1 - Entrance

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ISeries OSR I
55/3
Code No.
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Candidates must write the Code on the
title page of the answer-book.
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Please check that this questio n paper contai ns 15 printe d pages.
Code numbe r given on the right hand side of the questi on paper should
be
writte n on the title page of the answe r-book by the candid ate.
Please check that this questio n paper contai ns 30 questio ns.
Pleas e write down the Serial Numb er of the quest ion befor
e
attem pting it.
15 minute s time has been allotte d to read this questi on paper. The questi
on
paper will be distrib uted at 10.15 a.m. From 10.15 a.m. to 10.30 a.m., the
studen ts will read the questi on paper only and will not write any answe r
on
the answe r-book during this period.
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PHY SIC S (The ory)
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Time allowed : 3 hours
55/3
Maxim um Marks : 70
1
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(i)
(ii)
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8
c = 3 x 10 m/s
34
h = 6·63 x 10- Js
= 1·6 X 10-19 C
1
7
1-lo = 41t x 10- T mA-
e
1
- 4m; 0
ffie
= 9 X 109 N m 2 c-2
= 9·1 X 10-31 kg
Gen eral Inst ruct ions :
(i)
(ii)
(iii)
(iv)
5513
All ques tions are compulsory.
8 are very shor t answ er
There are 80 questions in total. Questions No. 1 to
type questions and carry one mar k each.
tions 19 to 27 carry
Questions No. 9 to 18 carry two mar ks each, ques
mar ks each.
thre e mar ks each and questions 28 to 80 carry five
htage is valu e base d
One of the questions carr ying three mar ks weig
question.
2
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(v)
There is no overall choice. However, an interna l choice has been provide d
in one question of two marks, one question of three marks and all three
questions of five marks each weightage. You have to attemp t only one of
the choices in such questions.
Use of calculators is not permitted. However, you may use log tables if
necessary.
(vi)
(vii)
You may use the following values of physica l constants wherever
necessary:
c = 3 x 108 m/s
h
= 6·63 x lo-34 Js
e = 1·6 X 10-19 C
!lo = 4n x 10_7 .T mA-1
1
- -= 9
4nE 0
X 109
N m 2 c-2
me= 9·1 X 10-3 1 kg
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A conduc ting loop is held below a current carryin g wire PQ as shown.
Predict the directio n of the induced current in the loop when the current
in the wire is constan tly increas ing.
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55/3
0
3
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2.
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The graph shows variation of stopping potential V0 versus frequency of
incident radiation v for two photosensitive metals A and B. Which of the
two metals has higher threshold frequency and why?
i
Metal B
Metal A
Stopping
potential
(Vo)
Frequency of incident
radiation (v) ｾ＠
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55/3
4
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Using the concept of force between two .infinitely long parallel current
carrying conductors, define one ampere of current.
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1
A biconcave lens made of a transparent material of refractive index 1·25
is immersed in water of refractive index 1·33. Will the lens behave as a
converging or a diverging lens ? Give reason.
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Why do the electric field lines never cross each other ?
1
6.
1
To which part of the electromagnetic spectrum does a wave of frequency
5 x 1011 Hz belong?
7.
1
Why is it found experimentally difficult to detect neutrinos in nuclear
13-decay?
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Why is the use of a.c. voltage preferred over d.c. voltage ? Give two
reasons.
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Considering the case of a parallel plate capacitor being charged, show
how one is required to generalize Ampere's circuital law to include the
term due to displacement current.
55/3
5
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of cros s-se ctio nal area 2·5 x 10- 7 m 2 carr
ying a curr ent of 2·7 A. Ass ume
the den sity of con duc tion elec tron s to be 9
x 1028 m-3 .
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A cell of emf 'E' and inte rnal resi stan ce 'r'
is con nect ed acro ss a vari able
resi stor 'R'. Plot a grap h show ing vari atio
n of term inal volt age 'V' of the
cell vers us the curr ent 'I'. Usi ng the plot
, show how the emf of the cell
and its inte rnal resi stan ce can be dete rmi
ned .
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A para llel plat e cap acit or of capa cita nce
Cis cha rged to a pote ntia l V. It
is then con nect ed to ano ther unc harg
ed cap acit or hav ing the sam e
capa cita nce. Fin d out the rati o of the
ene rgy stor ed in the com bine d
syst em to tha t stor ed init ially in the sing le
capa cito r.
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Using Rutherford model of the atom, derive the expression for the total
energy of the electron in hydrogen atom. What is the significance of total
negative energy possessed by the electron?
OR
Using Bohr's postulates of the atomic model, derive the expression for
radius of nth electron orbit. Hence obtain the expression for Bohr's
radius.
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Show diagrammatically the behaviour of magnetic field lines in the
presence of (i) paramagnetic and (ii) diamagnetic substances. How does
one explain this distinguishing feature ?
