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# Board Paper of Class 12-Science 2012 Physics (SET 2) - 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

What is the angle of dip at a place where the horizontal and vertical components of the Earth’s magnetic field are equal?

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• Question 2

Show on a graph the variation of the de Broglie wavelength (λ) associated with an electron, with the square root of accelerating potential (V).

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• Question 3

Write the relationship between the size of a nucleus and its mass number (A).

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• Question 4

How does focal length of a lens change when red light incident on it is replaced by violet light? Give reason for your answer.

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• Question 5

Name the electromagnetic waves which (i) maintain the Earth’s warmth and (ii) are used in aircraft navigation.

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• Question 6

Define dipole moment of an electric dipole. Is it a scalar or a vector?

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• Question 7

The closed loop (PQRS) of wire is moved into a uniform magnetic field at right angles to the plane of the paper as shown in the figure. Predict the direction of the induced current in the loop. VIEW SOLUTION

• Question 8

Why is there no work done in moving a charge from one point to another on an equipotential surface?

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• Question 9

Explain briefly how electromagnetic waves are produced by an oscillating charge. How is the frequency of the em waves produced related to that of the oscillating charge?

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• Question 10

A magnetised needle of magnetic moment 4.8 × 10−2 JT−1 is placed at 30° with the direction of uniform magnetic field of magnitude 3 × 10−2 T. Calculate the torque acting on the needle.

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• Question 11

Write two characteristic features to distinguish between n-type and p-type semiconductors.

OR

How does a light emitting diode (LED) work? Give two advantages of LED’s over the conventional incandescent lamps.

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• Question 12

Trace the path of the ray (P) of light passing through the glass prism as shown in the figure. The prism is made of glass with critical angle ic = 41°. VIEW SOLUTION

• Question 13

In a given sample, two radioisotopes, A and B, are initially present in the ration of 1 : 4. The half lives of A and B are respectively 100 years and 50 years. Find the time after which the amounts of A and B become equal.

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• Question 14

Calculate the quality factor of a series LCR circuit with L = 4.0 H, C = 1, μF and R = 20 Ω.

Mention the significance of quality factor in LCR circuit.

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• Question 15

Figure shows a block diagram of a detector for amplitude modulated signal. Identify the boxes ‘X’ and ‘Y’ and write their functions. VIEW SOLUTION

• Question 16

Two students ‘X’ and ‘Y’ perform an experiment on potentiometer separately using the circuit given below: Keeping other parameters unchanged, how will the position of the null point be affected if

(i) ‘X’ increases the value of resistance R in the set-up by keeping the key K1 closed and the Key K2 opens?

(ii) ‘Y’ decreases the value of resistance S in the set-up, while the key K2 remains open and they K1 closed?

Justify.

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• Question 17

A particle of charge ‘q’ and mass ‘m’ is moving with velocity . It is subjected to a uniform magnetic field directed perpendicular to its velocity. Show that it describes a circular path. Write the expression for its radius.

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• Question 18

A conductor of length ‘l’ is connected to a dc source of potential ‘V’. If the length of the conductor is tripled by gradually stretching it, keeping ‘V’ constant, how will (i) drift speed of electrons and (ii) resistance of the conductor be affected? Justify your answer.

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• Question 19

Using Bohr’s postulates for hydrogen atom, show that the total energy (E) of the electron in the stationary states can be expressed as the sum of kinetic energy (K) and potential energy (U), where K = −2U. Hence deduce the expression for the total energy in the nth energy level of hydrogen atom.

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• Question 20

Define modulation index. Given its physical significance.

For an amplitude modulated wave, the maximum amplitude is found to be 10 V while the minimum amplitude is 2 V. Determine the modulation index μ.

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• Question 21

Define a wavefront. Use Huygens’ geometrical construction to show the propagation of plane wavefront a rarer medium (1) to a denser medium (2) undergoing refraction.

Hence derive Snell’s law of refraction.

OR

(a) Use Huygens’ geometrical construction to show the behavior of a plane wavefront.

(i) Passing through a biconvex lens;

(ii) Reflecting by a concave mirror.

(b) When monochromatic light is incident on a surface separating two media, why does the refracted light have the same frequency as that of the incident light?

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• Question 22

Two cells of emf E1, E2 and internal resistance r1 and r2 respectively are connected in parallel as shown in the figure. Deduce the expressions for

(i) the equivalent e.m.f of the combination

(ii) the equivalent resistance of the combination, and

(iii) the potential difference between the point A and B.

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• Question 23

(a) State Gauss’s law in electrostatics.
(b) A cube which each side ‘a’ is kept is an electric field given by (as is shown in the figure) where C is a positive dimensional constant. Find out (i) The electric flux through the cube, and

(ii) The net charge inside the cube.

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• Question 24

Draw a labelled diagram of a moving coil galvanometer and explain its working. What is the function of radial magnetic field inside the coil?

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• Question 25

Write two characteristic features observed is photoelectric effect which supports the photon pictures of electromagnetic radiation.

Draw a graph between the frequency of incident radiation (υ) and the maximum kinetic energy of the electrons emitted from the surface of a photosensitive material state clearly how this graph can be used to determine (i) Planck’s constant and (ii) work function of the material.

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• Question 26

A capacitor of 150 pF is charged by a 200 V battery. The battery is then disconnected and the charge capacitor is connected to another uncharged capacitor of 50 pF. Calculate the difference between the final energy stored in the combined system and the initial energy stored in the single capacitor.

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• Question 27

Define power of a lens. Write its units. Deduce the relation for two thin lenses kept in contact coaxially.

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• Question 28

(a) Sate the principle on which AC generator works. Draw a labeled diagram and explain its working.

(b) A conducting rod held horizontally along East- West direction is dropped from rest from a certain height near the Earth’s surface. Why should there be an induced emf across the end of the rod? Draw a plot showing the instantaneous variation of emf as a function of time from the instant it begins to fall.

OR

(a) State the principle of a step-up transformer. Explain, with the help of a labeled diagram, its working.

(b) Describe briefly and two energy losses, giving the reasons for their occurrence in actual transformers.

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• Question 29

(a) Draw the circuit for studying the input and output characteristics of and transistor in CE configuration. Show, how, from the output characteristics, the information about the current amplification factor (βac) can obtained.

(b) Draw a plot of the transfer characteristics (V0 versus Vi) for a base-biased transistor in CE configuration. Show for which regions in the plot, the transistor can operate as a switch.

OR

(a) Why is a zener diode considered as a special purpose semiconductor diode?

Draw the I − V characteristics of zener diode and explain briefly how reverse current suddenly increase at the breakdown voltage.

Describe briefly with the help of a circuit diagram how a zener diode works to obtain a constant dc voltage from the unregulated dc output of a rectifier.

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• Question 30

(a) What is the effect on the interference fringes to a Young’s double slit experiment when

(i) the separation between the two slits is decreased?

(ii) the width of a source slit is increased?

(iii) the monochromatic source is replaced by a source of white light?

(b) The intensity at the central maxima in Young’s double slit experimental set-up is I0. Show that the intensity at a point where the path difference is λ/3 is I0/4.

OR

(a) Obtain the conditions for the bright and dark fringes in diffraction pattern due to a single narrow slit illuminated by a monochromatic source.

Explain clearly why the secondary maxima go on becoming weaker with increasing.

(b) When the width of the slit is made double, how would this affect the size and intensity of the central diffraction band? Justify.

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