ru  98.90594u; m  n  = 1.008665u
99
44
1
0 Unit-VIII 3
6. How can you differentiate whether a pattern is produced by a single slit or double slits?
Derive the expression for the angular position of (i) bright and (ii) dark fringes produced in a
single slit diffraction. Unit-VI 3
7.(a) (i) Define Sl unit of power of a lens. Unit-VI 3
(ii) A plano convex lens is made of glass of refractive index 1.5. The radius of
curvature of the convex surface is 25 cm.

(ii.i) Calculate the focal length of the lens.
(ii.ii) If an object is placed 50 cm in front of the lens, find the nature and position of the
image formed.
OR

(b) A slit of width 0.6 mm is illuminated by a beam of light consisting of two
wavelengths 600 nm and 480 nm. The diffraction pattern is observed on a screen
1.0 m from the slit. Find: Unit-VI 3
(i) The distance of the second bright fringe from the central maximum pertaining to
light of 600 nm.

(ii) The least distance from the central maximum at which bright fringes due to both
the wavelengths coincide.
8. (a) Calculate the energy and momentum of a photon in a monochromatic beam of
wavelength 331.5 nm.
(b) How fast should a hydrogen atom travel in order to have the same momentum as
that of the photon in part (a)? Unit-VII 3
9. A ray of light passes through a prism of refractive index 2 as shown in the figure. Find: 3

(i) The angle of incidence (  r2) at face AC.
(ii) The angle of minimum deviation for this prism. Unit-VI
10. (a) (i) Arrange the following electromagnetic radiation in the ascending order of their
frequencies: Unit-V 3
X-rays, microwaves, gamma rays, radio waves
(ii) Write two uses of any two of these radiation.
OR
(b)With the help of a ray diagram explain the working of a reflecting telescope.
Mention two advantages of a reflecting telescope over refracting telescope. Unit-VI 3
SECTION C
11. A ray of light travels from a denser to a rarer medium. After refraction, it bends away from
the normal. When we keep increasing the angle of incidence, the angle of refraction also
increases till the refracted ray grazes along the interface of two media. The angle of incidence
for which it happens is called critical angle. If the angle of incidence is increased further the
ray will not emerge and it will be reflected back in the denser medium. This phenomenon is
called total internal reflection of light. Unit-VI 5
(i) A ray of light travels from a medium into water at an angle of incidence of 18°. The
refractive index of the medium is more than that of water and the critical angle for the
interface between the two media is 20°. Which one of the following figures best represents
the correct path of the ray of light?

(ii) A point source of light is placed at the bottom of a tank filled with water, of refractive index
 , to a depth d. The area of the surface of water through which light from the source can
emerge, is:
d2 d2
(a) (b)
2   2  1   2  1

d2 (d) 22 d
2
(c)
2  2 1    1
(iii) For which of the following media, with respect to air, the value of critical angle is maximum?
(a) Crown glass
(b) Flint glass
(c) Water
(d) Diamond
(iv) The critical angle for a pair of two media A and B of refractive indices 2.0 and 1.0
respectively is:
(a) 0°
(b) 30°
(c) 45°
(d) 60°
(v) The critical angle of pair of a medium and air is 30°. The speed of light in the medium is:
(a) 1×108 ms-1
(b) 1.5×108 ms-1
(c) 2.2 × 108 ms-1
(d) 2.8×108 ms-1

Paper-13
SECTION A

1. What is meant by energy band gap in a solid? Draw the energy band diagrams for a
conductor, an insulator and a semiconductor. Unit-IX 2
2. (a) Name the spectral series for a hydrogen atom which lies in the visible region.
Find the ratio of the maximum to the minimum wavelengths of this series. Unit-VIII 2
OR
(b) What are matter waves? A proton and an alpha particle are accelerated through
the same potential difference. Find the ratio of the de Broglie wavelength
associated with the proton to that with the alpha particle. Unit-VIII 2

SECTION B
3. (a) Differentiate between nuclear fission and nuclear fusion.
(b) Deuterium undergoes fusion as per the reaction:
2
1 H 12 H 32 He 10 n  3.27MeV
Find the duration for which an electric bulb of 500 W can be kept glowing by the fusion of
100 g of deuterium. Unit-VIII 3
4. Answer the following, giving reason: Unit-IX 2×1=2
(a) The resistance of a p-n junction is low when it is forward biased and is high when it is
reversed biased.
(b) Doping of intrinsic semiconductors is a necessity for making electronic devices.
5. (a) In Geiger-Marsden experiment, calculate the distance of closest approach for an alpha
particle with energy 2.56×10-12 J. Consider that the particle approaches gold nucleus (Z=79)
in head-on position. Unit-VII
(b) If the above experiment is repeated with a proton of the same energy, then what will be
value of the distance of closest approach? 3
6. Briefly explain how bright and dark fringes are formed on the screen in Young's double slit
experiment. Hence, derive the expression for the fringe width. Unit-VI 3
7. (a) (i) Draw a labelled ray diagram showing the formation of the image at infinity by
an astronomical telescope.
(ii) A telescope consists of an objective of focal length 150 cm and an eyepiece of focal
length 6.0 cm. If the final image is formed at infinity, then calculate: Unit VI
(I) the length of the tube in this adjustment, and
(II) the magnification produced. 3
OR
(b) (i) Draw a labelled ray diagram showing the formation of the image at least distance of
distinct vision by a compound microscope. Unit VI 3
(ii) A small object is placed at a distance of 3.0 cm from a magnifier of focal length 4.0 cm.
Find:

(I) the position of the image formed, and
(II) the linear magnification produced. 3
8. (a) Use Einstein's photoelectric equation to depict the variation of the maximum kinetic energy
(Ek) of electrons emitted, with the frequency (v) of the incident radiation. Unit-VII 3

(b) A photosensitive surface is illuminated with a beam of (i) yellow light, and (ii) red light,
both of the same intensity. Unit-VII
In which case will
(I) photoelectrons have more Ek?
(II) more numbers of electrons be emitted?
Justify your answer in each case. 3
9. A ray of light is incident on a prism at an angle of 45o and passes symmetrically as shown in
the figure. Calculate: Unit-VI 3

(a) the angle of minimum deviation,
(b) the refractive index of the material of the prism, and
(c) the angle of refraction at the point P.
10. (a) Identify electromagnetic waves which:
(i) are used in radar system.
(ii) affect a photographic plate.
(iii) are used in surgery.
Write their frequency range. Unit-VI 3
OR
(b) A plane wavefront is propagating from a rarer into a denser medium. Use Huygens principle
to show the refracted wavefront and verify Snell's law. Unit-VI 3
11. Two transparent media of refractive indices n1 and n2 are separated by a spherical transparent
surface. The rays of light incident on the surface get refracted into the medium on the other
side. The laws of refraction are valid at each point of the spherical surface. A lens is a
transparent optical medium bounded by two surfaces, at least one of which should be
spherical. The focal length of a lens is determined by the radii of curvature ( R 1 and R2) of its
two surfaces and the refractive index (n) of the medium of the lens with respect to the
surrounding medium. Depending on R1 and R2 a lens behaves as a diverging or a converging
lens. The ability of a lens to diverge or converge a beam of light incident on it defines its
power. Unit-VI
(a) An object is placed at the point B as shown in the figure. The object distance (u) and the
image distance (v) are related as

