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Board Paper of Class 12-Science 2008 Physics (SET 1) - Solutions

General Instructions:
(i) All questions are compulsory.
(ii) There are 30 questions in total. Question Nos. 1 to 8 are very short answer type questions and carry one mark each.
(iii) Question Nos. 9 to 18 carry two marks each, question 19 to 27 carry three marks each and question 28 to 30 carry five marks each.
(iii) There is no overall choice. However, an internal choice has been provided in one question of two marks; one question of three marks and all three questions of five marks each. You have to attempt only one of the choice in such questions.
(iv) Use of calculators is not permitted.

• Question 1

State two characteristic properties of nuclear force.

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• Question 2

How does the angle of minimum deviation of a glass prism vary, if the incident violet light is replaced with red light?

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• Question 3

The instantaneous current and voltage of an a.c. circuit are given by

i = 10 sin 300 t A and

V = 200 sin 300 t V.

What is the power dissipation in the circuit?

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• Question 4

Why should the spring/suspension wire in a moving coil galvanometer have low torsional constant?

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• Question 5

Why does the bluish colour predominate in a clear sky?

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• Question 6

Which orientation of an electric dipole in a uniform electric field would correspond to stable equilibrium?

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• Question 7

Two lines, A and B, in the plot given below show the variation of de Broglie wavelength, λ versus , where V is the accelerating potential difference, for two particles carrying the same charge.

Which one of two represents a particle of smaller mass? VIEW SOLUTION

• Question 8

State the reason why GaAs is most commonly used in making of a solar cell.

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• Question 9

Draw a labelled ray diagram of an astronomical telescope in the near point position. Write the expression for its magnifying power.

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• Question 10

The following figure shows the variation of intensity of magnetisation versus the applied magnetic field intensity, Hj for two magnetic materials A and B: (a) Identify the materials A and B.

(b) Why does the material B have a larger susceptibility than A for a given field at constant temperature?

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• Question 11

Two metallic wires of the same material have the same length but cross-sectional area is in the ratio 1:2. They are connected (i) in series and (ii) in parallel. Compare the drift velocities of electrons in the two wires in both the cases (i) and (ii).

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• Question 12

Draw a block diagram of a simple amplitude modulation. Explain briefly how amplitude modulation is achieved.

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• Question 13

Calculate the energy released in MeV in the following nuclear reaction: [Mass of Mass of Mass of 1u = 931.5 MeV/c2]

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• Question 14

Using Ampere’s circuital law, obtain an expression for the magnetic field along the axes of a current carrying solenoid of length l and having N number of turns.

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• Question 15

Derive an expression for the resistivity of a good conductor, in terms of the relaxation time of electrons.

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• Question 16

The circuit arrangement given below shows that when an a.c. passes through the coil A, the current starts flowing in the coil B. (i) State the underlying principle involved.

(ii) Mention two factors on which the current produced in the coil B depends.

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• Question 17

State one feature by which the phenomenon of interference can be distinguished from that of diffraction.

A parallel beam of light of wavelength 600 nm is incident normally on a slit of width ‘a’. If the distance between the slits and the screen is 0.8 m and the distance of 2nd order maximum from the centre of the screen is 15 mm, calculate the width of the slit.

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• Question 18

Two point charges q1 = 10 × 10−8 C and q2 = −2 × 10−8 C are separated by a distance of 60 cm in air.

(i) Find at what distance from the 1st charge, q1, would the electric potential be zero.

(ii) Also calculate the electrostatic potential energy of the system.

OR

Two point charges 4Q, Q are separated by 1 m in air. At what point on the line joining the charges is the electric field intensity zero? Also calculate the electrostatic potential energy of the system of charges, taking the value of charge, Q = 2 × 10−7 C.

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• Question 19

Identify the following electromagnetic radiations as per the wavelengths given below. Write one application of each.

(a) 10−3 nm

(b) 10−3 m

(c) 1 nm

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• Question 20

Explain why high frequency carrier waves are needed for effective transmission of signal. A message signal of 12 KHz and peak voltage 20 V is used to modulate a carrier wave of frequency 12 MHz and peak voltage 30 V. Calculate the (i) modulation index (ii) side-band frequencies.

