physics and maths 12th
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Numerical Questions (1 marks)
1. The output of an OR gate is connected to both the inputs of a NAND gate. Draw the logic
circuit of this combination of gates and write its truth table.
2. A convex lens of refractive index 1.5 has a focal length of 18 cm in air. Calculate the
change in its focal length when it is immersed in water of refractive index 1.33.
3. Two point charges and are separated by a distance of 1 m in air. Calculate at what point
on the line joining the two charges is the electric potential zero.
4. A voltage of 30 V is applied across a carbon resistor with first, second and third rings of
blue, black and yellow colours respectively. Calculate the value of current, in mA, through
the resistor.
5. Calculate the current drawn by the primary of a transformer which steps down 200 V to
20 V to operate a device of resistance. Assume the efficiency of the transformer to be
80%.
6. An a.c. voltage of 100 V, 50 Hz is connected across a 20 ohm resistor and mH inductor in
series. Calculate
i. impedance of the circuit,
ii. rms current in the circuit
7. In an ammeter (consisting of a galvanometer and a shunt), 0.5% of the main current
passes through the galvanometer. Resistance of the galvanometer coil is G. Calculate
the resistance of the shunt in terms of galvanometer resistance, G.
8. An electric bulb B and a parallel plate capacitor C are connected in series to the
a.c. mains as shown in the given figure. The bulb glows with some brightness. How will
the glow of the bulb be affected on introducing a dielectric slab between the plates of the
capacitor? Give reasons in support of your answer.
9. The output of a 2-input NOR gate is fed to a NOT gate. Draw the logic circuit of this
combination of gates and write the truth table for the output of the combination for all
inputs.
10. The electric field and electric potential at any point due to a point charge kept in air is 20
N/C and 10 J/C respectively. Compute the magnitude of this charge.
11. Draw and explain the output waveform across the load resistor R, if the input waveform is
as shown in the given figure.
12.
13. Two cells E1 and E2 in the given circuit diagram have an emf of 5 V and 9 V and internal
resistance of 0.3Ω and 1.2Ω respectively.
14. Calculate the value of current flowing through
the resistance of 3Ω.
15. Two capacitors of capacitance of 6µF and 12µF are connected in series with a battery.
The voltage across the 6µF capacitor is 2 V. Compute the total battery voltage.
16. A parallel plate capacitor with air between the plates has a capacitance of 8 pF. The
separation between the pates is now reduced by half and the space between them is
filled with a medium of dielectric constant 5. Calculate the value of capacitance of the
capacitor in the second case.
17. A 4µF capacitor is charged by a 200 V supply. The supply is then disconnected and the
charged capacitor is connected to another uncharged 2 µF capacitor. How much
electrostatic energy of the first capacitor is lost in the process of attaining the steady
situation?
18. Find the wavelength of electromagnetic waves of frequency 5 x 1019 Hz in free space.
19. A compound microscope with an objective of 1.0 cm focal length and an eye-piece of 2.0
cm focal length has a tube length of 20 cm. Calculate the magnifying power of the
microscope, if the final image is formed at the near point of the eye.
20. The magnifying power of an astronomical telescope in the normal adjustment position is
100. The distance between the objective and the eye-piece is 101 cm. Calculate the focal
lengths of the objective and of the eye-piece.
21. An electric dipole of length 4 cm, when placed with its axis making an angle of 600 with a
uniform electric field experiences a torque 4√3 Nm. Calculate the
i. magnitude of the electric field.
ii. potential energy of the dipole, if the dipole has charges of ±8nC.
22. ATV tower has a height of 400 m at a given place. Calculate coverage range, if the radius
of the earth is 6400 km.
23. Give the logic symbol for an OR gate. Draw the output wave form for input wave forms A
and B for this gate.
24. In the figure below, circuit symbol of a logic gate and input wave from is shown.
i. Name the logic gate,
ii. write its truth table and
iii. give the output wave form.
25. Two point charges qA= +3µc and qB= -3µc are located 20 cm apart in vacuum,
i. Find the electric field at the mid -point of the line AB joining the two charges,
ii. If a negative test charge of magnitude 1.5×10-9 C is placed at the centre, find the
force experienced by the test charge.
26. Name the gate obtained from the combination of gates shown in the figure. Draw its logic
symbol. Write the truth table of the combination.
27. Draw a circuit diagram for use of NPN transistor as an amplifier in common emitter
configuration. The input resistance of a transistor is1000Ω. On changing its base current
by 10µA, the collector current increases by 2 m A. If a load resistance of 5 kΩ is used in
the circuit, calculate:
i. the current gain
ii. voltage gain of the amplifier.
28. When an inductor L and a resistor R in series are connected across a 12 V, 50Hz supply,
a current of 0.5 A flows in the circuit. The current differs in phase from applied voltage by
π/3 radian. Calculate the value of R.
29. Two cells of emf 1.5 V and 2 V and internal resistance 1 ohm and 2 ohm respectively are
connected in parallel to pass a current in the same direction through an external
resistance of 5 ohm.
i. Draw the circuit diagram.
ii. Using Kirchhoff's laws, calculate the current through each branch of the circuit
and potential difference across the 5 ohm resistor.
30. A galvanometer with a coil of resistance 120 ohm shows full scale deflection for a current
of 2.5 mA. How will you convert the galvanometer into an ammeter of range 0 to 7.5 A?
Determine the net resistance of the ammeter. When an ammeter is put in a circuit, does it
read slightly less or more than the actual current in the original circuit? Justify your
answer.
31. Explain, with the help of a circuit diagram, how the thickness of depletion layer in a p-n
junction diode changes when it is forward biased. In the following circuits which one of
the two diodes is forward biased and which is reverse biased?
32. In a series R - C circuit, R= 30Ω, C= 0.25µF, V= 100 V and ω= 100 rad/second. Find the
current in the circuit and calculate the voltage across the resistor and the capacitor.
Is the algebraic sum of these voltages more than the source voltage? If yes, resolve the
paradox.
33. In a double slit experiment with monochromatic light, fringes are obtained on a screen
placed at some distance from the slits. If the screen is moved by 5 x 10-2 m towards the
slits, the change in fringe width is 3x 10-5 m. If the distance between slits is 10-3 m,
calculate the wavelength of light used.
34. Six resistors, each of value 4Ω are joined together in a circuit as shown in the figure.
Calculate equivalent resistance across the points A and B. If a cell of emf 2V is
connected across AB, compute the current through the arms AB and DF of the circuit.
35. The horizontal component of the earth's magnetic field at a given place is 0.4×10-
2 Wb/m2 and angle of dip is 300. Calculate the value of
i. vertical component,
ii. the total intensity if the earth's magnetic field.
36. Calculate the temperature at which the resistance of a conductor becomes 20% more
than its resistance at 270C. The value of the temperature coefficient of resistance of the
conductor is 2.0×10-2 /k.
37. A 8Ω resistance wire is bent at the middle by 1800. Both the halves are twisted together.
What is the new resistance?
38. A galvanometer with a coil of resistance 12Ω shows the full scale deflection for a current
of 2.5 mA. How will you convert the galvanometer into
i. an ammeter of range 0 to 7.5A,
ii. voltmeter of range 0 to 10 v?
39. In a young’s double slit experiment, the slit are separated by 0.28 mm and the screen is
placed 1.4m away. The distance between the central bright fringe and the fourth bright
fringe is measured to be 1.2 cm. Determine the wavelength of light used in the
experiment.
