1 SAMPLE PAPER

Time Allowed: 3 |Hours Maximum Marks: 70

General Instructions:
(1) There are 33questions in all. All questions are compulsory.
(2) This question paper has five sections: Section A, Section B, Section C, Section Dand Section E.
(3) All thesections are compulsory.
(3) Section A
contains sixteen questions, twclve MCO and four Assertion Reasoning based of I mark each,
Section Bcontains five questions of two marks cach, Section Ccontains seven questions of three
marks each, Section D contains two case study based questions of four marks each and Section E
contains threc long answer questions of five marks cach.
(5) There is no overallchoice. However, an internalchoice has been provided in one
question in Section
B, one qucstion in Section C, one question in cach CBQ in Section D and all three questions in
Section E. You have to attempt only one of the choices in such questions.
(6) Use of calculators is not allowed.
(7) You may use the following values of physical constants wherever necessary.
(i) c = 3 × 10* m/s
(i) m, = 9,| x 10 kg
(iii) e = l.6 × 10- C
(iv) 4, 4n X 107 Tm4-!
(v) h = 6.63 × 104 Js
(vi) E = 8.854 x 10-12 C² N-'m-2
(vii) Avogadro's number = 6.023 x 10 per gram mole

SECTION - A
1. When two point charges are placed at a certain
distance r in air, they
Find the distance at which these charges willexperience the same exert force F on each other.
a
force when kept in amedium of
dielectric constant K.
(a) K (b) r
(c) (d) rx K
VK
2. A 5 C charge is taken from a point Ato point B. The amount of work done during the
is 8mJ. Find the potential difference proceSS
between the points.
(u) 1600 V (b) 160 V
(c) 16 V (d) 16 kV
3. Find the cffective capacitance between the points P and O in the given circuit of the five
capacitors, cach of capacity (C
identical

(a) C2 (b) 2C (c) 5C (d) Cs

4. The current and voltage graphs for a certain material are plotted at two temperatures T, and T,
as shown below. The conclusion is:
T,

(a) T, < T, (b) T, > T, (c) 27, = T, (d) T, = T,

5. What is the magnetic induction at point O in the given figure?

H
(a) (b) (c) (d)
4Tur 4r 4r 4r 4r 4
6. A prOton and an a-particle enter normally at the same velocities into auniform magnetic field.
Find the ratio of the radii of their paths.
(a) 1:2 (b) 1:4 (c) 2:1 (d) 4:1
7. A diamagnetic gas when allowed to ascend in between the poles of a magnet spreads across the
field.
The statement is
(a) true. (b) false.
(c) true for paramagnetic gas. (d) not applicable.
8. Which physical quantity remains unchanged in atransformer?
(a) Voltage (b) Amplitude (c) Current (d) Power
9. Find the induced emf across the terminals of a coil of self inductance 40 mB, when the current
flowing through it is raised from 1A to l1A in 4 millisecond.
(a) 40 V (b) 440 V (c) 100 V (d) 0.4 V
10. The potential drops across a resistance and an inductance joined in series with an ac. source are
16 V and 12 V respectively. What is the total potential drop across the circuit:?
(a) 28 V (b) 32 V (c) 24 V (d) 20V
11. Which e.m. waves are used in radars and communication through satellites?
(a) IR radiation (b) Radio waves (c) Micro waves (d) None of the above
 limits of Lyman series in H-atom.
12. Calculate the short and long wavelength 3 R 4R
(c) R2 and (a) and
and 1R
1 4 4
(a) and (b) 4R 2 3
R 3R 3R
Assertion (A) and the other labelled Reason
For Q.13 to 16, two statements are given-one labelled
(b), (c) and (d) as given below.
Select the correct answer to these questions from the codes (a),
explanation of Assertion.
(a) If both Assertion and Reason are true and Reason is correct
of Assertion.
(b) If both Assertion and Reason are true but Reason is not the correct explanation
(c) If Assertion is true but Reason is false.
(d) If both Assertion and Reason are false.
13. Assertion (A): The speed of the light in glass is independent of the colour of light.
Reason (R): The speed of the light in a medium does not depend on its wavelength.
14. Assertion (A): de Broglie suggested that in dealing with atomic and sub-atomic particles, Newtonian
mechanics has to be modified.
Reason (R): The wave properties are displayed by particles whose mass is of the order of that of
a proton or less.
15. Assertion (A): The binding energy per nucleon for nuclei with atomic mass number A> 100.
decrease with A.
Reason (R): The forces are weak for heavier nuclei.
16. Assertion (A): Photoelectric current depends on the intensity of incident light.
Reason (R): Number of photoelectrons emitted per second is directly proportional to the intensity
of incident radiation.