1 1  n 2 -n1  1
(i) - = 
V u  n1  R

1 1  n1 -n 2  1
(ii) - = 
V u  n2  R

n 2 n1 (n 2 -n1 )
(iii) - =
v u R
n1 n 2 (n1 -n 2 )
(iv) - =
v u R
(b) A point object is placed in air at a distance 'R' in front of a convex spherical refracting
surface of radius of curvature R. If the medium on the other side of the surface is glass, then
the image is:
(i) real and formed in glass.
(ii) real and formed in air.
(iii) virtual and formed in glass.
(iv) virtual and formed in air.
(c) An object is kept at 2F in front of an equiconvex lens. The image formed is:
(i) real and of the size of the object.
(ii) virtual and of the size of the object.
(iii) real and enlarged.
(iv) virtual and diminished.
(d) A thin converging lens of focal length 10 cm and a thin diverging lens of focal length 20 cm
are placed coaxially in contact. The power of the combination is:
(i) -5D
(ii) +5 D
(iii) +15 D
(iv) -15 D
(e) An equiconcave lens of focal length 'f' is cut into two identical parts along the dotted line as
shown in the figure. The focal length of each part will be:

f
(i)

4
f
(ii)
2
(iii) F

(iv) 2f

Paper-14

SECTION A

1. A point charge situated at a distance 'r' from a short electric dipole on its axis,

experiences a force F . If the distance of the charge is '2r', the force on the charge will
be: Unit-I 1
   
F F F F
(a) (b) (c) (d)
16 8 4 2
2. For a metallic conductor, the correct representation of variation of resistance R with
temperature T is: Unit-VI 1

3. The potential difference across a cell in an open circuit is 8 V. It falls to 4 V when a
current of 4 A is drawn from it. The internal resistance of the cell is: Unit-II 1
(a) 4  (b) 3  (c) 2  (d) 1 
4. A steady current flows through a metallic wire whose area of cross-section (A)
increases continuously from one end of the wire to the other. The magnitude of drift
velocity (vd) of the free electrons as a function of 'A' can be shown by: Unit-II 1

5. A diamagnetic substance is brought near the north or south pole of a bar magnet. It will be: 1
(a) repelled by both the poles. Unit-III
(b) attracted by both the poles.
(c) repelled by the north pole and attracted by the south pole.
(d) attracted by the north pole and repelled by the south pole.
6. A circular coil of radius 8.0 cm and 40 turns is rotated about its vertical diameter with an
25
angular speed of rad s-¹ in a uniform horizontal magnetic field of magnitude 3.0 × 10-2 T. The

maximum emf induced in the coil is: Unit-IV 1

(a) 0.12V (b) 0.19 V
(c) 0.15 V (d) 0.22 V

7. Figure shows a rectangular conductor PSRQ in which movable arm PQ has a resistance 'r'
and resistance of PSRQ is negligible. The magnitude of emf induced when PQ is moved with a

velocity v does not depend on: Unit-IV 1

X

X
X
X
X

X

 
(a) magnetic field ( B ) (b) velocity ( v )
(c) resistance (r) (d) length of PQ
8. In the process of charging of a capacitor, the current produced between the plates of the
capacitor is: Unit-V 1
d 1 dE
(a) 0 E (b)
dt 0 dt
d E 1 dE
(c)  0 (c)
dt  0 dt
where symbols have their usual meanings.
9. For a concave mirror of focal length 'f', the minimum distance between the object and
its real image is: Unit-VI 1
(a) zero (b) f
(c) 2f (d) 4f
th
10. The radius of the n orbit in Bohr model of hydrogen atom is proportional to: Unit – VIII 1
1 1
(a) 2 (b)
n n
2
(c) n (d) n
11. Hydrogen atom initially in the ground state, absorbs a photon which excites it to n = 5 level.
The wavelength of the photon is: Unit – VIII 1
(a) 975 nm (c) 523 nm
(b) 740 nm (d) 95 nm
12. The mass density of a nucleus of mass number A is: Unit-VIII 1
1/3 2/3
(a) proportional to A (b) proportional to A
3
(c) proportional to A (d) independent of A
13. An ac source of voltage is connected in series with a p-n junction diode and a load resistor.
The correct option for output voltage across load resistance will be: Unit-IX 1

(a)

(b)

14. When an intrinsic semiconductor is doped with a small amount of trivalent impurity,
then: Unit-IX 1
(a) its resistance increases.
(b) it becomes a p-type semiconductor.
(c) there will be more free electrons than holes in the semiconductor.
(d) dopant atoms become donor atoms.
15. In the energy-band diagram of n-type Si, the gap between the bottom of the
conduction band EC and the donor energy level ED is of the order of:
(a) 10 eV (b) 1 eV
(c) 0.1 eV (d) 0.01 eV Unit-IX
Questions number 16 to 18 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.
16. Assertion (A) : When a bar of copper is placed in an external magnetic field, the
field lines get concentrated inside the bar. Unit-IV
Reason (R) : Copper is a paramagnetic substance. 1
17. Assertion (A) : The phase difference between any two points on a wavefront is
zero. Unit-VI
Reason (R) : All points on a wavefront are at the same distance from the source
and thus oscillate in the same phase. 1
18. Assertion (A) : Photoelectric effect demonstrates the particle nature of light. Unit-VII
Reason (R) : Photoelectric current is proportional to intensity of incident
radiation for frequencies more than the threshold frequency. 1
SECTION-B
 
19. An alpha particle is projected with velocity v = (3.0 × 105 m/s) i into a region in which
  
magnetic field B = [(0.4 T) i + (0.3 T) j ] exists. Calculate the acceleration of the particle in
  
the region. i , j and k are unit vectors along x, y and z axis respectively and charge to mass
ratio for alpha particle is 4.8 × 107 C/kg. Unit-III 2
20. Consider an induced magnetic field due to changing electric field and an induced
electric field due to changing magnetic field. Which one is more easily observed?
Justify your answer. Unit V 2
21. (a) Using Huygens' principle, draw a ray diagram showing the propagation of a plane
wave refracting at a plane surface separating two media. Also verify Snell's law of

refraction. Unit-VI 2
OR
(b)Why is a reflecting telescope preferred over a refracting telescope? Justify your
answer giving two reasons. Unit-VI 2