40. A 25 µF capacitor, a 0.10 henry inductor and a 25 ohm resistor are connected in series
with an a.c. source, whose emf is given by E= 310 sin314t volts
a. What is frequency of the emf?
b. What is impedance of the circuit?
c. What is the phase angle of the current by which it leads or lags the applied
e.m.f?
d. what is expression for the instantaneous value of current in the circuit?
e. construct a phase diagram for these voltages.
41. What is the De Broglie wavelength associated with
a. an electron moving with a speed of 5.4×106 m/s, and
b. a ball of mass 150g travelling at 30.0 m/s?
42. The half-life of 92U238 undergoing α- decay is 4.5×109 years. What is the activity of 1g
sample of 92U238 ?
43. A regular hexagon of side 10 cm has a charge 5µc at each of its vertices. Calculate the
potential at the centre of the hexagon.
44. Double convex lenses are to be manufactured from a glass of refractive index 1.55 with
both faces of the same radius of curvature. What is the radius of curvature required if the
focal length is to be 20 cm?
45. Three capacitors of capacitance 2pF, 3pF and 4pF are connected in parallel.
a. What is the total capacitance of the combination?
b. Determine the charge on each capacitor if the combination is connected to a
100V supply.
46. What is the focal length of a convex lens of focal length 30 cm in contact with a concave
lens of focal length 20 cm? Is the system a converging or a diverging lens?
47. Fig. shows a light bulb (B) and iron cored inductor connected to a DC battery through a
switch (S).
i. What will one observe when switch (S) is closed?
ii. How will the glow of the bulb change when the battery is replaced by an ac
source of rms voltage equal to the voltage of DC battery? Justify your answer in
each case.
42. The given figure shows the experimental set up of a metre bridge. The null point is found
to be 60cm away from the end A with X and Y in position as shown.
When a resistance of 15Ω is connected in series with ‘Y’, the null point is found to shift by
10cm towards the end A of the wire. Find the position of null point if a resistance of 30Ω
were connected in parallel with ‘Y’.
43. Why is a potentiometer preferred over a voltmeter for determining the emf of a cell? Two
cells of emf E1 and E2 are connected together in two ways shown here.
The 'balance points' in a given potentiometer experiment for these two combinations of
cells are found to be at 351.0cm and 70.2cm respectively. Calculate the ratio of the emfs
of the two cells
SHORT TYPE QUESTIONS -02 MARKS
1.
Name the reaction which takes place when a slow neutron beam strikes 92U235 nuclei.
Write the nuclear reaction involved.
2. Define the terms 'Magnetic Dip' and 'Magnetic Declination' with the help of relevant
diagrams.
3. Define 'electric line of force' and give its important properties.
4. State the condition under which the phenomenon of resonance occurs in a series LCR
circuit. Plot a graph showing variation of current with frequency of a.c. source in a series
LCR circuit.
5. How does the resistivity of
i. a conductor and
ii. a semiconductor vary with temperature? Give reason for each case.
6. Explain how the width of depletion layer in a p-n junction diode changes when the
junction is
i. forward biased
ii. reverse biased.
7. Define resolving power of a compound microscope. How does the resolving power of a
compound microscope change when
i. refractive index of the medium between the object and objective lens increases?
ii. Wavelength of the radiation used is increased?
8. Write the relation for the force acting on a charge carrier q moving with a velocity through
a magnetic field in vector notation. Using this relation, deduce the conditions under which
this force will be
i. maximum
ii. minimum.
9. You are given ‘a’ resistors, each of resistance ‘r’. These are first connected to get
minimum possible resistance. In the second case, these are again connected differently
to get maximum possible resistance. Compute the ratio between the minimum and
maximum values of resistance so obtained.
10. Draw a circuit diagram using a metre bridge and write the necessary mathematical
relation used to determine the value of an unknown resistance. Why cannot such an
arrangement be used for measuring very low resistances?
11. What does the term LOS communication mean? Name the types of waves that are used
for this communication. Which of the two-height of transmitting antenna and height of
receiving antenna can affect the range over which this mode of communication remains
effective?
12. Draw a ray diagram to show the refraction of light through a glass prism. Hence obtain
the relation for the angle of deviation in terms of the angle of incidence, angle of
emergence and the angle of the prism.
13. We do not choose to transmit an audio signal by just directly converting it to an e.m.
wave of the same frequency. Give two reasons for the same.
14. State Bohr’s postulate for the ‘permitted orbits’ for the electron in a hydrogen atom. Use
this postulate to prove that the circumference of the nth permitted orbit for the electron
can ‘contain’ exactly n wave lengths of the de Broglie wavelength associated with the
electron in that orbit.
15. What is photoelectric effect? Drive Einstein’s photoelectric equation.
16. Explain the essential difference between interference and diffraction.
17. What is the basic difference between the atom or molecule of a diamagnetic and a
paramagnetic material? Why are elements with even atomic number more likely to be
diamagnetic?
Short Type Questions (3 marks)
1. (a) Draw a labelled ray diagram to show the formation of an image by a compound
microscope. Write the expression for its magnifying power. (b) How does the resolving
power of a compound microscope change, when (i) refractive index of the medium
between the object and the objective lens increases; and (ii) wavelength of the radiation
used is increased?
2. Which two main considerations are kept in mind while designing the ‘objective’ of an
astronomical telescope? Obtain an expression for the angular magnifying power and the
length of the tube of an astronomical telescope in its (a) normal adjustment’ position.
3. Give the principle of working of a Van de Graff generator. With the help of a labelled
diagram, describe its construction and working. How is the leakage of charge minimised
from the generator?
4. Define the term 'resolving power' of an astronomical telescope. How does it get affected
on
a. increasing the aperture of the objective lens?
b. Increasing the wavelength of the light used? Justify your answer in each case.
5. State the principle of potentiometer. Draw a circuit diagram used to compare the e.m.f. of
two primary cells. Write the formula used. How can the sensitivity of a potentiometer be
increased?
6. What is meant by 'drift velocity of free electrons'? Derive Ohm's law on the basis of the
theory of electron.
7. Explain, with the help of a schematic diagram, the principle and working of a Light
Emitting Diode. What criterion is kept in mind while choosing the semiconductor material
for such a device? Write any two advantages of Light Emitting Diode over conventional
incandescent lamps.
8. Write any four characteristics of electromagnetic waves. Give two uses each of
a. Radio-waves
b. Micro-waves.
9. State the laws of radioactive decay. Establish a mathematical relation between half-life
period and disintegration constant of a radioactive nucleus.
10. How is the mutual inductance of a pair of coils affected when
a. separation between the coils is increased?
b. the number of turns of each coil is increased ?
c. a thin iron sheet is placed between the two coils, other factors remaining the
same? Explain your answer in each case.
11. What are eddy currents. How are these produced? In what sense are eddy currents
considered undesirable in a transformer and how are these reduced in such a device?
12. On the basis of the energy band diagrams distinguish between metals, insulators and
semiconductors.
13. An electric dipole is held in a uniform electric field. (a) Using suitable diagram, show that
it does not undergo any translatory motion and (ii) derive an expression for the torque
acting on it and specify its direction.
14. What is Wheatstone bridge? Deduce the condition for which Wheatstone bridge is
balanced.
15. A uniform magnetic field gets modified as shown below, when two specimens X and Y
are placed in it.
16. Identify the two specimens X and Y (b) State the reason for the behaviour of the field
lines in X and Y.
17. A pure inductor is connected across an a.c. source. Show mathematically that the
current in it lags behind the applied emf by a phase angle of π/2. What is its inductive
reactance? Draw a graph showing the variation of inductive reactance with the frequency
of the a.c. source.
18. Distinguish between analogue and digital communication. Write any two modulation
techniques employed for the digital data. Describe briefly any one of the techniques used.
