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# Board Paper of Class 12-Science 2016 Physics (SET 1) - Solutions

General Instructions:

(i) There are 26 questions in all. All questions are compulsory.

(ii) This question paper has five sections : Section A, Section B, Section C, Section D and Section E.

(iii) Section A contains five questions of one mark each, Section B contains five questions of two marks each, Section C contains twelve questions of three marks each, Section D contains one value based question of four marks and Section E contains three questions of five marks each.

(iv) 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 the three questions of five marks weightage. You have to attempt only one of the choices in such questions.

• Question 1
A point charge +Q is placed at point O, as shown in the figure. Is the potential difference VAVB positive, negative or zero?

VIEW SOLUTION
• Question 2
How does the electric flux due to a point charge enclosed by a spherical Gaussian surface get affected when its radius is increased? VIEW SOLUTION
• Question 3
Write the underlying principle of a moving coil galvanometer. VIEW SOLUTION
• Question 4
Why are microwaves considered suitable for radar systems used in aircraft navigation? VIEW SOLUTION
• Question 5
Define 'quality factor' of resonance in a series LCR circuit. What is its SI unit? VIEW SOLUTION
• Question 6
Explain the terms (i) Attenuation and (ii) Demodulation used in Communication System. VIEW SOLUTION
• Question 7
Plot a graph showing variation of de Broglie wavelength λ versus $\frac{1}{\sqrt{\mathrm{V}}},$ where V is accelerating potential for two particles A and B, carrying the same charge but different masses m1, m2 (m1 > m2). Which one of the two represents a particle of smaller mass and why? VIEW SOLUTION
• Question 8
A nucleus with mass number A = 240 and BE/A = 7.6 MeV breaks into two fragments, each of A = 120 with BE/A = 8.5 MeV. Calculate the released energy.

OR

Calculate the energy in fusion reaction:

${}_{1}{}^{2}\mathrm{H}+{}_{1}{}^{2}\mathrm{H}\to {}_{2}{}^{3}\mathrm{He}+\mathrm{n},$ where BE of ${}_{1}{}^{2}\mathrm{H}=2.23$ MeV and of ${}_{2}{}^{3}\mathrm{He}=7.73$ MeV VIEW SOLUTION
• Question 9
Two cells of emf 1.5 V and 2.0 V, respectively, having internal resistances 0.2 Ω and 0.3 Ω, respectively, are connected in parallel. Calculate the emf and internal resistance of the equivalent cell. VIEW SOLUTION
• Question 10
State Brewster's law.

The value of Brewster's angle for a transparent medium is different for light of different colours. Give reason. VIEW SOLUTION
• Question 11
A charge is distributed uniformly over a ring of radius 'a'. Obtain an expression for the electric intensity E at a point on the axis of the ring. Hence, show that for points at large distance from the ring, it behaves like a point charge. VIEW SOLUTION
• Question 12
Write three characteristic features in photoelectric effect that cannot be explained on the basis of wave theory of light, but can be explained only using Einstein's equation. VIEW SOLUTION
• Question 13
(a) Write the expression for the magnetic force acting on a charged particle moving with velocity v in the presence of magnetic field B.

(b) A neutron, an electron and an alpha particle, moving with equal velocities, enter a uniform magnetic field going into the plane of the paper, as shown. Trace their paths in the field and justify your answer.

VIEW SOLUTION
• Question 14
(i) Define mutual inductance.

(ii) A pair of adjacent coils has a mutual inductance of 1.5 H. If the current in one coil changes from 0 to 20 A in 0.5 s, what is the change of flux linkage with the other coil? VIEW SOLUTION
• Question 15
Two parallel-plate capacitors X and Y have the same area of plates and same separation between them. X has air between the plates, while Y contains a dielectric medium of εr = 4.

(i) Calculate capacitance of each capacitor if the equivalent capacitance of the combination is 4 μF.
(ii) Calculate the potential difference between the plates X and Y.
(iii) Estimate the ratio of electrostatic energies stored in X and Y. VIEW SOLUTION
• Question 16
Two long, straight, parallel conductors carry steady currents, I1 and I2, separated by a distance d. If the currents are flowing in the same direction, show how the magnetic field set up in one produces an attractive force on the other? Obtain the expression for this force. Hence, define one ampere. VIEW SOLUTION
• Question 17
How are em waves produced by oscillating charges?
Draw a sketch of linearly polarized em waves propagating in the Z-direction. Indicate the directions of the oscillating electric and magnetic fields.

