*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**In what way is the behaviour of a diamagnetic material different from that of a paramagnetic, when kept in an external magnetic field?

VIEW SOLUTION**Q2**The plot of the variation of potential difference across a combination of three identical cells in series, versus current is shown below. What is the emf and internal resistance of each cell ?

VIEW SOLUTION

**Q3**Why does sun appear red at sunrise and sunset?

VIEW SOLUTION**Q4**A charge '

VIEW SOLUTION*q*' is moved from a point A above a dipole of dipole moment '*p*' to a point B below the dipole in equatorial plane without acceleration. Find the work done in the process.

**Q5**Name the essential components of a communication system.

VIEW SOLUTION

**Q6**Calculate the de-Broglie wavelength of the electron orbitting in the n = 2 state of hydrogen atom.

VIEW SOLUTION**Q7**A battery of emf 12 V and internal resistance 2 Ω is connected to a 4 Ω resistor as shown in the figure.

VIEW SOLUTION

(a) Show that a voltmeter when placed across the cell and across the resistor, in turn, gives the same reading.

(b) To record the voltage and the current in the circuit, why is voltmeter placed in parallel and ammeter in series in the circuit?

**Q8**Define ionization energy.

How would the ionization energy change when electron in hydrogen atom is replaced by a particle of mass 200 times that of electron but having the same charge ?

**OR**

Calculate the shortest wavelength of the spectral lines emitted in Balmer series.

[Given Rydberg constant, R = 10^{7}m^{–1}] VIEW SOLUTION**Q9**Define modulation index. Why is it kept low? What is the role of a bandpass filter ?

VIEW SOLUTION**Q10**A ray PQ incident normally on the refracting face BA is refracted in the prism BAC made of material of refractive index 1.5. Complete the path of ray through the prism. From which face will the ray emerge? Justify your answer.

VIEW SOLUTION

**Q11**(i) Derive an expression for drift velocity of free electrons.

VIEW SOLUTION

(ii) How does drift velocity of electrons in a metallic conductor vary with increase in temperature? Explain.**Q12**(a) Write the basic nuclear process involved in the emission of β

^{+}in a symbolic form, by a radioactive nucleus.

(b) In the reactions given below:

(i) ${}_{6}{}^{11}\mathrm{C}\to {}_{y}{}^{z}\mathrm{B}+x+v$

(ii) ${}_{6}{}^{12}\mathrm{C}+{}_{6}{}^{12}\mathrm{C}\to {}_{\mathrm{a}}{}^{20}\mathrm{Ne}+{}_{\mathrm{b}}{}^{\mathrm{c}}\mathrm{He}$

Find the values of*x, y*, and*z*and*a, b*and*c*. VIEW SOLUTION**Q13**Sketch the graphs showing variation of stopping potential with frequency of incident radiations for two photosensitive materials A and B having threshold frequencies

VIEW SOLUTION*v*_{A}>*v*_{B}.

(i) In which case is the stopping potential more and why?

(ii) Does the slope of the graph depend on the nature of the material used? Explain.**Q14**(i) State law of Malus.

VIEW SOLUTION

(ii) Draw a graph showing the variation of intensity (I) of polarised light transmitted by an analyser with angle (θ) between polariser and analyser.

(iii) What is the value of refractive index of a medium of polarising angle 60°?**Q15**Define an equipotential surface. Draw equipotential surfaces:

VIEW SOLUTION

(i) in the case of a single point charge and

(ii) in a constant electric field in Z-direction.

Why the equipotential surfaces about a single charge are not equidistant?

(iii) Can electric field exist tangential to an equipotential surface? Give reason.**Q16**Use Biot-Savart law to derive the expression for the magnetic field on the axis of a current carrying circular loop of radius

VIEW SOLUTION*R*.

Draw the magnetic field lines due to a circular wire carrying current*I*.**Q17**Define the term wave front. State Huygen's principle.

Consider a plane wave front incident on a thin convex lens. Draw a proper diagram to show how the incident wave front traverses through the lens and after refraction focusses on the focal point of the lens, giving the shape of the emergent wave front.

**OR**

Explain the following, giving reasons:

(i) When monochromatic light is incident on a surface separating two media, the reflected and refracted light both have the same frequency as the incident frequency.

(ii) When light travels from a rarer to a denser medium, the speed decreases. Does this decrease in speed imply a reduction in the energy carried by the wave?