19. Define the terms threshold frequency and stopping potential in relation to the
phenomenon of photoelectric effect. How is the photoelectric current affected on
increasing the
i. frequency
ii. intensity of the incident radiations and why?
2. Draw a schematic diagram of a single optical fibre structure. On what principle does such
a device work? Explain the mechanism of propagation of light signal through an optical
fibre.
3. (a) Draw the block diagram of a communication system. (b) What is meant by ‘detection’
of a modulated carrier wave? Describe briefly the essential steps for detection.
4. Give reasons for the following :
a. Astronomers prefer to use telescopes with large objective diameters to observe
astronomical objects.
b. Two identical but independent monochromatic sources of light cannot be coherent.
c. The value of the Brewster angle for a transparent medium is different for lights of different
colours.
Long Type Questions (5 marks)
1. Define electric field intensity at a point. Derive an expression for the electric field intensity
at a point on the axial line of a short dipole.
2. Show that the potential on the equatorial line of an electric dipole is zero
3. What is an electric dipole? Derive an expression for the torque acting on an electric
dipole, when held in a uniform electric field. Hence, define the dipole moment.
4. State Gauss theorem in electrostatics. Using this theorem, derive an expression for the
electric field intensity due to an infinite plane sheet of charge of charge density σ
5. Show mathematically that for any point out side the shell, the field due to a uniformly
charged thin spherical shell is the same as if the entire charge of the shell is concentrated
at the centre.
6. Apply gauss theorem to find electric field intensity at a point due to an infinitely long thin,
uniformly charged straight wire.
7. Define the capacitance of a capacitor. Give its S.I unit for a parallel plate capacitor, prove
that the total energy stored in a capacitor is ½ cv2 and hence derive expression for the
energy density of the capacitor.
8. Derive an expression for the capacitance of a parallel plate capacitor when the space
between the plates is partially filled with a dielectric medium of dielectric constant k.
9. Obtain the equivalent capacitance of the network in figure shown below. For a 300V
supply determine the charge and voltage across each capacitor.
10. Give the principle of working of a Van –De – Graff generator. With the help of a labeled
diagram describe its construction and working. How is the leakage of charge minimized
from the generator?
11. Establish a relation between drift velocity of an electron in a conductor of cross section A
carrying current I and concentration ‘n’ of free electrons per unit volume of conductor.
12. Define the term resistivity and write its S.I unit. Derive the expressions for
i. resistance
ii. the resistivity of a conductor in terms of number density of free electrons and
relaxation time.
13. Draw a circuit diagram for a meter bridge two determine the unknown resistance of a
resistor why are the connections between the resistors of a meter bridge made of thick
copper strips? Find the shift in the balance point of a meter bridge, when the two resistors
in the two gaps are interchanged.
14. With the help of a circuit diagram explain how the internal resistance of a cell can be
determine by using a potentiometer? Write the formula used?
15. Show graphically the variation of resistivity with temperature for
i. Metals
ii. alloys
iii. semi conductors
iv. non conductor (carbon)
16. Why is potentiometer preferred over voltmeter to measure the emf of a cell? The
potentiometer wire AB shown in the fig. is 400 cm long. Where should the free end of a
galvanometer be connected so that the galvanometer shows zero deflection.
17. Derive the relation between the focal length of a convex lens in terms of the radii of
curvature of the two surfaces and refractive index of its material. A convex lens of focal
length 40 cm and a concave lens of focal length 25 cm are kept in contact with each
other. What is the value of power of this combination?
18. State the essential condition for diffraction of light to take place. Use Huygen's principle to
explain diffraction of light due to a narrow single slit and the formation of a pattern of
fringes obtained on the screen. Sketch the pattern of fringes formed due to diffraction at a
single slit showing variation of intensity with angle.
19. State Huygens’ principle. Using the geometrical construction of secondary wavelets,
explain the refraction of a plane wave front incident at a plane surface. Hence verify laws
of reflection and refraction.
20. With the help of a ray diagram, show the formation of image of a point object by refraction
of light at a spherical surface separating two media of refractive indices n1 and n2 (n2 > n1)
respectively. Using this diagram, derive the relation.
What happens to the focal length of convex lens when it is immersed in water?
21. Define the term dipole moment of an electric dipole indicating its direction. Write its SI
unit. An electric dipole is placed in a uniform electric field, Deduce the expression for the
torque acting on it. In a particular situation, it has its dipole moment aligned with the
electric field. Is the equilibrium stable or unstable?
22. Obtain the expression for the capacitance of a parallel plate capacitor. Three capacitors
of capacitances C1 , C2 and C3are connected
i. in series,
ii. in parallel. Show that the energy stored in the series combination is the same as
that in the parallel combination.
23. Define the term magnetic inclination (Dip) and horizontal component of earth’s magnetic
field at a place. Establish the relationship between them with the help of a diagram.
24. Distinguish the magnetic properties of dia, para, and ferromagnetic substances in terms
of
i. susceptibility
ii. magnetic permeability
iii. coercivity. Give one example of each.
25. Derive a mathematical expression for the force per unit length experienced by each of the
two long current carrying conductors placed parallel to each other in air. Hence define
one ampere of current. Explain why two parallel straightconductors carrying current in the
opposite direction kept near each other in air repel?
26. With the help of a neat and labelled diagram, explain the underlying principle and working
of a moving coil galvanometer. What is the function of:
i. uniform radial field
ii. soft iron core, in such a device? Write two factors on which the current sensitivity
of a moving coil galvanometer depend.
27. Draw a neat and labelled diagram of a cyclotron. State the underlying principle and
explain how a positively charged particle gets accelerated in this machine. Show
mathematically that the cyclotron frequency does not depend upon the speed of the
particle.
28. State the Biot - Savart law for the magnetic field due to a current carrying element. Use
this law, obtain a formula for magnetic field
a. at the centre of a circular loop of radius R carrying a steady current I. Sketch the
magnetic field lines for a current loop clearly indicating the direction of the field. OR
b. derive the expression for the magnetic field due to a current carrying circular loop of
radius 'R', at a point which is at a distance 'x' from its centre along the axis of the loop.
2. Derive an expression for the torque acting on a loop of N turns, area A, carrying current i,
when held in a uniform magnetic field. With the help of circuit, show how a moving coil
galvanometer can be converted into an ammeter of given range. Write the necessary
mathematical formula.
3. Derive the expression for the de Broglie wavelength of an electron moving under a
potential difference of V volt. Describe Davisson and Germer experiment to establish the
wave nature of electrons. Draw a labelled diagram of the apparatus used.
4. State the principle of working of p-n diode as a rectifier. Explain, with the help of a circuit
diagram, the use of p-n diode as
a. a full wave rectifier
b. Half wave rectifier. Draw a sketch of the input and output waveforms.
5. State Bohr’s postulates for an atom? Calculate energy of moving electron for nth orbit?
What is the significance of negative energy?
6. State Gauss’ theorem in electrostatics. Using this theorem, derive the expression for the
electric field intensity
a. at any point outside a uniformly charged thin spherical shell
b. at a point due to an infinitely long, thin, uniformly charged straight wire
c. at a point due to an infinite plane sheet of charge.
7. What is a phasor diagram? With its help, drive an expression for the impedance of an ac
series L-c-R circuit. In series LCR circuit, voltage across an inductor, a capacitor and a
resistor are 30v, 30v and 60v respectively. What is the phase difference between the
applied voltage and current in the circuit.
1. Name the device which works under the principle of velocity selector?
2. Define 1 Ampere the unit of a.c current and how does it vary from d.c current?
3. Is the magnitude of displacement current less, equal or greater than the conduction
current?explain
4. a)Why secondary rainbow is fainter than the primary rainbow? b) why clouds are
appearing white?