SECTION - B
17. Two charges -g and tq are located at points (0, 0, - a) and (0, 0,
a). Find the electrostatic potential
at the points (0, 0, z), (0, 0, - z) and (, y, 0).
18. Deduce the exxpression for the magnetic field at a
loop of radius R, situated at a distance x from the point on the axis of a current carrying circular
at the centre of the loop?
centre. What is the value of the magnetic field
19. (a) In a plane
electromagnetic wave, the electric field oscillates sinusoidally with amplitude
48 Vm. Find the amplitude of the
oscillating magnetic field.
(b) Show that the average energy
density of the electric field E equals the average
of the magnetic field B. energy density
20. A ray of light incident on one of the
The refracted ray in the prism strikes faces of a glass prism of angle A has
the opposite face which is angle of incidence 2A.
retraces its path. Draw the ray diagram and find the silvered. The reflected ray from it
material of the prism and the angle of the prism. relation between the refractive index of the
21. The ground state energy of
energy level -1.51 eV to -3.4hydrogen atom is -13.6 eV. If an electron
eV, calculate the makes a transition from any
the series of hydrogen spectrum to wavelength the spectral line emitted and name
which it belongs.
or
Or
(a) Why is the mass of a
nucleus always less than the sum of the masses of
(b) Define mass defect of a its constituents'?
nucleus.
 SECTION -C

22. Two identical circular coils A and B, each of radius R are lying in perpendicular planes such that
they have a common centre. Calculate the magnitude and direction of the magnetic field at the
common centre of the coils if the currents carried by them are Iand /3 I respectively.
23. Explain how a moving coil galvanometer can be converted into (a) an ammeter (b) a voltmeter by
suitable combination of resistances. Derive the requircd expressions.
24. An alternating potential of 100 V and 50Hz is applied across a series circuit having an inductance
of S H, a resistance of 100 Qand a variable capacitance. At what value of capacitance will the
current in the circuit be in phase with the applied voltage?
Or
Aseries LCR circuit is connected to an a.c. source.Using the phasor diagram, derive the expression
for the impedance of the circuit. Plot a graph to show the variation of current with frequency of
the source, explaining the nature of its variation.
25. State Einstein's photoelectric equation explaining the symbols used.
Light of frequency v is incident on a photosensitive surface. A graph of the square of the maximum
speed of electrons (V) v/s v is obtained as shown here.

max

Using Einstein's photoelectric equation, obtain the expresions for (1) Planck's constant (ii) work
function of the given photOsensitive material in terms of the parameters l, n and n (the mass of
the electron).
26. (a) Distinguish between nuclear fission and nuclear fusion. Explain the release of energy in both
the processes.
(b) Calculate the energy release in MeV in the deuterium-tritium fusion reaction.
H +H He + n
Given that:
m((H) = 2.014102 u
m((H) =3.016049 u
m(He) = 4.002603 u
m, = 1.008665 u
1u = 931.5 MeV/c
27. In the experiment on diffraction due to a single slit, show that
(a) the intensity of diffraction fringes decreases as the order (n) increases.
(b) angular width of the central maximum is twice that of the first order secondary maximum.
28. Descritbe briefly, with the help of a diagram, the role of the two important processes involvedin
the formation of ap-n junction.
 SECTION-D
29. Case Study
Read the following paragraph and answer the questions that follow.
Combination of lenses
In many optical instrumentstwo or more than two lenses are used. They may be at some distan.
or in contact. Different lens combinations are used in the objectives of cameras, microsconex
telescopes and other optical instruments.
When 'n lenses of powers P,,P, P, ...P, are used in contact than the power of the combination i
P= P, + P, +... t P,
And the total magnification is
m = m, X m, X ... X m,
() A convex lens and a concave lens, each having same focal length of 25 cm, are put in contact
to form acombination of lenses. The power of thecombination is
(a) zero (b) 25 D (c) S0 D (d) infinite
(ü) For anormal eye, the cornea of eye provides a converging power of 40 D and the least
converging power of eye lens behind the cornea is 20 D.Using this information, the distance
between retina and the cornea eye lens can be estimated to be
(a) 5 cm (b) 2.5 cm (c) 1.67 cm (d) 1.5 cm
(iiü) We combine two lenses, one is convex and other concave having focal lengths f and f, and
their combined focal length is f. The combination of lenses will behave like concave lens, if
(a) f > fa (6) f, =f (c) f <f (d) f sf,
(iv) Two identical glass (, = 3/2) equiconvex lenses of focal length f are kept in contact. The
shape between the two lenses if filled with water (.. = 4/3).
The focal length of the combination is

