Board Paper of Class 12-Science 2019 Physics All India(Set 1) - Solutions

General Instructions:

1. All questions are compulsory. There are 27 questions in all.

2. This question paper has four sections: Section A, Section B, Section C and Section D.

3. Section A contains five questions of one mark each, Section B contains seven questions of two marks each, Section C contains twelve questions of three marks each, and Section D contains three questions of five marks each.

4. There is no overall choice. However, internal choices have been provided in two questions of one mark, two questions of two marks, four questions of three marks and three questions of five marks weightage. You have to attempt only one of the choices in such questions.

5. You may use the following values of physical constants wherever necessary.

c = 3 × 10⁸ m/s

h = 6.63 × 10^–34 Js

e = 1.6 × 10^–19 C

μ_o = 4π × 10^–7 T m A^–1

ε₀ = 8.854 × 10^–12 C² N^–1 m^–2

$fraction numerator 1 over denominator 4 pi epsilon subscript 0 end fraction$ = 9 × 10⁹ N m² C^–2

m_e = 9.1 × 10^–31 kg

mass of neutron = 1.675 × 10^–27 kg

mass of proton = 1.673 × 10^–27 kg

Avogadro’s number = 6.023 × 10²³ per gram mole

Boltzmann constant = 1.38 × 10^–23 JK^–1

Question 1
Two metallic spheres A and B kept on insulating stands are in contact with each other. A positively charged rod P is brought near the sphere A as shown in the figure. The two spheres are separated from each other, and the rod P is removed. What will be the nature of charges on spheres A and B?

OR

A metal sphere is kept on an insulating stand. A negatively charged rod is brought near it, then the sphere is earthed as shown. On removing the earthing, and taking the negatively charged rod away, what will be the nature of charge on the sphere ? Give a reason for your answer.

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Question 2
A carbon resistor is shown in the figure. Using color code, write the value of the resistance.

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Question 3
i) State the condition under which a large magnification can be achieved in an astronomical telescope.
ii) How does the angle of minimum deviation of a glass prism vary if the incident violet light is replaced by red light? VIEW SOLUTION

Question 4

On the basis of the graphs shown in the figure, answer the following questions :

(a) Which physical parameter is kept constant for the three curves?
(b) Which is the highest frequency among v₁, v₂ and v₃? VIEW SOLUTION

Question 5
Define amplitude modulation in communication system. VIEW SOLUTION

Question 6
Five point charges, each of charge + q are placed on five vertices of a regular hexagon of side 'l'. Find the magnitude of the resultant force on a charge − q placed at the centre of the hexagon

OR

A simple pendulum consists of a small sphere of mass m suspended by a thread of length l. The sphere carries a positive charge q. The pendulum is placed in a uniform electric field of strength E directed vertically downwards. Find the period of oscillation of the pendulum due to the electrostatic force acting on the sphere, neglecting the effect of the gravitational force. VIEW SOLUTION

Question 7

The figure shows a network of five capacitors connected to a 100 V supply. Calculate the total energy stored in the network. VIEW SOLUTION

Question 8
A 0⋅5 m long solenoid of 10 turns/cm has the area of cross-section 1 cm². Calculate the voltage induced across its ends if the current in the solenoid is changed from 1 A to A in 0⋅1 s.

OR

A small flat search coil a of area 5 cm² with 140 closely wound turns is placed between the poles of a powerful magnet producing magnetic field 0⋅09 T and then quickly removed out of the field region. Calculate:
(a) Change of magnetic flux through the coil, and
(b) emf induced in the coil. VIEW SOLUTION

Question 9
For paraxial rays, show that the focal length of a spherical mirror is one-half of its radius of curvature. VIEW SOLUTION

Question 10
Obtain Bohr's quantization condition for the angular momentum of the electron orbiting in n^thorbit in hydrogen atom on the basis of the wave picture of an electron using de-Broglie hypothesis. VIEW SOLUTION

Question 11
Plot a graph showing the variation of undecayed nuclei N versus time t. From the graph, find out how one can determine the half-life and average life of the radioactive nuclei. VIEW SOLUTION

Question 12

(a) Write two distinguishing features of nuclear forces.
(b) Two nuclei have mass number in the ratio 1 : 3. What is the ratio of their nuclear densities

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Question 13
(a) Explain briefly, using a proper diagram, the difference in behavior of a conductor and a dielectric in the presence of an external electric field.