5. In a wave picture of light, the intensity of light is determined by square of amplitude of
wav e. What determines the intensity of light in photon picture of light?
6. The maximum K.E of emitted photo electron is 15eV. Find its stopping potential.
7. Draw a graph to show the variation of impact parameter (in alpha particle scattering)with
scattering angle Ѳ.
8. Name a communication channel which can offer a transmission bandwidth in excess of
100 GHZ.
9. If accelerating voltage of anode is doubled what will be the change in De Broglie’s wave
length of electron?
10. Waves from which portion of EM spectrum are utilized to identify defects in crystals. Write
the frequency rangecorresponding to this zone
11. Why does the electric field inside a dielectric decrease when it is placed in an external
electric field?
12. Draw the symbol and write truth table of NOR gate.?
13. A wire is stretched to double its length. What will be the effect on its resistivity ?
14. Two thin lenses of power +7D and -3D are in contact. What is the focal length of the
combination ?
15. The radii of curvature of the faces of a double convex lens are 10 cm and 15 cm. If focal
length is 12 cm, what is the refractive index of glass ?
16. What is the distance of closest approach when a 5.0 MeV proton approaches a gold
nucleus?
17. It is observed that only 6.25% of a given radioactive sample is left undecayed after a
period of 16 days. What is the decay constant of this sample, in day-1 ?
18. For a transistor connected in common emitter mode, the voltage drop across the collector
is 2 V and β is 50. Find the base current, if RC is 2 K
19. State the reason , why GaAs is most commonly used in making of a solar cell.
20. A square wave is applied to p-n junction diode as shown in the figure. Draw the output
waveform.
21. A diode is connected to 220 V (r.m.s.) a.c. in series with a capacitor, as shown in the
figure. What is the voltage V across the
capacitor ?
22. An electron, an alpha-particle and a proton have the same kinetic energy. Which one of
these particles has the largest d- Broglie wavelength.
23. Write an expression for resistivity of a metallic conductor showing its variation over a
limited range of temperature.
24. Magnetic field lines can be entirely confined with in the core of a toroid, but not with in
a straight solenoid why?
25. How much average power dissipates, over a complete cycle of an A.C. source supply
when connected to a capacitor?
26. A glass lens of refractive index 1.45 disappears when immerse in a liquid. What is the
value of refractive index of the liquid?
27. The radioactive isotope D decays according to the sequence
D........DECAY.........D1..........ἁ DECAY............D2 If the mass number and atomic number
of D2 are 176 and 71 respectively, what is the
i. mass number and
ii. atomic number of D
28.
Two lines A and B in the plot given below show
the variation of de Broglie wavelength, λ versus
1/√v, where V is accelerating potential
difference, for the two particles carrying the
same charge. Which one of two represent a particle of smaller mass?
29. Two nuclei have mass number in the ratio 1: 2 what is the ratio of their nuclear densities?
30. An electron moving through a magnetic field does not experiences a force. Under what
condition is this possible?
31. The instantaneous value of voltage from an a.c. Source is given by E=300 Sin 314t. What
is the r.m.s. voltage of the source?
32. A bulb and a capacitor are connected in series to an a.c. source of variable frequency.
How will the brightness of the bulb change on increasing the frequency of the a.c. source.
33. Name the part of electromagnetic spectrum that has largest penetrating power.
34. When light undergoes refraction. What happens to its frequency.
35. In the given diagram, is the diode D forward or reversed
biased?
36. Write the truth table for the gate shown below.
37. Two point charges 4µc and —2µc are separated by a distance of 1m in air. At what point
on the line joining the two charges is the electric potential is zero.
38. Four resistors of resistance each of 10Ω is connected as given below.
Calculate the equivalent resistance between points X and Y
39. Explain how the width of depletion layer in a p-n junction diode changes when the
junction is
i. forward biased
ii. reverse biased.
40. How does the resistivity of
i. a conductor and
ii. a semiconductor vary with temperature? Give reason for each case.
41. An alternating voltage of frequency f is applied across a series LCR circuit. Let fr be the
resonance frequency for the circuit. Will the current in the circuit lag, lead or remain in
phase with the applied voltage when
i.
ii. Explain your answer in each case.
42. Define 'electric line of force' and give its two important properties.
43. Define the terms 'Magnetic Dip' and 'Magnetic Declination' with the help of relevant
diagrams.
44. Find the wavelength of electromagnetic waves of frequency 5 x 1019Hz in free space.
Give its two applications.
45. What is an 'analog signal' and a 'digital signal'? How can an analog signal be converted
into & digital signal?
46. A T.V. tower has a height of 400 m at a given place. Calculate as coverage range, if the
radius of the earth is 6400 km.
47. With the help of a diagram, show the biasing of a light emitting diode (LED). Give its two
advantages over conventional incandescent lamps.
48. An a.c. voltage of 100 V, 50 Hz is connected across a 20 ohm resistor and 2mH inductor
in series. Calculate
i. impedance of the circuit,
ii. rms current in the circuit.
49. A galvanometer has a resistance of It gives full scale deflection with a current of 2 mA.
Calculate the value of the resistance needed to convert it into an ammeter of range 0-0.3
A.
50. The output of an OR gate is connected to both the inputs of a NAND gate. Draw the logic
circuit of this combination of getes and write its truth table.
51. Two point charges and are separated by a distance of 1 m in air. Calculate at what point
on the line joining the two charges is the electric potential zero.
52. The output of a 2-input NOR gate is fed to a NOT gate. Draw the logic circuit of this
combination of gates and write the truth table for the output of the combination for all
inputs.
53. Write any four characteristics of electromagnetic waves. Give two uses each of
a. Radio-waves
b. Micro-waves
42. Explain with the help of a labelled diagram the underlying principle and working of a step-
up transformer. Why cannot such a device be used to step-up d.c. voltage ?
43. State the laws of radioactive decay. Establish a mathematical relation between half-life
period and disintegration constant of a radioactive nucleus.
44. How is the mutual inductance of a pair of coils affected when
a. separation between the coils is increased?
b. the number of turns of each coil is increased ?
c. a thin iron sheet is placed between the two coils, other factors remaining the same?
Explain your answer in each case.
45. Define the terms threshold frequency and stopping potential in relation to the
phenomenon of photoelectric effect. How is the photoelectric current affected on
increasing the
i. frequency
ii. intensity of the incident radiations and why?
42. State Gauss' theorem. Apply this theorem to obtain the expression for the electric field
intensity at a point due to an infinitely long, thin, uniformly charged straight wire and at
any point outside a uniformly charged thin spherical shell.
43. Explain
i. forward biasing,
ii. reverse biasing of a P-N junction diode. With the help of a circuit diagram, explain the use
of this device as a half - wave rectifier.
44. Define self-inductance and give its S. I . unit. Derive an expression for self- inductance of
a long, air-cored solenoid of length l, radius r, and having N number of turns.
61. Draw a labelled ray diagram to show the formation of an image by a compound
microscope. Write the expression for itsmagnifying power. How does the resolving power
of a compound microscope change, when
i. refractive index of the medium between the object and the objective lens
increases; and
ii. wavelength of the radiation used is increased?
62. An electric dipole is held in a uniform electric field.
i. Using suitable diagram, show that it does not undergo any translatory motion and
ii. derive an expression for the torque acting on it and specify its direction.
63. Draw a graph to show the variation of the angle of deviation 'D' with that of the angle of
incidence 'i' for a monochromatic ray of light passing through a glass prism of refracting
angle 'A'. Hence deduce the relation.