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2
Explain, with the help of a circuit diagram, the working of a p-n junction
diode as a half-wave rectifier.
16.
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55/3
7
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Two mono chrom atic rays of light are incide nt norma lly on the face
AB of
an isosceles right- angle d prism ABC. The refrac tive indice s of the
glass
prism for the two rays '1' and '2' are respec tively 1·38 and 1·52. Trace
the
path of these rays after enteri ng throu gh the prism .
A
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17.
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2
Draw a circui t diagr am of n-p-n transi stor ampli fier in CE config
uratio n.
Unde r what condi tion does the transi stor act as an ampli fier ?
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Write the functions of the following in comm unicat ion system s :
(i)
Receiver
(ii)
Demo dulato r
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A convex lens of focal length 20 em is placed coaxially with a
convex
mirro r of radius of curva ture 20 em. The two are kept 15 em apart
.A
point object is placed 40 em in front of the convex lens. Find the
positi on
of the image formed by this combination. Draw the ray diagra m
showi ng
the image forma tion.
t
55/3
3
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3
An electron microscope uses electrons accelerated by a voltage of 50 kV.
Determine the de-Broglie wavelength associated with the electrons.
Taking other factors, such as numerical aperture etc. to be same, how
does the resolving power of an electron microscope compare with that of
an optical microscope which uses yellow light ?
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Write
any
two
distinguishing
features
between
conductors,
semiconductors and insulators on the basis of energy band diagrams.
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3
Write two basic modes of communication. Explain the process of
amplitude modulation. Draw a schematic sketch showing how amplitude
modulated signal is obtained by superposing a modulating signal over a
sinusoidal carrier wave.
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W hy ar e th e co nn ec tio
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(b)
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V is
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ac t is in th e mi dd le of th
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For the past some time, Aarti had been observing some erratic body
movement , unsteadin ess and lack of coordinati on in the activities of her
sister Radha, who also used to complain of severe headache occasionally.
Aarti suggested to her parents to get a medical check-up of Radha. The
doctor thoroughl y examined Radha and diagnosed that she has a brain
tumour.
25.
What, according to you, are the values displayed by Aarti?
(b)
How can radioisoto pes help a doctor to diagnose brain tumour?
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A rod of length l is moved horizontal ly with a uniform velocity 'v' in
a direction perpendic ular to its length through a region in which a
uniform magnetic field is acting vertically downward . Derive the
expression for the emf induced across the ends of the rod.
How does one understan d this motional emf by invoking the
Lorentz force acting on the free charge carriers of the conductor ?
Explain.
11
P.T.O.
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(b)
In Young's double slit experiment, describe briefly how bright and
dark fringes are obtained on the screen kept in front of a double
slit. Hence obtain the expression for the fringe width.
The ratio of the intensities at minima to the maxima in the
Young's double slit experiment is 9 : 25. Find the ratio of the
widths of the two slits.
( )
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OR
29.
(a)
Describe briefly how a diffraction pattern is obtained on a screen
due to a single narrow slit illuminated by a monochromatic source
of light. Hence obtain the conditions for the angular width of
secondary maxima and secondary minima.
(b)
Two wavelengths of sodium light of 590 nm and 596 nm are used
in turn to study the diffraction taking place at a single slit of
aperture 2 x 10- 6 m. The distance between the slit and the screen
is 1·5 m. Calculate the separation between the positions of first
maxima of the diffraction pattern obtained in the two cases.
(a)
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(a)
Deduce an express ion for the frequency of revolut ion of a charged
particle in a magnet ic field and show that it is indepen dent of
velocity or energy of the particle .
(b)
Draw a schema tic sketch of a cyclotron. Explain, giving the
essenti al details of its constru ction, how it is used to acceler ate the
charged particle s.
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OR
(a)
Draw a labelled diagram of a moving coil galvano meter. Describ e
briefly its princip le and working.
(b)
Answer the following :
(i)
Why is it necessa ry to introdu ce a cylindr ical soft iron core
inside the coil of a galvano meter ?
(ii)
Increas ing the current sensitiv ity of a galvano meter may not
necessa rily increas e its voltage sensitiv ity. Explain, giving
reason.
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Draw a labelled diagram of Van de Graaff generator. State its working
principle to show how by introducin g a small charged sphere into a larger
sphere, a large amount of charge can be transferre d to the outer sphere.
State the use of this machine and also point out its limitation s.
OR
(a)
Deduce the expression for the torque acting on a dipole of dipole
moment
(b)
55/3
p in the presence of a uniform electric field "Ef .
Consider two hollow concentric spheres, S1 and S2, enclosing
charges 2Q and 4Q respectively as shown in the figure. (i) Find out
the ratio of the electric flux through them. (ii) How will the electric
flux through the sphere sl change if a medium of dielectric
constant 'Er' is introduced in the space inside S1 in place of air ?
Deduce the necessary expression.
4Q
15
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