22. Two coherent monochromatic light beams of intensities I and 4I superpose each other. Find
the ratio of maximum and minimum intensities in the resulting beam, Unit VI 2
23. The ground state energy of hydrogen atom is -13.6 eV. What is the potential energy
and kinetic energy of an electron in the third excited state? Unit-VIII 2
24. (a) Differentiate between intrinsic and extrinsic semiconductors. Unit- IX 2
OR
(b) Draw the circuit arrangement for studying the V-I characteristics of a p-n junction
diode in forward bias and reverse bias. Show the plot of V-I characteristic of a
silicon diode. Unit- IX 2
25. Briefly explain how the diffusion and drift currents contribute to the formation of
potential barrier in a p-n junction diode. Unit-IX 2
SECTION C
26. (a) Twelve negative charges of same magnitude are equally spaced and fixed on the
circumference of a circle of radius R as shown in Fig. (i) Relative to potential being
zero at infinity, find the electric potential and electric field at the centre C of the
circle. 3
(b) If the charges are unequally spaced and fixed on an arc of 120° of radius R as
shown in Fig. (ii), find electric potential at the centre C. Unit-I 3

27. (a) How does the resistance differ from impedance? With the help of a suitable
phasor diagram, obtain an expression for impedance of a series LCR circuit,
connected to a source v = vm sin  t. Unit-IV 3
OR
(b) Find the condition for resonance in a series LCR circuit connected to a source
v =Vm sin  t, where  can be varied. Give the factors on which the resonant
frequency of a series LCR circuit depends. Plot a graph showing the variation
of electric current with frequency in a series LCR circuit. Unit-IV 3
28. A long solenoid of radius r consists of n turns per unit length. A current I = Io sin  t
flows in the solenoid. A coil of N turns is wound tightly around it near its centre.
What is: Unit-IV
(a) the induced emf in the coil?
(b) the mutual inductance between the solenoid and the coil? 3

29. How does Einstein's photoelectric equation explain the emission of electrons from a
metal surface? Explain briefly. Unit-VII
Plot the variation of photocurrent with:
(a) collector plate potential for different intensity of incident radiation, and
(b) intensity of incident radiation. 3

30. (a)Draw the energy level diagram for hydrogen atom. Mark the transitions
corresponding to the series lying in the ultraviolet region, visible region and
infrared region. Unit-VIII 3
OR
(b) Draw a diagram to show the variation of binding energy per nucleon with mass
number for different nuclei and mention its two features. Why do lighter nuclei
usually undergo nuclear fusion? Unit-VIII 3
SECTION D
31. (a) (i) State Coulomb's law in electrostatics and write it in vector form, for two
charges.
(ii) ‘Gauss’s law is based on the inverse-square dependence on distance contained
in the Coulomb's law.’ Explain.
(iii) Two charges A (charge q) and B (charge 2q) are located at points (0, 0) and (a,
 
a) respectively. Let . i and j be the unit vectors along x-axis and y-axis
 
respectively. Find the force exerted by A on B, in terms of i and j . Unit-I 5
OR
b) (i) Derive an expression for the electric field at a point on the equatorial plane of
an electric dipole consisting of charges q and-q separated by a distance 2a.
(ii) The distance of a far off point on the equatorial plane of an electric dipole is
halved. How will the electric field be affected for the dipole?
(iii) Two identical electric dipoles are placed along the diagonals of a square
ABCD of side 2 m as shown in the figure. Obtain the magnitude and
direction of the net electric field at the centre (O) of the square. Unit-I 5

32. (a) (i) State Biot-Savart's law for the magnetic field due to a current carrying element. Use this
law to obtain an expression for the magnetic field at the centre of a circular loop of
radius 'a' and carrying a current ‘T’. Draw the magnetic field lines for a current loop
indicating the direction of magnetic field.
(ii) An electron is revolving around the nucleus in a circular orbit with a speed of
107 m s-1. If the radius of the orbit is 10-10 m, find the current constituted by the

revolving electron in the orbit. Unit-III 5
OR
(b) (i) Derive an expression for the force acting on a current carrying straight
conductor kept in a magnetic field. State the rule which is used to find the
direction of this force. Give the condition under which this force is (1)
maximum, and (2) minimum. Unit-III

(ii) Two long parallel straight wires A and B are 2.5 cm apart in air. They carry 5.0
A and 2.5 A currents respectively in opposite directions. Calculate the
magnitude of the force exerted by wire A on a 10 cm length of wire B. 5
33. (a) (i) (1) Write two points of difference between an interference pattern and a
diffraction pattern.
(2) Name any two factors on which the fringe width in a Young's double-
slit experiment depends.
(ii) In Young's double-slit experiment, the two slits are separated by a distance
equal to 100 times the wavelength of light that passes through the slits.
Calculate:
(1) the angular separation in radians between the central maximum and the
adjacent maximum.
(2) the distance between these two maxima on a screen 50 cm from the
slits. Unit-VI 5
OR
(b) (i) A spherical surface of radius of curvature R separates two media of refractive
indices n₁ and n2. A point object is placed in front of the surface at distance u in
medium of refractive index n₁ and its image is formed by the surface at distance v, in
the medium of refractive index n2. Derive a relation between u and v.
(ii) A solid glass sphere of radius 6.0 cm has a small air bubble trapped at a distance 3.0
cm from its centre C as shown in the figure. The refractive index of the material of
the sphere is 1.5. Find the apparent position of this bubble when seen through the
surface of the sphere from an outside point E in air. Unit-VI 5

SECTION E
34. The following figure shows a circuit diagram. We can find the currents through and
potential differences across different resistors using Kirchhoff's rules.

Answer the following questions based on the above: Unit-II
(a) Which points are at the same potential in the circuit? 1
(b) What is the current through arm bg? 1
(c) Find the potential difference across resistance R2?. 2
OR
(c) What is the power dissipated in resistance R3? 2
35. Strontium titanate is a rare oxide – a natural mineral found in Siberia. It is used as a substitute
for diamond because its refractive index and critical angle are 2.41 and 24.5°, respectively,
which are approximately equal to the refractive index and critical angle of diamond. It has all
the properties of diamond. Even an expert jeweller is unable to differentiate between diamond
and strontium titanate. A ray of light is incident normally on one face of an equilateral
triangular prism ABC made of strontium titanate.

Answer the following questions based on the above: Unit-VI
(a) Trace the path of the ray showing its passage through the prism. 1
(b) Find the velocity of light through the prism. 1
(c) Briefly explain two applications of total internal reflection. 2
OR
(c) Define total internal reflection of light. Give two conditions for it. 2

Paper-15
SECTION-A

1. The magnitude of the electric field due to a point charge object at a distance of 4.0 m
is 9 N/C. From the same charged object the electric field of magnitude, 16 N/C will
be at a distance of Unit-I 1
(a) 1 m (b) 2 m
(c) 3 m (d) 6 m