(b) Define the term polarization of a dielectric and write the expression for a linear isotropic dielectric in terms of electric field. VIEW SOLUTION

Question 14
Twelve wires each having a resistance of 3 Ω are connected to form a cubical network. A battery of 10 V and negligible internal resistance is connected across the diagonally opposite corners of this network. Determine its equivalent resistance and the current along each edge of the cube. VIEW SOLUTION

Question 15
A student uses the circuit diagram of a potentiometer as shown in the figure (a) for a steady current I passing through the potentiometer wire, he gets a null point for the cell ε₁. and not for ε₂. Give the reason for this observation and suggest how this difficulty can be resolved. (b) What is the function of resistance R used in the circuit? How will the change in its value affect the null point? (c) How can the sensitivity of the potentiometer be increased?
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Question 16
(a) Show that the time period (T) of oscillations of a freely suspended magnetic dipole of magnetic moment (m) in a uniform magnetic field (B) is given by T = $2 π \sqrt{\frac{I}{mB}}$ , where I is a moment of inertia of the magnetic dipole.

(b) Identify the following magnetic materials :
(i) A material having susceptibility (χ_m) = −0⋅00015.
(ii) A material having susceptibility (χ_m) = 10⁻⁵
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Question 17
(a) How are eddy currents generated in a conductor which is subjected to a magnetic field?
(b) Write two examples of their useful applications.
(c) How can the disadvantages of eddy currents be minimized ? VIEW SOLUTION

Question 18
(a) An ac circuit as shown in the figure has an inductor of inductance L and a resistor of resistance R connected in series. Using the phasor diagram, explain why the voltage in the circuit will lead the current in phase.
(b) The potential difference across the resistor is 160 V and that across the inductor is 120 V. Find the effective value of the applied voltage. If the effective current in the circuit is 1⋅0 A, calculate the total impedance of the circuit.
(c) What will be the potential difference in the circuit when direct current is passed through the circuit?

OR

An ac circuit consists of a series combination of circuit elements X and Y. The current is ahead of the voltage in phase by $\frac{π}{4}$ . If element X is a pure resistor of 100 Ω,

(a) name the circuit element Y.
(b) calculate the rms value of current, if rms of voltage is 141 V.
(c) what will happen if the ac source is replaced by a dc source
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Question 19
Name the radiation of the electromagnetic spectrum which is used for the following:
(a) Radar
(b) To photograph internal parts of human body
(c) For taking photographs of the sky during night and foggy conditions
Give the frequency range in each case. VIEW SOLUTION

Question 20

A converging beam of light travelling in air converges at a point P as shown in the figure. When a glass sphere of refractive index 1⋅5 is introduced in between the path of the beam, calculate the new position of , the image. Also draw the ray diagram for the image formed.

OR

A point 'O' marked on the surface of a glass sphere of diameter 20 cm is viewed through glass from the position directly opposite to the point O. If the refractive index of the glass is 1⋅5, find the position of the image formed. Also, draw the ray diagram for the formation of the image

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Question 21
(a) Explain how an unpolarised light gets polarised when incident on the interface separating the two transparent media.
(b) Greenlight is incident at the polarising angle on a certain transparent medium. The angle of refraction is 30°. Find
(i) polarising angle, and
(ii) refractive index of the medium.
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Question 22
(a) Plot a graph to show the variation of stopping potential with the frequency of incident radiation in relation to photoelectric effect.
(b) Use Einstein's photoelectric equation to show how from this graph, (i) Threshold frequency, and (ii) Planck's constant can be determined.
OR

