*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.*

**Q1**A long straight current carrying wire passes normally through the centre of circular loop. If the current through the wire increases, will there be an induced emf in the loop? Justify.

VIEW SOLUTION**Q2**How is the speed of em-waves in vacuum determined by the electric and magnetic field?

VIEW SOLUTION**(1)****Q3**Name the junction diode whose I-V characteristics are drawn below:

VIEW SOLUTION**(1)**

**Q4**At a place, the horizontal component of earth's magnetic field is B and angle of dip is 60°. What is the value of horizontal component of the earth's magnetic field at equator?

VIEW SOLUTION**(1)****Q5**Does the charge given to a metallic sphere depend on whether it is hollow or solid? Give reason for your answer.

VIEW SOLUTION**(1)**

**Q6**Define the distance of closest approach. An α-particle of kinetic energy 'K' is bombarded on a thin gold foil. The distance of the closest approach is 'r'. What will be the distance of closest approach for an α-particle of double the kinetic energy?

**(2)**

**OR**

Write two important limitations of Rutherford nuclear model of the atom. VIEW SOLUTION**Q7**When are two objects just resolved? Explain. How can the resolving power of a compound microscope be increased? Use relevant formula to support your answer.

VIEW SOLUTION**(2)****Q8**(i) What is the line of sight communication?

VIEW SOLUTION**(2)**

(ii) Why is it not possible to use sky waves for transmission of TV signals? Upto what distance can a signal be transmitted using an antenna of height '*h*'?**Q9**An α-particle and a proton are accelerated through the same potential difference. Find the ratio of their de Broglie wavelength.

VIEW SOLUTION**(2)****Q10**How does Ampere-Maxwell law explain the flow of current through a capacitor when it is being charged by a battery? Write the expression for the displacement current in terms of the rate of change of electric flux.

VIEW SOLUTION**(2)**

**Q11**Describe the working principle of a moving coil galvanometer. Why is it necessary to use (i) a radial magnetic field and (ii) a cylindrical soft iron core in a galvanometer? Write the expression for current sensitivity of the galvanometer.

**(3)**

Can a galvanometer as such be used for measuring the current? Explain.

**OR**

(a) Define the term 'self-inductance' and write its S.I. unit.

(b) Obtain the expression for the the mutual inductance of two long co-axial solenoids S_{1}and S_{2}wound one over the other, each of length L and radii r_{1}and r_{2}and n_{1}and n_{2}number of turns per unit length, when a current I is set up in the outer solenoid S_{2}. VIEW SOLUTION**Q12**(i) A radioactive nucleus 'A' undergoes a series of decays as given below:

**(3)**$\mathrm{A}\stackrel{\mathrm{\alpha}}{\to}{\mathrm{A}}_{1}\stackrel{\mathrm{\beta}}{\to}{\mathrm{A}}_{2}\stackrel{\mathrm{\alpha}}{\to}{\mathrm{A}}_{3}\stackrel{\mathrm{\gamma}}{\to}{\mathrm{A}}_{4}$

The mass number and atomic number of A_{2}are 176 and 71 respectively. Determine the mass and atomic numbers of A_{4}and A.

(ii) Write the basic nuclear process underlying β^{+}and β^{–}decays. VIEW SOLUTION**Q13**For a CE-transistor amplifier, the audio signal voltage across the collector resistance of 2 kΩ is 2 V. Given the current amplification factor of the transistor is 100, find the input signal voltage and base current, if the base resistance is 1 kΩ.

VIEW SOLUTION**Q14**(i) State two important features of Einstein's photoelectric equation.

VIEW SOLUTION**(3)**

(ii) Radiation of frequency 10^{15}Hz is incident on two photosensitive surface P and Q. There is no photoemission from surface P. Photoemission occurs from surface Q but photoelectrons have zero kinetic energy. Explain these observations and find the value of work function for surface Q.**Q15**(i) Find the value of the phase difference between the current and the voltage in the series LCR circuit shown below. Which one leads in phase : current or voltage ?

VIEW SOLUTION

(ii) Without making any other change, find the value of the additional capacitor C_{1}, to be connected in parallel with the capacitor C, in order to make the power factor of the circuit unity.

**Q16**(i) Obtain the expression for the torque $\overrightarrow{\tau}$ experienced by an electric dipole of dipole moment $\overrightarrow{\mathrm{P}}$ in a uniform electric field, $\overrightarrow{\mathrm{E}}$.