2. A point P lies at a distance x from the mid point of an electric dipole on its axis. The
electric potential at point P is proportional to Unit-I 1
1 1
(a) 2 (b) 3
x x
1 1
(c) 4 (d) 1/ 2
x x
3. A current of 0.8 A flows in a conductor of 40  for 1 minute. The heat produced in the
conductor will be Unit-II 1
(a) 1445 J (b) 1536 J
(c) 1569 J (d) 1640 J
4. A cell of emf E is connected across an external resistance R. When current ‘I’ is
drawn from the cell, the potential difference across the electrodes of the cell drops to
V. The internal resistance 'r' of the cell is Unit-II 1
 E-V   E-V 
(a)  R (b)  
 E   R 
E - V R  E - V 
(c) (d)  R
I  V 
5. Beams of electrons and protons move parallel to each other in the same direction.
They Unit-III 1
(a) attract each other.
(b) repel each other.
(c) neither attract nor repel.
(d) force of attraction or repulsion depends upon speed of beams.
6. A long straight wire of radius 'a' carries a steady current I. The current is uniformly
distributed across its area of cross-section. The ratio of magnitude of magnetic field
 
a
B1 at and B2 at distance 2a is Unit-III 1
2
1
(a) (b) 1
2
(c) 2 (d) 4
 

7. E and B represent the electric and the magnetic field of an electro-magnetic wave
respectively. The direction of propagation of the wave is along Unit-V 1
 
(a) B (b) E
   
(c) E × B (d) B × E

8. A ray of monochromatic light propagating in air, is incident on the surface of water.
Which of the following will be the same for the reflected and refracted rays? Unit-VI 1
(a) Energy carried (b) Speed
(c) Frequency (d) Wavelength
9. A beam of light travels from air into a medium. Its speed and wavelength in the
medium are 1.5×108 ms-1 and 230 nm respectively. The wavelength of
light in air will be Unit-VI 1
(a) 230 nm (b) 345 nm
(c) 460 nm (d) 690 nm
10. Which one of the following metals does not exhibit emission of electrons from its
surface when irradiated by visible light? Unit-VII 1
(a) Rubidium (b) Sodium
(c) Cadmium (d) Caesium
11. A hydrogen atom makes a transition from n = 5 to n = 1 orbit. The wavelength of photon
emitted is  . The wavelength of photon emitted when it makes a transition from n = 5 orbit
is n = 2 orbit is Unit-VIII 1
8 16
(a)  (b) 
7 7
24 32
(c)  (d) 
7 7
12. The curve of binding energy per nucleon as a function of atomic mass number has a
sharp peak for helium nucleus. This implies that helium nucleus is Unit-VIII 1
(a) radioactive
(b) unstable
(c) easily fissionable
(d) more stable nucleus than its neighbours
13. In an extrinsic semiconductor, the number density of holes is 4×1020 m-3. If the
number density of intrinsic carriers is 1.2×1015 m-3, the number density of electrons
in it is Unit-IX 1
(a) 1.8 × 109 m-3 (b) 2.4 × 1010 m-3
(c) 3.6 × 109 m-3 (d) 3.2 × 1010 m-3
14. Pieces of copper and of silicon are initially at room temperature. Both are heated
to temperature T. The conductivity of Unit-II 1
(a) both increases.
(b) both decreases.
(c) copper increases and silicon decreases.
(d) copper decreases and silicon increases.
15. The formation of depletion region in a p-n junction diode is due to Unit-IX 1
(a) movement of dopant atoms (b) diffusion of both electrons and holes
(c) drift of electrons only (d) drift of holes only
Note: In question number 16 to 18, two statements are given one labelled Assertion (A) and the

other labelled Reason (R). Select the correct answer to these questions 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 Assertion (A).
(b) Both Assertion (A) and Reason (R) are true and Reason (R) is NOT the correct
explanation of Assertion (A).

(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R) is also false.
16. Assertion (A): Diamagnetic substances exhibit magnetism. Unit-III
Reason (R): Diamagnetic materials do not have permanent magnetic dipole moment. 1
17. Assertion (A): Work done in moving a charge around a closed path, in an electric
field is always zero. Unit-1
Reason (R): Electrostatic force is a conservative force. 1
18. Assertion (A): In Young's double slit experiment all fringes are of equal width. Unit-VI
Reason (R): The fringe width depends upon wavelength of light (  ) used. distance
of screen from plane of slits (D) and slits separation (d). 1

SECTION-B
19. Briefly explain why and how a galvanometer is converted into an ammeter. Unit-III 2

20. (a) How are infrared waves produced? Why are these waves referred to as heat
waves? Give any two uses of infrared waves. Unit-V 2
OR
(b) How are X-rays produced? Give any two uses of these. Unit-V 2
21. In the given figure the radius of curvature of curved face in the plano-convex and the
plano-concave lens is 15 cm each. The refractive index of the material of the lenses is
1.5. Find the final position of the image formed. Unit-VI 2

22. What happens to the interference pattern when two coherent sources are Unit-VI 2
(a) infinitely close, and
(b) far apart from each other
23. (a) What is meant by ionisation energy? Write its value for hydrogen atom. Unit-VIII 2
OR
(b) Define the term, mass defect. How is it related to stability of the nucleus? Unit-VIII 2
24. Draw energy band diagram for an n-type and p-type semiconductor at T > 0 K. Unit-IX 2
25. Answer the following giving reasons: Unit-IX 2
i) A p-n junction diode is damaged by a strong current.
ii) Impurities are added in intrinsic semiconductors.

SECTION-C
26. (a) Two charged conducting spheres of radii a and b are connected to each other by a

wire. Find the ratio of the electric fields at their surfaces. Unit-I 3
OR
(b) A parallel plate capacitor (A) of capacitance C is charged by a battery to voltage V.
The battery is disconnected and an uncharged capacitor (B) of capacitance 2C is
connected across A. Find the ratio of Unit-I 3
(i) final charges on A and B.

(ii) total electrostatic energy stored in A and B finally and that stored in A initially.
27. Define current density and relaxation time. Derive an expression for resistivity of a
conductor in terms of number density of charge carriers in the conductor and
relaxation time. Unit-II 3
28. A series CR circuit with R = 200  and C = (50/  ) µF is connected across an ac
source of peak voltage  0 = 100 V and frequency v = 50 Hz. Calculate Unit-IV 3
(a) impedance of the circuit (Z), (b) phase angle (  ), and (c) voltage across the
resistor.
29. Define critical angle for a given pair of media and total internal reflection. Obtain the
relation between the critical angle and refractive index of the medium. Unit-VI 3
30. (a) (i) Distinguish between nuclear fission and fusion giving an example of each.
(ii) Explain the release of energy in nuclear fission and fusion on the basis of
binding energy per nucleon curve. Unit-VIII 3
OR
(b) (i) How is the size of a nucleus found experimentally? Write the relation between
the radius and mass number of a nucleus. Unit-VIII
(ii) Prove that the density of a nucleus is independent of its mass number. 3

SECTION-D
31. (a) (i) Use Gauss' law to obtain an expression for the electric field due to an infinitely
long thin straight wire with uniform linear charge density λ.
(ii) An infinitely long positively charged straight wire has a linear charge density
λ. An electron is revolving in a circle with a constant speed v such that the wire
passes through the centre, and is perpendicular to the plane, of the circle. Find the
kinetic energy of the electron in terms of magnitudes of its charge and linear
charge density  on the wire. Unit-I
(iii) Draw a graph of kinetic energy as a function of linear charge density λ. 5
OR
(b) (i) Consider two identical point charges located at points (0, 0) and (a, 0).
(1) Is there a point on the line joining them at which the (1) electric field is zero?
(2) Is there a point on the line joining them at which the electric potential is zero?
Justify your answers for each case. Unit-I
(ii) State the significance of negative value of electrostatic potential energy of a
system of charges.
Three charges are placed at the corners of an equilateral triangle ABC of side
2.0 m as shown in figure. Calculate the electric potential energy of the system of
three charges. Unit-I 5

32. (a) (i) Define coefficient of self-induction. Obtain an expression for self-inductance of
a long solenoid of length l, area of cross-section A having N turns.