(a) How does one explain the emission of electrons, from a photosensitive surface with the help of Einstein's photoelectric equation ?
(b) The work function of aluminum is 4⋅2 eV. If two photons each of energy 2⋅5 eV are incident on its surface, will the emission of electrons take place? Justify your answer.
(c) The stopping potential in an experiment on the photoelectric effect is 1⋅5 V. What is the maximum kinetic energy of the photoelectrons emitted? Calculate in Joules.
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Question 23
(a) (i) Write the truth tables of the logic gates marked P and Q in the given circuit.
(ii) Write the truth table for the circuit.

(b) Why are NOR gates considered as universal gates?

OR

(a) Explain how a potential barrier is developed in a p-n junction diode.
(b) Draw the circuit arrangement for studying the V-I characteristics of a p-n junction diode in reverse bias. Plot the V-I characteristics in this case

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Question 24
(a) What do you mean by bandwidth of a signal ? Give its importance.
(b) Differentiate between Analog and Digital communication.
(c) Write the functions of transducer and repeaters. VIEW SOLUTION

Question 25
(a) State and explain the law used to determine the magnetic field at a point due to a current element. Derive the expression for the magnetic field due to a circular current carrying loop of radius r at its center.

(b) A long wire with a small current element of length 1 cm is placed at the origin and carries a current of 10 A along the X-axis. Find out the magnitude and direction of the magnetic field due to the element on the Y-axis at a distance 0⋅5 m from it.

OR

(a) Derive the expression for the magnetic field due to a current carrying coil of radius r at a distance x from the center along the X-axis.
(b) A straight wire carrying a current of 5 A is bent into a semicircular arc radius 2 cm as shown in the figure. Find the magnitude and direction of the magnetic field at the center of the arc

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Question 26
(a) Can the interference pattern be produced by two independent monochromatic sources of light? Explain.
(b) The intensity at the central maximum (O) in Young's double slit experimental set-up shown in the figure is I_O. If the distance OP equals one-third of the fringe width of the pattern, show that the intensity at point P, would equal $\frac{I_{O}}{4}$ .

(c) In Young's double slit experiment, the slits are separated by 0⋅5 mm and the screen is placed 1⋅0 m away from the slit. It is found that the 5th bright fringe is at a distance of 4⋅13 mm from the 2nd dark fringe. Find the wavelength of light used.

OR

(a) Derive the relation a sin θ = λ for the first minimum of the diffraction pattern produced due to a single slit of width 'a' using light of wavelength λ.
(b) State with reason, how the linear width of central maximum will be affected if (i) monochromatic yellow light is replaced with red light, and (ii) distance between the slit and the screen is increased.
(c) Using the monochromatic light of same wavelength in the experimental set-up of the diffraction pattern as well as in the interference pattern where the slit separation is 1 mm, 10 interference fringes are found to be within the central maximum of the diffraction pattern. Determine the width of the single slit, if the screen is kept at the same distance from the slit in the two cases.

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Question 27
(a) Draw a circuit diagram of an n-p-n transistor with its emitter-base junction forward biased and base-collector junction reverse biased. Briefly describe its working.
Explain how a transistor in its active state exhibits a low resistance at its emitter-base junction and high resistance at its base-collector junction.
(b) Derive the expression for the voltage gain of a transistor amplifier in CE configuration in terms of the load resistance R_L, current gain β_a and input resistance.
Explain why input and output voltages are in opposite phase.

OR

(a) Write the important considerations which are to be taken into account while fabricating a p-n junction diode to be used as a Light Emitting Diode (LED). What should be the order of band gap of an LED, if it is required to emit light in the visible range? Draw a circuit diagram and explain its action.
(b) Draw the V-I characteristics of an LED. State two advantages of LED lamps over conventional incandescent lamps.
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