VIEW SOLUTION**(3)**

(ii) What will happen if the field were not uniform?**Q17**Explain briefly with the help of necessary diagrams, the forward and the reverse biasing of a p-n junction diode. Also draw their characteristic curves in the two cases.

VIEW SOLUTION**(3)****Q18**(i) A ray of light incident on face AB of an equilateral glass prism, shows minimum deviation of 30°. Calculate the speed of light through the prism.

VIEW SOLUTION

(ii) Find the angle of incidence at face AB so that the emergent ray grazes along the face AC.**Q19**Define the term 'amplitude modulation'. Explain any two factors which justify the need for modulating a low frequency base-band signal.

VIEW SOLUTION**Q20**Two identical capacitors of 12 pF each are connected in series across a battery of 50 V. How much electrostatic energy is stored in the combination? If these were connected in parallel across the same battery, how much energy will be stored in the combination now?

VIEW SOLUTION

Also find the charge drawn from the battery in each case.**(3)****Q21**(a) Write the expression for the force $\overrightarrow{\mathrm{F}}$ acting on a particle of mass m and charge q moving with velocity $\overrightarrow{\mathrm{V}}$ in a magnetic field $\overrightarrow{\mathrm{B}}$, Under what conditions will it move in (i) a circular path and (ii) a helical path?

VIEW SOLUTION**(3)**

(b) Show that the kinetic energy of the particle moving in a magnetic field remains constant.**Q22**A resistance of R draws current from a potentiometer. The potentiometer wire, AB, has a total resistance of R

VIEW SOLUTION_{o}. A voltage V is supplied to the potentiometer. Derive an expression for the voltage across R when the sliding contact is in the middle of potentiometer wire.

**Q23**Mrs. Rashmi Singh broke her reading glasses. When she went to the shopkeeper to order new spects, he suggested that she should get spectacles with plastic lenses instead of glass lenses. On getting the new spectacles, she found that the new ones were thicker than the earlier ones. She asked this question to the shopkeeper but he could not offer satisfactory explanation for this. At home, Mrs. Singh raised the same question to her daughter Anuja who explained why plastic lenses were thicker.

VIEW SOLUTION**(4)**

(a) Write two qualities displayed each by Anuja and her mother.

(b) How do you explain this fact using lens maker's formula?

**Q24**(i) Derive an expression for drift velocity of electrons in a conductor. Hence deduce Ohm's law.**(5)**

(ii) A wire whose cross-sectional area is increasing linearly from its one end to the other, is connected across a battery of V volts.Which of the following quantities remain constant in the wire?

(a) drift speed

(b) current density

(c) electric current

(d) electric field**OR**(i) State the two Kirchhoff's laws. Explain briefly how these rules are justified.(ii) The current is drawn from a cell of emf E and internal resistance r connected to the network of resistors each of resistance r as shown in the figure. Obtain the expression for (i) the current draw from the cell and (ii) the power consumed in the network.VIEW SOLUTION

**Q25**(a) Draw a labelled diagram of AC generator. Derive the expression for the instantaneous value of the emf induced in the coil.

(b) A circular coil of cross-sectional area 200 cm^{2}and 20 turns is rotated about the vertical diameter with angular speed of 50 rad s^{−1}in a uniform magnetic field of magnitude 3.0 × 10^{−2}T. Calculate the maximum value of the current in the coil.

**OR**

(a) Draw a labelled diagram of a step-up transformer. Obtain the ratio of secondary to primary voltage in terms of number of turn and currents in the two coils.

(b) A power transmission line feeds input power at 2200 V to a step-down transformer with its primary windings having 300 turns. Find the number of turns in the secondary to get the power output at 220 V. VIEW SOLUTION**Q26**(a) Distinguish between unpolarized light and linearly polarized light. How does one get linearly polarised light with the help of a polaroid?

**(5)**

(b) A narrow beam of unpolarised light of intensity I_{0}is incident on a polaroid P_{1}. The light transmitted by it is then incident on a second polariod P_{2}with its pass axis making angle of 60° relative to the pass axis of P_{1}. Find the intensity of the light transmitted by P_{2}.

**OR**

(a) Explain two features to distinguish between the interference pattern in Young's double slit experiment with the diffraction pattern obtained due to a single slit.

(b) A monochromatic light of wavelength 500 nm is incident normally on a single slit of width 0.2 mm to produce a diffraction pattern. Find the angular width of the central maximum obtained on the screen.

Estimate the number of fringes obtained in Young's double slit experiment with fringe width 0.5 mm, which can be accommodated within the region of total angular spread of the central maximum due to single slit. VIEW SOLUTION

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