(a) f (b) (c) (d) 4

Or
(iv) If two thin lenses are kept coaxially together, then their power is proportional to (R, and R,
being the radii of caused surfaces)
(a) R, + R, (6) RR, (c)
R+ R,
(d) None of these
30. Case study R+ R, RR,
Read the following paragraph and answer the questions that follow.
A semiconductor has same electron and hole concentration equals to 6 x 10°/m². On doping the
semiconductor with certain impurity, the electron concentration becomes 9 x 10/m'.
(i) Which of the following atoms are used as impurity material?
(a) Aluminium (b) Phosphorus (c) Carbon (d) Sodium
(ii) Identify the new semiconductor after doping.
(a) p-type (b) n-type
(c) Half-wave rectifier (d) Full-wave rectifier
(iiü) What is the new hole concentration?
(a) 0.4 x 10'/m (b) 14 x 10/m (c) 4 x 10/m (d) 40 x 10'/m
 (i) A square wave (-SV to + S V) is applicd to a p-n junction diode.
+5 V
A
o

0 R

-5 V Bo
Which of the following is the output waveform across the resistor R?
(a) 5 V (b) 10 V

(c)
(d)

-5 V

-10 V
Or
(i) The reading of the ammeter for a silicon diode in the given circuit is
200 2

(a) zero (b) 15 mA (c) 11.5 mA (d) 13.5 mA

SECTION - E
31. (a) A dielectric slab of thickness t is kept between the
plates of a
by a distance d. Derive an expression for the capacity of the parallel plate capacitor separated
(b) Find the effective capacity, the charge and the capacitor.
circuit below.
potential across each capacitor given in the

Or
(a) Find the potential energy of an electric dipole placed in a uniform
(b) In which orientation, a dipole placed in a electric field,
uniform electric field is in () stable (ii) unstable
equilibrium.
(c) An electric dipole with dipole moment 4 x 10Cm is
aligned at 30° withdirection of auniform
electric field of magnitude 5 x 10NCCalculate the magnitude of the torque acting on the dipole.
32. (a) Plot a graph showing the variation of current
densityj
of different materials. What information from this plot versus electric field E for two conductors
material can be obtained which may be used to select regarding the properties of the conducting
(i) standard resistance (ü) connecting wires in electric suitable materials for use in making
to be of the order of mm/s. Yet large circuits. Electron drift velocity is estimated
current of the order of a few amperes can be set up in
the wire. Explain briefly.
 (b) Two cells of emfs E, and E, and internal resistances r, and r, are connected in parallel. Obtain
the expression for the emf and internal resistance of a single equivalent cell that can replace
this combination?
Or

(a) A standard 50 w bulb in series with a room heater is connected across the mains. If the
50 W bulb is replaced by 100 W bulb, then how will the output of the heater change?
(b) In the given circuit, with steady current, calculate the potential drop across the capacitor and
the charge stored in it.
4V
A
22 F

4V 10 uF
B
H E

D
4 Q
8V
increasing linearly from its one end to the other, is
(c) A wire whose cross-sectional area is Current density, Electric current
connected across a battery of V volts. Out of Drift velocity,
in the wire?
and Electric field, which quantity remains constant
symmetric biconvex lens of radius of curvature R and made of glass of refractive index 1.5
33. (a) A a plane mirror as shown in the diagram. An
of
is placed on a layer of liquid placed on topaxis of the lens is moved along the axis until its
optical needle with its tip on the principal the lens
needle itself. The distance of the needle from
real, inverted image coincides with the distance
liquid layer and repeating the experiment, the
is measured to be x'. On removing the index of the liquid in terms of r
expression for the refractive
is found to be y. Obtain the
and y'.

Lens
Liquid
Plane mirror

Give its two applications.

(b) What is an optical fibre? Or
the light ray passing through a prism. Draw
deviation suffered by
total
(a) Find the expression for of angle of incidence. Derive an expression for the
deviation with the
a graph between angle prism.
refractiveindex of the material of the focal length 15 cm to obtain
should an object be placed from a convex lens of
(b) At what distance virtual), three times the size of the object?
images (both real and