OR

Write Maxwell's generalization of Ampere's circuital law. Show that in the process of charging a capacitor, the current produced within the plates of the capacitor is

$I={\epsilon }_{\mathit{0}}\frac{\mathit{d}{\mathit{\Phi }}_{\mathit{E}}}{\mathit{d}\mathit{t}}$, where ΦE is the electric flux produced during charging of the capacitor plates. VIEW SOLUTION
• Question 18
(a) Explain any two factors that justify the need of modulating a low-frequency signal.

(b) Write two advantages of frequency modulation over amplitude modulation. VIEW SOLUTION
• Question 19
(i) Write the functions of three segments of a transistor.

(ii) Draw a circuit diagram for studying the input and output characteristics of a n-p-n transistor in common emitter configuration. Using the circuit, explain how input, output characteristics are obtained. VIEW SOLUTION
• Question 20
(a) Calculate the distance of an object of height h from a concave mirror of radius of curvature 20 cm, so as to obtain a real image of magnification 2. Find the location of image also.

(b) Using mirror formula, explain why does a convex mirror always produce a virtual image. VIEW SOLUTION
• Question 21
(i) State Bohr's quantization condition for defining stationary orbits. How does the de Broglie hypothesis explain the stationary orbits?

(ii) Find the relation between three wavelengths λ1, λ2 and λ3 from the energy-level diagram shown below.

VIEW SOLUTION
• Question 22
Draw a schematic ray diagram of a reflecting telescope showing how rays coming from a distant object are received at the eyepiece. Write its two important advantages over a refracting telescope. VIEW SOLUTION
• Question 23
Meeta's father was driving her to school. At the traffic signal, she noticed that each traffic light was made of many tiny lights instead of a single bulb. When Meeta asked this question to her father, he explained the reason for this.

Answer the following questions based on above information:

(i) What were the values displayed by Meeta and her father?
(ii) What answer did Meeta's father give?
(iii) What are the tiny lights in traffic signals called and how do these operate? VIEW SOLUTION
• Question 24
(i) An a.c. source of voltage V = V0 sin ωt is connected to a series combination of L, C and R. Use the phasor diagram to obtain expression for impedance of a circuit and the phase angle between voltage and current. Find the condition when current will be in phase with the voltage. What is the circuit in this condition called?

(ii) In a series LR circuit, XL = R and power factor of the circuit is P1. When capacitor with capacitance C such that XL = XC is put in series, the power factor becomes P2. Calculate P1/P2.

OR

(i) Write the function of a transformer. State its principle of working with the help of a diagram. Mention various energy losses in this device.

(ii) The primary coil of an ideal step-up transformer has 100 turns and the transformation ratio is also 100. The input voltage and power are 220 V and 1100 W, respectively. Calculate the

(a) number of turns in secondary

(b) current in primary

(c) voltage across secondary

(d) current in secondary

(e) power in secondary VIEW SOLUTION
• Question 25
(i) In Young's double-slit experiment, deduce the condition for (a) constructive and (b) destructive interferences at a point on the screen. Draw a graph showing variation of intensity in the interference pattern against position 'x' on the screen.

(b) Compare the interference pattern observed in Young's double-slit experiment with single-slit diffraction pattern, pointing out three distinguishing features.

OR

(i) Plot a graph to show variation of the angle of deviation as a function of angle of incidence for light passing through a prism. Derive an expression for refractive index of the prism in terms of angle of minimum deviation and angle of prism.

(ii) What is dispersion of light? What is its cause?

(iii) A ray of light incident normally on one face of a right isosceles prism is totally reflected, as shown in fig. What must be the minimum value of refractive index of glass? Give relevant calculations.

VIEW SOLUTION
• Question 26
(i) Define the term drift velocity.
(ii) On the basis of electron drift, derive an expression for resistivity of a conductor in terms of number density of free electrons and relaxation time. On what factors does resistivity of a conductor depend?
(iii) Why alloys like constantan and manganin are used for making standard resistors?

OR

(i) State the principle of working of a potentiometer.
(ii) In the following potentiometer circuit, AB is a uniform wire of length 1 m and resistance 10 Ω. Calculate the potential gradient along the wire and balance length AO (= l).

VIEW SOLUTION
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