(ii) Calculate the self-inductance of a coil using the following data obtained when an
AC source of frequency  200  Hz and a DC source is applied across the
  
coil. Unit-IV 5
AC Source DC Source
Sl. No. V(Volts) I(A) S. No. V(Volts) I(A)
1 3.0 0.5 1 4.0 1.0
2 6.0 1.0 2 6.0 1.5
3 9.0 1.5 3 8.0 2.0
OR
(b) (i) With the help of a labelled diagram, describe the principle and working of an ac
generator. Hence, obtain an expression for the instantaneous value of the emf
generated. Unit-IV
(ii) The coil of an ac generator consists of 100 turns of wire, each of area 0.5 m².
The resistance of the wire is 100  . The coil is rotating in a magnetic field of 0.8
T perpendiculars to its axis of rotation, at a constant angular speed of 60 radian
per second. Calculate the maximum emf generated and power dissipated in the
coil. 5
33. (a) (i) State Huygen's principle. With the help of a diagram, show how a plane wave is
reflected from a surface. Hence verify the law of reflection. Unit-VI
(ii) A concave mirror of focal length 12 cm forms a three times magnified virtual image
of an object. Find the distance of the object from the mirror. 5
OR
(b) (i) Draw a labelled ray diagram showing the image formation by a refracting telescope.
Define its magnifying power. Write two limitations of a refracting telescope over a
reflecting telescope.
(ii) The focal lengths of the objective and the eye-piece of a compound microscope are
1.0 cm and 2.5 cm respectively. Find the tube length of the microscope for obtaining a
magnification of 300. Unit-VI 5
SECTION-E
Note: Questions number 34 and 35 are Case Study based questions: Read the following paragraph
and answer the questions.
34. (a) Consider the experimental set up shown in the figure. This jumping ring experiment is an
outstanding demonstration of some simple laws of Physics. A conducting non-magnetic
ring is placed over the vertical core of a solenoid. When current is passed through the
solenoid, the ring is thrown off. Unit-IV

Answer the following questions:
(i) Explain the reason of jumping of the ring when the switch is closed in the circuit.
(ii) What will happen if the terminals of the battery are reversed and the switch is closed?
Explain.
(iii) Explain the two laws that help us understand this phenomenon. 4
OR
(b) Briefly explain various ways to increase the strength of magnetic field produced by a
given solenoid.
35. (a) Figure shows the variation of photoelectric current measured in a photo cell circuit as a
function of the potential difference between the plates of the photo cell when light beams
A, B, C and D of different wavelengths are incident on the photo cell. Examine the given
figure and answer the following questions: Unit-VII

(i) Which light beam has the highest frequency and why?
(ii) Which light beam has the longest wavelength and why?
(iii) Which light beam ejects photoelectrons with maximum momentum and why? 4
OR
(b) What is the effect on threshold frequency and stopping potential on increasing the
frequency of incident beam of light? Justify your answer. Unit-VII 4

Paper-16
SECTION-A

1. An electric dipole of length 2 cm is placed at an angle of 30° with an electric field
2×105 N/C. If the dipole experiences a torque of 8×10-3 Nm, the magnitude of either
charge of the dipole, is Unit-I 1
(A) 4 μC (Β) 7 μC
(C) 8 mC (D) 2 mC
2. Two long parallel wires kept 2 m apart carry 3A current each, in the same direction.
The force per unit length on one wire due to the other is Unit-III 1
-5 -1 -7
(A) 4.5×10 Nm attractive (B) 4.5×10 N/m, repulsive
-7
(C) 9×10 N/m repulsive (D) 9×10-5 N/m, attractive
3. Which of the following has its permeability less than that of free space? Unit-III 1
(A) Copper (B) Aluminium
(C) Copper chloride (D) Nickel
4. A square shaped coil of side 10 cm. having 100 turns is placed perpendicular to a
magnetic field which is increasing at 1 T/s. The induced emf in the coil is Unit-IV 1
(A) 0.1 V (B) 0.5 V
(C) 0.75 V (D) 1.0 V
5. Which one of the following electromagnetic radiation has the least wavelength? Unit-V 1
(A) Gamma rays (B) Microwaves
(C) Visible light (D) X-rays
6. In a Young's double-slit experiment, the screen is moved away from the plane of the
slits. What will be its effect on the following? Unit-VI 1
(i) Angular separation of the fringes.
(ii) Fringe-width.
(A) Both (1) and (ii) remain constant,
(B) (i) remains constant, but (ii) decreases.
(C) (i) remains constant, but (ii) increases.
(D) Both (i) and (ii) increase.
7. The energy of a photon of wavelength  is Unit-VII 1
(A) hc  (B) hc/ 
(C)  /hc (D)  h/c
8. The ratio of the nuclear densities of two nuclei having mass numbers 64 and 125 is 1
64 4
(A) (B) Unit-VIII
125 5
5
(C) (D) 1
4
9. During the formation of a p-n junction: Unit-IX 1
(A) diffusion current keeps increasing.
(B) drift current remains constant.

(C) both the diffusion current and drift current remain constant.
(D) diffusion current remains almost constant but drift current increases till both
currents become equal.

10. The diagram shows four energy level of an electron in Bohr model of hydrogen
atom. Identify the transition in which the emitted photon will have the highest
energy. Unit-VIII 1

(A) I (B) II (C) III (d) IV
11. Which of the following graphs correctly represents the variation of a particle
momentum with its associated de-Broglie wavelength? Unit-VII 1

12. The capacitors, each of 4 µF are to be connected in such a way that the effective
capacitance of the combination is 6 µF. This can be achieved by connecting Unit-I 1
(A) All three in parallel
(B) All three in series
(C) Two of them connected in series and the combination in parallel to the third.
(D) Two of them connected in parallel and the combination in series to the third.
13. Which of the following statements about a series LCR circuit connected to an ac
source is correct? Unit-IV 1
(A) If the frequency of the source is increased, the impedance of the circuit first
decreases and then increases.
(B) If the net reactance (XL – XC) of circuit becomes equal to its resistance, then
the current leads the voltage by 45°.
(C) At resonance, the voltage drop across the inductor is more than that across the
capacitor.
(D) At resonance, the voltage drop across the capacitor is more than that across the
inductor.
14. According to Huygens principle, the amplitude of secondary wavelets is Unit-VI 1
(A) equal in both the forward and the backward directions.