(iii) In the wave picture of light, intensity of light is determined by the square of the amplitude of the wave. What determines the intensity in the photon picture of light? VIEW SOLUTION**Q18**For a CE-transistor amplifier, the audio signal voltage across the collector resistance of 2 kΩ is 2 V. Suppose 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**Q19**(i) Identify the part of the electromagnetic spectrum which is:

(a) suitable for radar system used in aircraft navigation.

(b) produced by bombarding a metal target by high speed electrons.

(ii) Why does a galvanometer show a momentary deflection at the time of charging or discharging a capacitor? Write the necessary expression to explain this observation. VIEW SOLUTION**Q20**(i) Which mode of propagation is used by shortwave broadcast services having frequency range from a few MHz upto 30 MHz? Explain diagrammatically how long distance communication can be achieved by this mode.

VIEW SOLUTION

(ii) Why is there an upper limit to frequency of waves used in this mode?**Q21**(i) Explain with the help of a diagram the formation of depletion region and barrier potential in a pn junction.

VIEW SOLUTION

(ii) Draw the circuit diagram of a half wave rectifier and explain its working.**Q22**(i) When an AC source is connected to an ideal inductor show that the average power supplied by the source over a complete cycle is zero.

VIEW SOLUTION

(ii) A lamp is connected in series with an inductor and an AC source. What happens to the brightness of the lamp when the key is plugged in and an iron rod is inserted inside the inductor? Explain.

**Q23**Ram is a student of class X in a village school. His uncle gifted him a bicycle with a dynamo fitted in it. He was very excited to get it. While cycling during night, he could light the bulb and see the objects on the road. He, however, did not know how this device works. he asked this question to his teacher. The teacher considered it an opportunity to explain the working to the whole class.

VIEW SOLUTION

Answer the following questions:

(a) State the principle and working of a dynamo.

(b) Write two values each displayed by Ram and his school teacher.

**Q24**(i) Derive the mathematical relation between refractive indices

*n*_{1}and*n*_{2}_{ }of two radii and radius of curvature*R*for refraction at a convex spherical surface. Consider the object to be a point since lying on the principle axis in rarer medium of refractive index*n*_{1}and a real image formed in the denser medium of refractive index*n*_{2}. Hence, derive lens maker's formula.

(ii) Light from a point source in air falls on a convex spherical glass surface of refractive index 1.5 and radius of curvature 20 cm. The distance of light source from the glass surface is 100 cm. At what position is the image formed?

**OR**

(a) Draw a labelled ray diagram to obtain the real image formed by an astronomical telescope in normal adjustment position. Define its magnifying power.

(b) You are given three lenses of power 0.5 D, 4 D and 10 D to design a telescope.(i) Which lenses should be used as objective and eyepiece? Justify your answer.VIEW SOLUTION

(ii) Why is the aperture of the objective preferred to be large?**Q25**(i) Use Gauss's law to find the electric field due to a uniformly charged infinite plane sheet. What is the direction of field for positive and negative charge densities?

(ii) Find the ratio of the potential differences that must be applied across the parallel and series combination of two capacitors C_{1}and C_{2}with their capacitances in the ratio 1 : 2 so that the energy stored in the two cases becomes the same.

**OR**

(i) If two similar large plates, each of area A having surface charge densities +σ and –σ are separated by a distance d in air, find the expressions for

(a) field at points between the two plates and on outer side of the plates. Specify the direction of the field in each case.

(b) the potential difference between the plates.

(c) the capacitance of the capacitor so formed.

(ii) Two metallic spheres of Radii R and 2R are charged so that both of these have same surface charge density σ. If they are connected to each other with a conducting wire, inn which direction will the charge flow and why? VIEW SOLUTION**Q26**(i) Draw a labelled diagram of a step-down transformer. State the principle of its working.

(ii) Express the turn ratio in terms of voltages.

(iii) Find the ratio of primary and secondary currents in terms of turn ratio in an ideal transformer.

(iv) How much current is drawn by the primary of a transformer connected to 220 V supply when it delivers power to a 110 V − 550 W refrigerator?

**OR**

VIEW SOLUTION

(a) Explain the meaning of the term mutual inductance. Consider two concentric circular coils, one of radius r_{1}and the other of radius r_{2}(r_{1}< r_{2}) placed coaxially with centres coinciding with each other. Obtain the expression for the mutual inductance of the arrangement.

(b) A rectangular coil of area A, having number of turns N is rotated at 'f' revolutions per second in a uniform magnetic field B, the field being perpendicular to the coil. Prove that the maximum emf induced in the coil is 2*πf*NBA.

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