64. Two long parallel straight wires X and Y separated by a distance of 5 cm in air carry
currents of 10 A and 5 A respectively in opposite directions. Calculate the magnitude and
direction of the force on a 20 cm length of the wire Y. A circ
65. circular coil of100 turns, radius 10 cm carries a current of 5 A. it is suspended vertically in
a uniform horizontal magnetic field of 0.5 T, the field lines making an angle of 600 with
the of the plane of the coil. Calculate of the torque must be applied on it to prevent it from
turning.
66. Two point charges are located 20 cm apart in vacuum,
i. Find the electric field at the mid point of the line AB joining the two charges,
ii. If a negative test charge of magnitude 1.5 x10-9c is placed at the centre, find the
force experienced by the test charge.
67. In a given circuit, inductor L and resistor R have identical resistance. Two similar electric
lamps B1 and B2 are connected as shown. When switch S is closed,
i. which one of the lamps lights up earlier,
ii. will the lamps be equally bright after some time? Justify your answer.
68. Write the mathematical relation for the resistivity of a material in terms of relaxation time,
number density and mass and charge of charge carriers in it. Explain, using this relation,
why the resistivity of a metal increases and that of a semi-conductor decreases with rise
in temperature.
69. Name the gate obtained from the combination of gates shown in the figure. Draw its logic
symbol. Write the truth table of the combination.
70. Force of attraction between two point charges placed at a distance ‘d’ apart in a medium
is ‘F’. What should be the distance in the same medium so that the force of attraction
between them becomes 9F ?
71. Two bulbs whose resistances are in the ratio of 1 : 2, are connected in parallel to a
source of constant voltage. What will be the ratio of power dissipation in these?
72. Write two properties of a material used as a suspension wire in a moving coil
galvanometer.
73. A plane electromagnetic wave of frequency 25 MHz travels in free space along the x-
direction. At a particular point in space and time the electric vector is .
Calculate at this point.
74. Define the term ‘activity’ of a radionuclide. Write its SI unit.
75. At what angle of incidence should a light beam strike a glass slab of refractive - index √3 ,
such that the reflected and the refracted rays are perpendicular to each other ?
76. A carrier wave of peak voltage 12 V is used to transmit a message signal. What should
be the peak voltage of the modulating signal in order to have a modulation index of 75
%?
77. Which mode of propagation is used by short wave broadcast services having frequency
range from a few MHz up to 30 MHz?
78. Derive an expression for the energy stored in a charged parallel plate capacitor with air
as the medium between its plates.
79. A bar magnet of magnetic moment 1.5 J/T lies aligned with the direction of a uniform
magnetic field of 0.22 T.
80. What is the amount of work required by an external torque to turn the magnet so as to
align its magnetic moment,normal to the field direction, & Opposite to the field direction?
81. Define self – inductance and give its S.I. unit.
82. Derive an expression for self inductance of a long, air-cored solenoid of length l, radius r
and having N number of turns.
83. Name the radiations of electromagnetic spectrum which are used in
i. Warfare to look through fog.
ii. Radar and geostationary satellites.
iii. Studying the structure and properties of atoms and molecules.
iv. To photograph internal parts of a human body.
84. The work function of cesium metal is 2 .14 eV. When light of frequency 6 x 10 14 Hz is
incident on the metal surface, photoemission of electrons occurs. What is theMaximum
kinetic energy of the emitted electrons.
85. An electron beam projected along +X axis, experiences a force due to a magnetic field
along the + Y- axis. What is the direction of the magnetic field?
86. The instantaneous current from an ac source is I = 6 sin 314t. What is the rms value of
the current?
87. A bulb connected in series with a solenoid is lit by ac source. If a soft iron core is
introduced in the solenoid, will the bulb glow brighter?
88. Which part of the electromagnetic spectrum is used in operating RADAR? Give its
wavelength range.
89. Two thin lenses + 6D and -2D are in contact. What is the focal length of the combination?
90. The ionization potential of hydrogen is 13.6 V. calculate the energy of its first excited
state.
91. How does the collector current change in a junction transistor, if the base region has
larger width?
92. How does the conductivity change of a semiconductor with increase of temperature?
93. Define the term temperature coefficient of resistivity. Draw a graph showing the variation
of reistivity with temperature for copper.
94. S1 and S2 are two hollow concentric sphere enclosing charges Q and 2Q respectively as
shown in fig.What is the ratio of electric flux through S1 & S2?
95. How will the electric flux through the sphere change, if a
medium of dielectric constant 5 is introduced in the space
inside S1 in place of air?
96. Two cells E1 and E2 in the given circuit diagram have an
emf of 4V and 8V and internal resistance 0.5W and 1.0W
respectively. Calculate the current flowing through the resistance of 3W.
97. How will a dia & ferro magnetic material behave when kept in a non-uniform external
field? Give two examples each.
98. Write two applications of each, microwaves and infrared rays.
99. A double concave lens of glass of RI 1.6 has radii of curvature of 40cm, 60cm. Calculate
its focal length. Also find the focal length of the lens if the lens is immersed in a liquid of
RI 1.3.
100. Show that the de-Broglie wavelength l of electrons of energy E is given by the
relation l =
An electrical element x, when connected to an alternating voltage source, has the current through
it leading the voltage by π/2 radii. Identify x and write an expression for its reactance.
Identify the logic gate 1 and 2 in the logic circuit given. Also, write the truth table for the final
output for all possible combination of inputs A and B.
A
1. Ч1 Ч2
2. B
What is the angle between the directions of electric field at any
i. axial point and
ii. equitorial point due to an electric dipole?
Whay should the spring/suspension wire in a moving coil galvanometer have low torsional
constant?
106. The de-Broglie wave lengths, associated with a proton and a neutron, are found
to be equal. Which of the two has a higher value for kinetic energy?
107. Why does a metallic plate become very hot when it is surrounded by a coil
carrying high frequency alternating current?
108. Name the characteristics of electromagnetic waves that
a. increases
b. remains constant.
109. Four nuclei of an element fuse together to form a heavier nucleus. If the process
is accompanied by release of energy, which of the two – the parent or the daughter
nucleus would have a higher binding energy/nucleon?
110. Two large parallel thin metallic plates are placed close to each other. The plates
have surface charge densities of opposite signs and of magnitude 20 x 10-12 C/m2.
Calculate the elctric field intensity
a. in the outer region of the plates and
b. in the interior region between the plates.
111. The following table gives the values of work function for a few photosensitive
metals. If each of these metals is exposed to radiation of wave length 300 nm, which of
them will not emit photo electrons? Why?
1. S. No
2. Metal 3. Work Function (ev)
4. 1 5. Na 6. 1.92
7. 2 8. K 9. 2.15
10. 3 11. Mo 12. 4.17
107. The value of ground state energy of hydrogen atom is -13.6 eV.What does the
negative sign signify?
108. Calculate De-broglie wavelength of an electron beam accelerated through a
potential difference of 60 volt.
109. An electric lamp, connected in series with a capacitor and a.c source, is glowing
with certain brightness. How does the brightness of lamp change on reducing the
capacitance?
110. Sketch a graph to show how the capacitance C of a capacitor varies with the
charge Q given to it.
111. What is the significance of the negative energy of electron in the orbit?
112. A parallel beam of light reflects from concave mirror. Show the reflected wave
front.
113. If the colour bands on a resistor are in the order of red, yellow, orange and silver.
What is the resistance of the resistor?
114. A carrier wave of peak voltage 20 V is used to transmit the message signal. What
should be the peak voltage of the modulating signal in order to have a modulation index
of 80%?
115. Inputs A and B applied to the logic gates set up as shown below .Write the truth
table and the name of gate formed by this set
up.