(B) maximum in the forward direction and zero in the backward direction.
(C) large in the forward direction and small in the backward direction.
(D) small in the forward direction and large in the backward direction.
15. The radius of the nth orbit in Bohr model of hydrogen atom is proportional to Unit-VIII 1
(B) 22 (D) 1
2
(A) n (C) n
n n

Note: In question number 16 to 18 two statements are given-one labelled Assertion (A) and the
other labelled Reason (R). Select the correct answer to these questions from the codes (a), (b), (c)
and (d) as given below:
(A) Both Assertion (A) and Reason (R) are true and (R) is the correct explanation of (A).
(B) Both Assertion (A) and Reason (R) are true and (R) is NOT the correct explanation of (A)
(C) Assertion (A) is true and Reason (R) is false.
(D) Assertion (A) is false and Reason (R) is also false.
16. Assertion(A): The resistance of an intrinsic semiconductor decreases with increase in its
temperature. Unit-IX
Reason(R): The number of conduction electrons as well as hole increase in an
intrinsic semiconductor with rise in its temperature. 1
17. Assertion(A): The equivalent resistance between points A and B in the given
network is 2R. Unit-II
Reason (R): All the resistors are connected in parallel 1

18. Assertion(A): The deflecting torque acting on a current carrying loop is zero when
its plane is perpendicular to the direction of magnetic field. Unit-III

Reason(R): The deflecting torque acting on a loop of magnetic moment m in a
  
magnetic field B is given by the dot product of m and B . 1

SECTION-B
19. Draw a graph showing the variation of potential energy of a pair nucleons as a
function of their separation. Indicate the region in which the nuclear force is (a)
attractive and (b) repulsive. Unit-VIII 2
20. (a) How will the De Broglie wavelength associated with an electron be affected when
the (i) velocity of the electron decreases ? and (ii) accelerating potential is increased?
Justify your answer. 2
OR
(b) How would the stopping potential for a given photosensitive surface change if (i) the
frequency of the incident radiation were increased and (ii) the intensity of incident radiation
were decreased? Justify your answer. Unit-VII 2
21. Identify the electromagnetic wave whose wavelengths range is from about Unit-V 2
-12 -8
(a) 10 m to about 10 m.
(b) 10-1 to about 10-1 m.
Write one use of each.

22. Depict the orientation of an electric dipole in (a) stable and (b) unstable equilibrium
in an external uniform electric field. Unit-I 2
Write the potential energy of the dipole in each case.

23. (a) Write the expression for the Lorentz force on a particle of charge q moving with a
 
velocity v in a magnetic field B . When is the magnitude of this force maximum? Show

that no work is done by this force on the particle during its motion from a point r 1 to

point r 2 . Unit-III 2
OR
(b) A long straight wire AB carries a current I. A particle (mass m and charge q) moves

with a velocity v parallel to the wire, at a distance d from it as shown in the figure.
Obtain the expression for the force experienced by the particle and mention its
directions. Unit-III 2

24. The potential difference applied across a given conductor is doubled. How will this affect (i)
the mobility of electrons and (ii) the current density in the conductor? Justify your answers.
Unit-II 2
25. Two coils C1 and C2 are placed close to each other. The magnetic flux  2 linked with the coil
C2 varies with the current I1 flowing in coil C1 as shown in the figure. Find Unit-IV 2

(i) the mutual inductance of the arrangement, and
 dI 
(ii) the rate of change of current in coil  1  that will induce an emf of 100 V in coil C2.
 dt 

SECTION-C
26. (a) A plane wave-front propagating in a medium of refractive index 1 is incident on a plane
surface making an angle of incidence (i). It enters into a medium of refractive index

2  2  1  . Unit-VI
Using Huygen's construction of secondary wavelets to trace the retracted wave-front.
Hence verify Snell's law of refraction. 3
OR

(b) Using Huygen's construction, show how a plane wave is reflected from a surface.
Hence verify the law of reflection. 3
27. An alternating voltage of 220 V is applied across a device X. A current of 0.22 A
flows in the circuit and it lags behind the applied voltage in phase by  /2 radian.
When the same voltage is applied across another device Y, the current in the circuit
remains the same and it is in phase with the applied voltage. Unit-IV 3
i) Name the devices X and Y and.
(ii) Calculate the current flowing in the circuit when the same voltage is applied
across the series combination of X and Y.
28. State the basic principle behind the working of an ac generator. Briefly describe its
working and obtain the expression for the instantaneous value of emf induced. Unit-IV 3
29. (a) Briefly describe how the current sensitivity of a moving coil galvanometer can be
increased. Unit-III
(b)A galvanometer shows full scale deflection for current Ig. A resistance R1 is
required to convert it into a voltmeter of range (0 - V) and a resistance R2 to
convert it into a voltmeter of range (0-2V). Find the resistance of the
galvanometer. 3

30. (a) (i) Differentiate between 'distance of closest approach' and 'impact parameter'. 3
(ii) Determine the distance of closest approach when an alpha particle of kinetic
energy 3.95 MeV approaches a nucleus of Z = 79, stops and reverses its directions.
OR
(b) (i) State three postulates of Bohr's theory of hydrogen atom. 3

(ii) Find the angular momentum of an electron revolving in the second orbit in Bohr's
hydrogen atom. Unit-VIII 3

SECTION - D
31. (a) (i) Explain how free electrons in a metal at constant temperature attain an average
velocity under the action of an electric field.
Hence obtain an expression for it. 3
(ii) Consider two conducting wires A and B of the same diameter but made of
different materials joined in series across a battery. The number density of
electrons in A is 1.5 times that in B. Find the ratio of drift velocity of electrons in
wire A to that in wire B. Unit-II 2
OR
(b) (i) A cell emf of (E) and internal resistance (r) is connected across a variable load
resistance (R). Draw plots showing the variation of terminal voltage V with (i) R
and (ii) the current (I) in the load. Unit-II 2
(ii) Three cells, each of emf E but internal resistances 2r, 3r and 6r are connected in
parallel across a resistor R.

Obtain expressions for (i) current flowing in the circuit, and (ii) the terminal
potential difference across the equivalent cell. Unit-II 3
32. (a) Draw the circuit arrangement for studying V-I characteristics of a p-n junction
diode in (i) forward biasing and (ii) reverse biasing.