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• Question 21

Distinguish between unpolarised and plane polarised light. An unpolarised light is incident on the boundary between two transparent media. State the condition when the reflected wave is totally plane polarised. Find out the expression for the angle of incidence in this case.

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• Question 22

Draw the labelled circuit diagram of a common-emitter transistor amplifier. Explain clearly how the input and output signals are in opposite phase.

OR

State briefly the underlying principle of a transistor oscillator. Draw a circuit diagram showing how the feedback is accomplished by inductive coupling. Explain the oscillator action.

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• Question 23

The ground state energy of hydrogen atom is − 13.6 eV.

(i) What is the kinetic energy of an electron in the 2nd excited state?

(ii) If the electron jumps to the ground state from the 2nd excited state, calculate the wavelength of the spectral line emitted.

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• Question 24

The following graph shows the variation of stopping potential V0 with the frequency ν of the incident radiation for two photosensitive metals X and Y: (i) Which of the metals has larger threshold wavelength? Give reason.

(ii) Explain giving reason, which metal gives out electrons, having larger kinetic energy, for the same wavelength of the incident radiation.

(iii) If the distance between the light source and metal X is halved, how will the kinetic energy of electrons emitted from it change? Give reason

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• Question 25

A circular coil of 200 turns and radius 10 cm is placed in a uniform magnetic field of 0.5 T, normal to the plane of the coil. If the current in the coil is 3.0 A, calculate the

(a) Total torque on the coil

(b) Total force on the coil

(c) Average force on each electron in the coil due to the magnetic field

Assume the area of cross-section of the wire to be 10−5 m2 and the free electron density is 1029/m3.

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• Question 26

The inputs A and B are inverted by using two NOT gates and their outputs are fed to the NOR gate as shown below. Analyze the action of the gates (1) and (2) and identify the logic gate of the complete circuit so obtained. Give its symbol and the truth table.

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• Question 27

(i) Calculate the equivalent resistance of the given electrical network between points A and B.

(ii) Also calculate the current through CD and ACB, if a 10 V d.c source is connected between A and B, and the value of R is assumed as 2 Ω. VIEW SOLUTION

• Question 28

Derive an expression for the energy stored in a parallel plate capacitor.

On charging a parallel plate capacitor to a potential V, the spacing between the plates is halved, and a dielectric medium of is introduced between the plates, without disconnecting the d.c source. Explain, using suitable expressions, how the (i) capacitance, (ii) electric field and (iii) energy density of the capacitor charge.

OR

(a) Define electric flux. Write its SI unit.

(b) The electric field components due to a charge inside the cube of side 0.1 m are as shown:  Where α = 500 N/C − m

Ey = 0, Ez = 0

Calculate (i) the flux through the cube and (ii) the charge inside the cube

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• Question 29

Derive the lens formula, for a concave lens, using the necessary ray diagram.

Two lenses of powers 10 D and − 5 D are placed in contact.

(i) Calculate the power of the new lens.

(ii) Where should an object be held from the lens, so as to obtain a virtual image of magnification 2?

OR

(a) What are coherent sources of light? Two slits in Young’s double slit experiment are illuminated by two different sodium lamps emitting light of the same wavelength. Why is no interference pattern observed?

(b) Obtain the condition for getting dark and bright fringes in Young’s experiment. Hence write the expression for the fringe width.

(c) If S is the size of the source and its distance from the plane of the two slits, what should be the criterion for the interference fringes to be seen?

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• Question 30

An a.c source generating a voltage is connected to a capacitor of capacitance C. Find the expression for the current i, flowing through it, plot a graph of v and i versus ωt to show that the current is , ahead of the voltage.

A resistor of 200 Ω and a capacitor of 15 μF are connected in series to a 220 V, 50 Hz a.c source. Calculate the current in the circuit and the rms voltage across the resistor and the capacitor. Is the algebraic sum of these voltages more than the source voltage? If yes, resolve the paradox.

OR

Explain briefly, with the help of a labelled diagram, the basic principle of the working of an a.c generator.

In an a.c generator, coil of N turns and area A is rotated at V revolutions per second in a uniform magnetic field B.

Write the expression for the emf produced. A 100-turn coil of area 0.1 m2 rotates at half a revolution per second. It is placed in a magnetic field 0.01 T perpendicular to the axis of rotation of the coil. Calculate the maximum voltage generated in the coil.

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