116. Use Ampere’s circuital law to derive the formula for the magnetic field due to an
infinitely long straight current carring wire.
117. A copper rod of length L rotates with an angular speed ω in a uniform magnetic
field B. Find the induced emf developed across the two ends of a rod. The field is
perpendicular to the motion of a rod.
118. Draw a labelled circuit diagram for a simple amplitude demodulator.
119. Obtain the B.E. of an α –particle in MeV.Given
120. Mass of proton = 1.007825 a.m.u, Mass of neutron = 1.00865 a.m.u, Mass of He
nucleus = 4.002800 a.m.u, 1a.m.u=931MeV.
121. What is the frequency of radio waves?
122. Define SI unit of Electric flux.A photon and an electron both have same energy E.
What is the Ratio of their wavelength?
123. What orientation of an electric dipole in a uniform electric field corresponds to its
stable equilibrium?
124. If distance between two charges is doubled and their individual charges are also
doubled. What would happen to the forces, between them.
125. The potential difference across a conductor of uniform cross-section is doubled.
What happen to the drift velocity of electrons inside the conductor?
131. Define space wave propagation?
132. Draw circuit diagram of NOR gate.
133. If Coulomb’s law involved dependence (instead of ), would Gauss’s law still true?
refractive index of the material of an equilateral triangular prism is . Find the angle of
minimum deviation for a monochromatic ray passing through it.
134. Prove that - I = Ane Vd.
135. Write the truth table of the following logic
gate.
136. In a hydrogen atom, an electron revolves around a proton. Which of these two
exerts a greater electrostatic force on the other?
137. What is the force experienced by a positively charges particle Q moving at right
angles to a uniform electric field E.
138. What is the order of voltages that can be built up using a Van De Graff
generator?
139. What is the angle b/w Electric field and Dipole moment at an axial point?
140. Define gyromagnetic ratio. What is it’s value?
141. State the condition in which terminal voltage across a secondary cell is equal to
its emf.
142. The dielectric strength of air is 3 x 106 V/m. What is the maximum charge that
can be safely stored on a sphere of radius 10m?
143. Name two types of commercially available resistors.
144. On the same graph plot the variation of E versus R and V versus R for a point
charge.
145. Define mobility and mention its SI unit
146. Two resistors are connected in parallel b/w A and B to give a net resistance of 2
ohms. When one of these resistors is broken, the net resistance becomes a 3 ohms.
What is the resistance of the resistor that was broken?
147. Using a suitable graph, explain why nichrome is used in standard resistance
coils.
148. A velocity selector is to be designed for particles of velocity 10m/s. What
magnetic field should be employed if the electric field in it is 100 N/C
149. Draw an equipotential surface for a uniform electric field.
150. In a certain arrangement a proton does not get deflected while passing through a
magnetic field region. Under what condition is this possible?
151. Why does a metallic piece become very hot when it is surrounded by a coil
carrying high frequency alternating current?
152. What is the focal length of a convex lens of focal length 30cm in contact with a
concave lens of focal length 20cm?
153. Ultraviolet radiations of different frequencies v1 and v2 are incident on two
photosensitive materials having work functions W1 and W2 (W1 > W2) respectively. The
kinetic energy of the emitted electrons is same in both the cases. Which one of the two
radiations will be of higher frequency? Draw the voltage current characteristics of a Zener
diode.
154. Define electric field intensity. Write its S.I. unit. Write the magnitude and direction
of electric field intensity due to an electric dipole of length 2a at the mid point of line
joining the charges.
155. Define the term magnetic dipole moment of a current loop. Write the expression
for the magnetic moment when an electron revolves at a speed v around an orbit of
radius r in hydrogen atom.
156. In the circuit shown below, R represents an electric bulb. If the frequency v of the
supply is doubled, how should the values of C and L be changed so that the glow in the
bulb remains unchanged?
157. Answer the following questions:
a. In any ac circuit, is the applied instantaneous voltage equal to the algebraic sum
of the instantaneous voltages across the series elements of the circuit? Is the
same true for rms voltage?
b. Why is choke coil needed in the use of fluorescent tubes with ac mains? Why
can we not use an ordinary resistor instead of the choke coil?
158. What is the equipotential due to an electric dipole at an equatorial point?
159. In a certain arrangement a proton does not get deflected while passing through a
magnetic field region. Under what condition is this possible?
160. Define self induction of a coil. Write its S I unit.
161. Name the radiations which are next to IR radiations in electromagnetic spectrum
having
162. Shorter wavelength & (ii) Longer wavelength
163. Two thin lenses of power +6D and -2D are in contact. What is the focal length of
the combination?
164. The stopping potential in an experiment on photoelectric effect is 1.5V. What is
the maximum kinetic energy of the emitted photoelectrons?
165. Draw the voltage current characteristics of a Zener diode.
166. What is the nuclear radius of 125Fe if that of 27Al is 3.6 fermi?
167. A diverging lens of focal length ‘F’ is cut into two identical parts each forming a
plano-concave lens. What is the focal length of each part?
168. How does resolving power of an astronomical telescope get affected on
i. increasing the aperture of objective lens?
ii. increasing the wavelength of light used?
169. How does the stopping potential applied to a photocell change, if the distance
between the light source and the cathode of the cell is doubled?
170. A 500µc charge is at the centre of a square of side 10 cm. Find the work done in
moving a charge of 10µc between two diagonally opposite points on the square.
171. Zener diodes hhave higher dopant densities as compared to ordinary p-n junction
diodes. How does it affect the
i. Width of the depletion layer?
ii. Junction field?
172. Name the characteristics of electromagnetic waves that
i. Increases
ii. remains constant
173. in an electromagnetic spectrum as one moves from radio wave region towards
ultraviolet region.What happens?
174. If an electron and a proton having same momenta enter perpendicularly to a
magnetic field, how will you compare the nature of the path followed by them?
175. A 50 Hz ac source of 20V is connected to a series combination of resistor R and
capacitor C. The voltage across R is 12V, what is the voltage across C?
176. Let the wavelengths of electromagnetic waves used quite often for:
177. killing of germs in a household water purifiers,
i. b.remote sensing&
ii. treatment of cancer
iii. be labelled as λ1, λ2 & λ3. Arrange λ1, λ2 & λ3 in increasing order.
A ray falls on a prism ABC ( AB = BC ) and travels as shown in the fig 1. What is the least
value of refractive index of material of the prism?
178. When photons energy hn are incident on the surface of photosensitive material
of work function hno, what is the kinetic energy of the ejected electrons?
179. The TV signals have a bandwidth of 4.7MHz. What is the number of channels in
a bandwidth of 4700GHz?
180. Two identical charged particles moving with same speed enter a region of
uniform magnetic field. If one of these enters normal to the field direction and the other
enters along a direction at 300 with the field, what would be the ratio of their angular
frequencies?
181. Why does a metallic piece become very hot when it is surrounded by a coil
carrying high frequency alternating current?
182. How is a sample of an n-type semiconductor electrically neutral though it has an
excess of negative charge carriers?
183. Name the characteristics of electromagnetic waves that
i. increases
ii. remains constant in the electromagnetic spectrum as one moves from radiowave
region towards ultravoilet region.
184. How would the angular separation of interference fringes in young’s double slit
experiment change when the
186. distance of separation between the slits and the screen is doubled?
187. Calculate the ratio of energies of photons produced due to transition of electron
of hydrogen atom from its,
i. Second permitted energy level to the first level, and
ii. Highest permitted energy level to the second permitted level
188. Give expression for the average value of the a c voltage V = V0 Sin t over the
time interval t = 0 and t =
189. How is the band gap, Eg, of a photo diode related to the maximum wavelength,
m , that can be detected by it?