Draw the typical V-I characteristics of a silicon diode. Describe briefly the
following terms: (i) minority carrier injection in forward biasing and (ii)
breakdown voltage in reverse biasing. Unit-IX 5
OR
(b) Name two important processes involved in the formation of a p-n junction diode.
With the help of a circuit diagram, explain the working of junction diode as a full
wave rectifier. Draw its input and output waveforms. State the characteristic
property of a junction diode that makes it suitable for rectification. Unit-IX 5
33. (a) (i) Draw a ray diagram to show the working of a compound microscope. Obtain
the expression for the total magnification for the final image to be formed at the near
point. 3
(i) In a compound microscope an object is placed at a distance of 1.5 cm from the objective
of focal length 1.25 cm. If the eye-piece has a focal length of 5 cm and the final image is
formed at the near point, find the magnifying power of the microscope. 2
OR
(b) (i) Draw a ray diagram for the formation of image of an object by an astronomical
telescope, in normal adjustment. Obtain the expression for its magnifying power.
(ii) The magnifying power of an astronomical telescope in normal adjustment is 2.9 and
the objective and the eyepiece are separated by a distance of 150 cm. Find the focal
lengths of the two lenses. Unit-VI 5

SECTION-E
Note: Questions number 34 and 35 are Case Study based questions. Read the following
paragraph and answer the questions.
34. A lens is a transparent optical medium bounded by two surfaces; at least one of which should
be spherical. Considering image formation by a single spherical surface successively at the two
surfaces of a lens, lens maker's formula is obtained. It is useful to design lenses of desired focal
length using surfaces of suitable radii of curvature. This formula helps us obtain a relation
between u, and f for a lens. Lenses form images of objects and they are used in a number of
optical devices, for example microscopes and telescopes. Unit-VI 4
(i) An object AB is kept in front of a composite convex lens, as shown in figure. Will the lens
produce one image? If not, explain.

(ii) A real image of an object formed by a convex lens is observed on a Screen. If the
screen is removed, will the image still be formed? Explain.

(iii) A double convex lens is made of glass of refractive index 1.55 with both faces of the
same radius of curvature. Find the radius of curvature required if focal length is
20 cm.
OR
(iii) Two convex lenses A and B of focal lengths 15 cm and 10 cm. respectively are
placed coaxially 'd' distance apart. A point object is kept at a distance of 30 cm in front of

lens A. Find the value of 'd' so that the rays emerging from lens B are parallel to its principal
axis.
35. A capacitor is a system of two conductors separated by an insulator. The two
conductors have equal and opposite charges with a potential difference between
them. The capacitance of a capacitor depends on the geometrical configuration
(shape, size and separation) of the system and also on the nature of the insulator
separating the two conductors. They are used to store charges. Like resistors,
capacitors can be arranged in series or parallel or a combination of both to obtain
desired value of capacitance. Unit-I 4
(i) Find the equivalent capacitance between points A and B in the given diagram.

(ii) A dielectric slab is inserted between the plates of a parallel plate capacitor. The
electric field between the plates decreases. Explain.
(iii) A capacitor A of capacitance C, having charge Q is connected across another
uncharged capacitor B of capacitance 2C. Find an expression for (a) the potential
difference across the combination and (b) the charge lost by capacitor A.
OR
(iii) Two slabs of dielectric constants 2K and K fill the space between the plates of a
parallel plate capacitor of plate area A and plate separation d as shown in figure.
Find an expression for capacitance of the system.

Paper-17
SECTION A
1. The charge on a body is 8×10-12 C. It means that the body has: Unit-I 1
-12 10
(a) lost 8×10 electrons (b) gained 4×10 electrons
(c) gained 2×108 electrons (d) lost 5×107 electrons
2. A current flows through a series combination of two copper wires of equal length but
their radii are in the ratio of 1: 2. The ratio of drift velocities of free electrons in the
wires will be: Unit-II 1
(a) 8 (b) 4 (c) 2 (d) 1

3. A charged particle at rest is subjected to an external magnetic field B . If no other
force acts on the particle, then it will: Unit-III 1

(a) accelerate along B (b) remain at rest

(c) move in a circular path (d) move with a constant speed along B
4. The magnetic flux (in SI units) through a coil varies with time as  = 3t2 + 4t + 7. The ratio
of emf induced in the coil at t = 2s to that at t = 1 s will be: Unit-IV 1
(a) 2 (b) 0.8
(c) 1.6 (d) 4
5. A current carrying loop is placed in a uniform magnetic field. The torque acting on
it does not depend upon the Unit-IV 1
(a) magnetic field (b) current in the loop
(c) area of the loop (d) shape of the loop
6. Two identical coils carrying equal currents are held concentric with their planes
perpendicular to each other. The ratio of the magnitude of magnetic field at the
centre of one coil to that of the resultant magnetic field at the centre is: Unit-IV 1
(a) 1 (b) 2
2

(c) 1 (d) 2
2
7. An electron is revolving around a nucleus in a circular orbit of radius r with a constant
speed v. The magnetic moment associated with the circulating current is: Unit-IV 1
evr
(a) (b) 4 evr
4
evr
(c) 2 evr (d)
2
8. Which of the following statements is not correct? Unit-IV 1
(a) Lenz's law is the consequence of the law of conservation of energy.
(b) The magnitude of induced emf in a coil is directly proportional to the rate of
change of magnetic flux.
(c) Inserting an iron core in a coil decreases its self-inductance.
(d) An emf can be induced in a straight conductor by moving it perpendicularly

through a uniform magnetic field.
9. In a plane electromagnetic wave, the magnetic field oscillates sinusoidally with a
frequency of 3×1010 Hz and amplitude 2.4×10-8 T. The amplitude of the
oscillating electric field is: Unit-V 1
-1 -1
(a) 1.6 Vm (b) 3.2 Vm
-1
(c) 7.2 Vm (d) 8 Vm-1

10. An object is placed at a distance of 10 cm in front of a concave mirror of radius of
curvature 15 cm. The nature and position the image formed is: Unit-VI 1
(a) real and inverted, 30 cm in front of the mirror
(b) real and inverted, 15 cm in front of the mirror
(c) virtual and erect, 30 cm behind the mirror
(d) virtual and erect, 15 cm behind the mirror
11. The energy of a photon in a beam of red light with a wavelength of 6.60×10 -7 m is
close to: Unit-VIII 1
-19
(a) 4.42×10 J
(b) 4.0×10-19 J
(c) 2.19 × 10-19 J
(d) 3.0 ×10-19 J
12. A photon absorbed by a hydrogen atom excites from n = 3 level to n = 5 level. The energy of
the photon is : Unit-VIII 1
(a) + 0.97 eV (b) – 0.97 eV
(c) + 1.51 eV (d) – 0.54 eV
237
13. The number of neutrons in 91 Pa is : Unit-VIII 1
(a) 91 (b) 146
(c) 237 (d) 164
14. Which of the following is not a semiconductor? Unit-IX 1
(a) Ge (b) Si
(c) Sn (d) CdS
15. In an intrinsic semiconductor, the intrinsic carrier concentration (ni), electron
concentration (ne) and hole concentration (nh) are related as: Unit-IX 1
(a) ne + nh = ni (b) n i = n e n h
ni
(c) ne = nh = ni (d) ne + nh =
2
Questions number 16 to 18 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.

16. Assertion(A): The speed of light decreases when it passes from air into a denser
medium. Unit-IX 1
The speed of light in a denser medium is given by v  c , where c is

Reason(R):

the speed of light in air and  is the refractive index of the denser medium.
17. Assertion(A): Silicon is preferred over Germanium for making semiconductor
devices. Unit-IX 1
Reason(R): Silicon can be used at a higher temperature as compared to Germanium.