190. Define mobility. What is its S.I unit?
191. Two electric bulbs are marked 220V, 60W and 220V, 100W. Which of the two
bulbs has greater resistance? Why?
192. What is the value of angle of dip at a place on the surface of the earth, where the
horizontal component of earth’s magnetic field is 0.5 times the resultant field at the
place?
193. An a.c. generator generates an emf ‘e’ given by: e = 311 sin (100 pt) volt. Find
the rms value of the emf generated by thegenerator.
194. A rectangular wire frame, shown below, is placed in a uniform magnetic field
directed upward and normal to the plane of the paper. The part AB is connected to a
spring. The spring is stretched and released when the wire AB has come to the position
A’B’ (t=0). How would the induced emf vary with time? Neglect
damping.
195. What is the ratio of speed of g-rays and radio waves in vacuum?
196. Two nuclei have mass numbers in the ratio 1:8. What is the ratio of their
densities?
197. The stopping potential obtained in an experiment on photoelectric effect is 2.5 V.
What is the value of maximum kinetic energy of the electrons emitted from the metal?
198. Can two equi-potential surfaces intersect each other? Explain.
199. (b)Two charges – q and + q are located at points A (0, 0, -a) and B (0, 0, +a)
respectively. How much work is done in moving a test charge 2 µC from point P (7, 0, 0) to Q (-
3, 0, 0)?
Explain what is meant by quantization of charge and conservation of charge, also give the
important property of charge ?
State and explain coulomb’s law, give the vector form of coulomb law.
Explain the concept of electric field . give the relation between electric field strength and force.
Derive expression for electric field intensity at a point due to a point charge.
Derive an expression for dipole field intensity at any point on
i. axial line
ii. equatorial line of dipole.
Derive an expression for torque acting on electric dipole in a uniform electric field
Derive an expression for potential energy of an electric dipole in a uniform electric field.
Derive an expression for potential at a point due to point charge and due to an electric dipole.
State gauss’s theorem in electrostatics . how will u prove it for spherically symmetric surfaces.
Using gauss’s theorem , derive an expression for electric field intensity at a point due to a
i. line charge
ii. a uniformly charged spherical shell
iii. an infinite plane sheet of charge
Explain the term electric field intensity .electric field inside conductor is zero. Explain.
A force F experienced by a particle of charge q moving with velocity v in a magnetic field B is
given by . Which pair of vectors is always at right angles to each other?
The closed loop PQRS is moving into uniform magnetic field acting at right angles to the plane
of the paper as shown in the figure. State the direction in which the induced current flows in the
loop.
Sketch the out put from a NAND gate having inputs A and B as shown
following
217. The energy of an electron in n th orbit is given by En = eV. Calculate the
energy required to excite an electron from ground state to the second excited state.
218. Which of the following has the shortest wavelength: microwaves, ultraviolet rays
and X-rays.
219. What will happen to the image formed by a mirror if half of it is covered with a
black paper?
220. The frequency of AC is being increased in a circuit containing bulb and a
capacitor in series. How will the brightness of the bulb be affected?
221. Derive an expression for electric potential on the axis of a dipole.
222. A cylindrical metallic wire is stretched to increase its length by 5%. Calculate the
percentage change in its resistance.
223. Define resistivity and conductivity of a conductor. Write their SI units.
224. Draw graph for ohmic and non ohmic conductor. Write one example of each.
225. What is the dielectric constant of a conductor?
226. Two protons are entering a magnetic field perpendicular to the magnetic field
with velocities in the ration 1:2. What is the ratio of their angular frequencies?
227. A magnetic field exits along –ve z-axis .coil A is kept with the magnetic field with
the plane of the coil in the x-y plane and coil b is kept with the plane of the coil in x-z
plane. In which coil will there be no induced emf when magnetic field varies with time?
228. Write the relationship between amplitudes of electric and magnetic field in free
space for an electromagnetic wave.
229. A converging lens and a diverging lens are kept in contact and the combination
produces a real image. Which of the lens has longer focal length?
230. Maximum kinetic energy of electron emitted by metal A is 4ev and metal B is 5ev.
Which metal has greater work function when exposed to same radiation?
231. 23Ne10 decay by b emission to 23Na11 .write down the decay equation.
232. An electric dipole of dipole moment 20 X 10-6 Cm is enclosed by a closed
surface. What is the net flux coming out of the surface?[1]
233. Which orientation of a magnetic diploe in a uniform magnetic field will correspond
to its stable equilibrium?[1]
234. Draw a graph to show the variation of capacitive reactance with frequency of an
a.c. source.[1]
235. Which part of electromagnetic spectrum has largest penetrating power?[1]
236. Draw a graph showing the variation of intensity of polarized light transmitted by
the analyser.[1]
237. Name the experiment, which establishes the wave nature of a particle.[1]
238. State two properties of nuclear forces.[1]
239. Write the truth table for the combination of gates shown here.[1]
240. A charge q is placed at the center of the line joining to equal charges Q. Show
that the system of three charges will be in equilibrium if q=-Q/4.
241. Show mathematically that potential at a point on the equatorial line of an electric
dipole is zero
242. A storage battery of emf 12 V and internal resistance 0.5 Ω is to be charged by a
120 V d.c. supply of negligible internal resistance. What resistance is required in the
circuit for the charging current to be 3 A ? What is the terminal voltage of
the battery during charging?
243. Using Ampere circuital law derive an expression for the magnetic field along the
axis of a torodial solenoid
244. Derive the expression for the self-inductance of a solenoid.
245. In a given circuit inductor L and resister R have identical resistance. Two similar
electric lamps B1 and B2 are connected as shown. When switch S is closed,
i. which one of the lamps lights up earlier
ii. will the lamps be equally bright after some time? Justify your answer.
246. Define one coulomb of charge.
247. The small ozone layer on the top of the stratosphere is crucial for human
survival, why?
248. Why can’t a transformer be used to step up dc voltage?
249. What is the nature of the magnetic field in a moving coil galvanometer?
250. The current is set up in a long copper pipe. Is there a magnetic field
i. inside
ii. outside the pipe?
251. Sketch three equipotential surfaces for a pt. charge.
252. How is the coulomb force between two charges affected by the presence of the
third charge?
253. What is the cause of induced emf?
254. Why are microwaves used in RADAR?
255. A uniform magnetic field gets modified as shown below, When two specimens X
and Y are placed in it.
dentify
the two specimens X and Y
256. State the reason for the behaviour of the field lines in X and Y.
257. Give any one difference between FAX and e-mail systems of communication.
258. Give the ratio of the number of holes and number of conduction electrons in an
intrinsic semiconductor.
259. How does focal length of a lens change when red light is replaced by blue light?
260. How does the intensity of central maximum change, if the width of the slit is
halved in a single slit diffraction experiment?
261. How will the photoelectric current change on decreasing the wavelength of
incident radiation for a given photosensitive material?
262. In which series of hydrogen spectra, the transitions involve the longest changes
energy?
263. What is the mass of pion plus (p+)?
264. Vehicles moving in foggy weather use yellow colour head-lights. Why?
265. Name the physical quantity whose S.I. unit is :
266. Coulomb Per Volt
267. Volt/ meter.
268. Force is given by F = Q (VxB). Of these, Name the Pairs of vectors which are
always at right angles to each other.
269. Mention one advantage and one disadvantage of AC over DC.
270. Name two electro magnetic waves that are emitted by an incandescent bulb.
271. Mention one advantage of reflecting type telescope.
272. With what purpose was famouse Davisson- Germer experiment with electrons
performed?
273. Draw the symbol of the universal logic gate.
274. Draw energy band diagram of P-type semiconductor.
275. Capacitor P, Q and R each have a capacitance ‘C’. A battery can charge the
capacitor P to a potential V. If after charging P, the battery is disconnected from it and the
charged capacitor P is connected in following separate instances to Q and R
i. In parallel to Q and
ii. In series to ‘R’
276. A metal wire is stretched to increase its length by 10% What is the percentage
change in its resistance? Will the resistivity of the wire change?
277. When a battery of emf. ‘E’ and internal resistance ‘r’ is connected to a resistance
‘R’, a current I flows through it. Derive a relation between E, I, r and R.
278. Mention 2 properties of alloys from which permanent magnets are made.
279. An inductor of 2mH carries a current of 5A. The direction of current is reversed in
it in half a second due to which a voltage is produced across the inductor. What is this
phenomenon known as? Find the Voltage Produced.
280. Plot a graph to show how the following quantities vary with the frequency of the
source.
i. Capacitive reactance
ii. Inductive reactance.
281. Vehicles moving in foggy weather use yellow color headlights. Why?
282. Give reasons for :
i. The sky appears blue
ii. Sun appears reddish at sunset and sunrise.
283. Draw a labeled block diagram for a communication system.
284. Define electric field intensity at a point. Derive an expression for the electric field
intensity at a point on the axial line of a short dipole.
285. Show that the potential on the equatorial line of an electric dipole is zero
286. What is an electric dipole? Derive an expression for the torque acting on an
electric dipole, when held in a uniform electric field. Hence, define the dipole moment.
287. State Gauss theorem in electrostatics. Using this theorem, derive an expression
for the electric field
288. intensity due to an infinite plane sheet of charge of charge density σ
289. Show mathematically that for any point out side the shell, the field due to a
uniformly charged thin
290. spherical shell is the same as if the entire charge of the shell is concentrated at
the centre.
291. Apply gauss theorem to find electric field intensity at a point due to an infinitely
long thin, uniformly
292. charged straight wire.
293. Define the capacitance of a capacitor. Give its S.I unit for a parallel plate
capacitor, prove that the total
294. energy stored in a capacitor is ½ cv2 and hence derive expression for the energy
density of the capacitor.
295. Derive an expression for the capacitance of a parallel plate capacitor when the
space between the plates is partially filled with a dielectric medium of dielectric constant
k.
296. In a hydrogen atom, an electron revolves around a proton. Which of these two
exerts a greater electrostatic force on the other?
297. What is the force experienced by a positively charges particle Q moving at right
angles to a uniform electric field E.
298. What is the order of voltages that can be built up using a Van De Graff
generator?
299. What is the angle b/w Electric field and Dipole moment at an axial point?
300. Define gyromagnetic ratio. What is it’s value?
301. State the condition in which terminal voltage across a secondary cell is equal to
its emf.
302. The dielectric strength of air is 3 x 106 V/m. What is the maximum charge that
can be safely stored on a sphere of radius 10m?
MATHS
Important Instruction
1. There are 3 section in this paper.2. In the beginning of each question, the number of parts to be attempted is early
mentioned.3. Marks allotted to the question are indicated against them.
SECTION A
1. If , where k is non-zero real number, then without actually evaluating adj A. Find the value of adj (A) .
2. Without expanding, find the value of the determinant
3. Find matrix X such that it satisfies the equation A - 2B + X = 0 , give that
and .
4. Prove that the tangent to the curve y = x3 + 9 at the points (-1, 5) and (1, -1 ) are parallel.
5. If A is an invertible matrix of order 3 and |A| = 3 then find the value of |Adj (A)|
SECTION B
6. If ω is the cube root of unity, evaluate the given determinant
7. Prove that
8. Find the equation of the tangent to the curve given by
9. Using elementary transformation, find inverse of the matrix
10. Find the points on the curve x2 - y2 - 2x - 3 = 0 at which the tangents are parallel to x axis.
11. If , verify A2 - 5A + 7I = 0hence find A-1 .
SECTION C
12. If find A-1 hence solve the following system of equations x + 2y - 3z = - 4; 2x + 3y + 2z = 2 and 3x - 3y - 4z = 11.
13. Find the equation of tangent and normal to the curve at the point where it cut the X axis.
OR
In a activity organized in the school, Rohan was given the task to put the slogan Sytyamev Jayte on a trapezium shaped card sheet. If the length of three sides of trapezium other than base are equal 10 cm each. Find the area of the trapezium when it is maximum. Explain the meaning of Satyamev Jayte.
14. Using elementary row transformation find the inverse of the following matrix .
OR
1. The aim of ‘Marketing, and ‘Selling’ is to maximize profit. Yet they differ in their approach.
Differentiate between the two by giving any six differences.
SECTION A
1. If find the value of x. find the value of x.
2. If find A + A'.
3. For what value of x, the matrix is singular? .
4. Find the slope of tangent to the curve y = 3x3 - 4x at x = 1.
5. If A is an invertible matrix of order 3 and |A| = 6 then find the value of |Adj (A)|
SECTION B
6. Prove using properties of
determinants
7. , find the value of A2 - 3A + 2I .
8. Find A-1 by using ERT for matrix
9. Find the equation of the tangent to the curve given
by
10. For the following matrices A and B , verifying that
11. Find the points on the curve x2 + y2 - 2x - 3 = 0 at which the tangents are parallel to x axis.
12. If , verify A2 - 5A + 7I = 0 hence find A-1.
SECTION C
13. Solve the following system of equations x + 2y - 3z = - 4; 2x + 3y + 2z = 2 and 3x - 3y - 4z = 11.
14. Find the equation of tangent and normal to the curve at the point where it cut the X axis.
OR
A given quantity of metal is to be cast into a half cylinder with a rectangular base and semi-circular ends. Show that in order that total surface area is minimum, the ratio of length of the cylinder to the diameter of its semi-circular ends is p : ( p + 2 ).
15. Using elementary row transformation find the inverse of the following matrix
OR
1. Find the equation of the ellipse with foci (± 5. 0 ) and as one directrix.
2. Find the lengths and equation of major and minor axes, centre, eccentricity, foci, equation of
directrices, vertices and length of L.R of the ellipse .
3. Find the centre, the length of the axes, eccentricity and the foci of the ellipse 12x2 + 4y2 +24x -16y + 25 = 0.
4. Find the equation of ellipse having centre at the point (2, -3) one focus at (3, -3)and one vertex at (4, -3) .
5. A rod of length 15 cm rests in between two coordinates axes in su.
PRACTICE SET - 3
SECTION A
1. For what value of a , is a singular matrix?
2. Find the equation of tangent to the curve √x + √y = a at the point
3. If and B= [ -2 -1 -4 ] find AB.
4. If A is a matrix of order 3 and |A| = 8 then find the value of |A dv A |.
5. Without expanding evaluate the determinant
SECTION B
6. Prove that
7. Find the points on the curve 6 y2 = x3 where normal to the curve makes equal intercepts with the axes.
8. Show that Matrix show that : A2 - 4A - 5I3 = 0 and hence find A-1.
9. Show that the semi vertical angle of a cone of given total surface area and maximum volume
is
10. Prove that
11. Using elementary operations, find the inverse of matrix
SECTION C
12. Determine the product and use it solve the system of equations: x – y + z = 4; x – 2y – 2z = 9 and 2x + y + 3z = 1.
OR
Using elementary transformations, find the inverse of the matrix :
13. If the length of the trapezium, other than base is equal to 10 cm each, then find the area of trapezium when it is maximum.
OR
Show that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius r is 4r / 3 .
14. Show that
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