18. Assertion(A): The energy (E) and momentum (p) of a photon are related as p  h 1
E
Reason(R): Photons behave as a wave. Unit-VII
SECTION B
19. The terminal potential difference of a cell is 19 V when a current of 1.0 A flows in
the circuit. It reduces to 17 V when the current supplied by the cell is 3.0 A. Find the
emf and internal resistance of the cell. Unit- II 2
20. (a) What is meant by displacement current? Explain. Give an example where such
current exists. Unit- V 2
OR
(b) Write the wavelength range of infrared waves. Why are these waves often called
'heat waves'? Explain. Unit-V 2
21. A glass jug is filled with water to a height of 9.6 cm. The depth of a coin lying on its
bottom as measured by a microscope is 7.2 cm. Find the refractive index of the water
and the speed of light in water. Unit-VI 2
22. A convex lens is made of the material of refractive index n₁. What will happen if it
were immersed in a medium of refractive index n2 in the following cases? Unit-VI 2
(a) n2 > n1
(b) n2 = n1
23. State Bohr's postulates of hydrogen atom. How is a photon emitted by an excited
hydrogen atom? Unit-VIII 2
24. Define the following terms in relation to the working of a p-n junction diode: Unit-IX 2
(i) Knee voltage
(ii) Reverse saturation current
25. (a) How are the potential barrier and width of the depletion region affected when a
p-n junction diode is (i) forward-biased, and (ii) reverse-biased? Unit-IX 2
OR
(b) Briefly explain doping of a semiconductor and its necessity. Unit-IX 2

SECTION-C
26. Name the factors on which electrical conductivity of a material depends. Obtain the
relation between current density in a conductor and the conductivity of its material. Unit-II 3
27. (a) (i) Differentiate between the resistance and reactance of a series LCR circuit.
(ii) Explain how a capacitor blocks a direct current and an inductor opposes an
alternating current. Unit-IV 3
OR
(b) Show mathematically that in an ac circuit containing a pure inductor, the current lags

behind the voltage in phase by . Unit-IV 3
2
28. Define the term ‘self-inductance’ of a coil. Obtain the expression for the self-

inductance of a long solenoid of length l, cross-sectional area A and having N turns. Unit-IV 3
29. Briefly explain how Einstein's photoelectric equation accounts for all observations on
photoelectric effect. Unit-VII 3
30. (a) Explain two main features of the plot of the binding energy per nucleon versus the
mass number of the nuclei. Mention two conclusions that can be drawn from these
features. Unit-VIII 3

OR
(b) Briefly explain the observations made in Geiger-Marsden experiment. Write the
important conclusions drawn about the structure of atom from these observations.
Unit-VIII 3
SECTION-D
31. (a) (i) What is an electric dipole? Derive an expression for the torque acting on an
electric dipole in a uniform electric field. Unit-I
(ii) An electric dipole with dipole moment 6×10-9 C-m is aligned at an angle of 30°
with the direction of a uniform electric field of magnitude 4×104 NC-1 Calculate
magnitude of the torque acting on the electric dipole. 5
OR
(b) (i) State Gauss's law in electrostatics. Using it, derive an expression for the electric
field due to a uniformly charged thin spherical shell of radius Rat a point (i) outside,
and (ii) inside the shell. Unit- I
(ii) A point charge of 4 µC is at the centre of a cubic Gaussian surface, 1.0 m on edge.
Find the electric flux through one of the faces of the Gaussian surface. 5
32. (a) (i) Two long parallel straight conductors carrying current I1 and I2 are kept r
distance apart in air. Obtain an expression for the force per unit length on one
conductor due to the magnetic field produced by the other conductor. Hence, define
one ampere. Under what condition will the force between the conductors be
attractive in nature?
(ii) A closely wound circular coil of radius 6.28 cm. having 50 turns carries a steady
current of 4 A. Find the magnetic field at the centre of the coil. How will the
magnitude of the magnetic field be affected if the radius of the coil is halved keeping
other factors same? Unit-III 5
OR

(b) (i) A particle of mass m and charge q, at the origin moves with a velocity v in xy-

plane making an angle  with x-axis. It is subjected to a uniform magnetic field B
along x-axis. Justify that the particle will move in a helical path. Hence, obtain
expression for the radius of the helix.
(ii) A long straight wire kept horizontally carries a current of 4 A from west to east

direction. Find the direction and magnitude of magnetic field B at a point 20 cm
below the wire. Unit-III 5
33. (a) (i) What is meant by total internal reflection of light? Write the two conditions
necessary for this phenomenon to occur. Briefly explain one of its technological
applications.
(ii) A thin converging lens of focal length 10 cm is placed coaxially in contact with a
thin diverging lens of focal length 15 cm. Find the nature and focal length of the
combined lens. Unit-VI 5
OR

(b) (i) Answer the following giving reasons:
(1) The angular size of the image equals the angular size of the object in a simple
microscope, yet it offers magnification.
(2) Both the objective and the eyepiece of a compound microscope have short
focal lengths.

(3) A microscope and a telescope play different roles with respect to resolution and
magnification of the image. Unit-VI
(ii) In Young's double-slit experiment, the two slits are 1.0 mm apart. They are
illuminated with light of wavelength 600 nm. Find the fringe width on a screen
2.0 m away from the slits. Unit-VI 5

SECTION-E

34. After centuries of efforts, careful studies, experiments and analysis by different scientists, it
was concluded that there are two kinds of entities called the electric charge. The property
which differentiates the two kinds is called the polarity of charge. The two kinds of charges
were named as positive (+) and negative (-) by American scientist Benjamin Franklin.
A small sphere S1 with charge -8q is 1.6 m away from another identical sphere S2 with
charge +2q. The two spheres are brought in contact with each other and then separated by a
distance 1-6 m. Initially the force between the two spheres was 8.1 × 10-4 N.
Based on the above facts, answer the following questions: Unit-I
(i) Which sphere will transfer the electrons to the other sphere after they were brought in
contact? 1
(ii) How does the net electric field at the midpoint on the line joining the two spheres
change after contact? 1
(iii) What was initial charge on spheres S1 and S2? 2
OR
(iii) What is the charge on spheres S1 and S2 after contact? 2
35. Diffraction of light: According to rectilinear propagation of light, light travels in a
straight line. But Italian scientist Grimaldi discovered that light bends near the edges
of the aperture of the obstacles whose size is comparable with the wavelength of
light. This phenomenon of bending of light around the corners of an obstacle is
called diffraction of light. If we place a screen in front of the slit, the diffraction
pattern observed on it is of unequal widths and unequal intensities. The diffraction
phenomenon can be explained on the basis of wave nature of light. Unit-VI
Based on the above facts, answer the following questions:
(i) What is the most essential condition for observing diffraction? 1
(ii) Which characteristic of light is used in X-ray crystallography? 1
(iii) How does the wave theory of light provide an explanation for diffraction?
Explain. 2
OR
(iii) In a single slit diffraction, if red light is replaced by blue light, then how does the
diffraction pattern change? 2

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