*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**Why does the Sun look reddish at sunset or sunrise ?

VIEW SOLUTION**Q2**The power factor of an a.c. circuit is 0.5. What is the phase difference between voltage and current in this circuit ?

VIEW SOLUTION**Q3**Is it necessary for a transmitting antenna to be at the same height as that of receiving antenna for LOS communication ?

VIEW SOLUTION**Q4**Plot a graph showing the variation of resistivity of a conductor with temperature.

VIEW SOLUTION**Q5**Write the expression for the torque $\overrightarrow{\tau}$ acting on a dipole of dipole moment $\overrightarrow{p}$ placed in an electric field $\overrightarrow{E}$.

VIEW SOLUTION

**Q6**(a) Write the

VIEW SOLUTION*β*-decay of tritium in symbolic form.

(b) Why is it experimentally found difficult to detect neutrinos in this process ?**Q7**Given the resistances of 1 Ω, 2 Ω and 3 Ω, how will you combine them to get an equivalent resistance of $\left(\mathrm{i}\right)\frac{11}{3}\mathrm{\Omega}\mathrm{and}\left(\mathrm{ii}\right)\frac{11}{5}\mathrm{\Omega}$?

VIEW SOLUTION**Q8**The

VIEW SOLUTION*V*−*I*characteristic of a silicon diode is as shown in the figure. Calculate the resistance of the diode at (i)*I*= 15 mA and (ii)*V*= −10 V.

**Q9**How does the refractive index of a transparent medium depend on the wavelength of incident light used ?

Velocity of light in glass is 2 × 10^{8}m/s and in air is 3 × 10^{8}m/s. If the ray of light passes from glass to air, calculate the value of critical angle.

**OR**

An equiconvex lens of focal length '*f*' is cut into two identical plane convex lenses. How will the power of each part be related to the focal length of the original lens ?

A double convex lens of + 5 D is made of glass of refractive index 1.55 with both faces of equal radii of curvature. Find the value of its radius of curvature. VIEW SOLUTION**Q10**The kinetic energy of the electron orbiting in the first excited state of hydrogen atom is 3.4 eV. Determine the de Broglie wavelength associated with it.

VIEW SOLUTION

**Q11**Write briefly the important processes that occur during the formation of

VIEW SOLUTION*p−n*junction. With the help of necessary diagrams, explain the term 'barrier potential'.**Q12**A beam of monochromatic radiation is incident on a photosensitive surface. Answer the following questions giving reasons :

(a) Do the emitted photoelectrons have the same kinetic energy?

(b) Does the kinetic energy of the emitted electrons depend on the intensity of incident radiation?

(c) On what factors does the number of emitted photoelectrons depend?

VIEW SOLUTION**Q13**(a) What is an 'integrated circuit (I.C.) ? Distinguish between (i) linear I.C. and (ii) digital I.C.

(b) Identify the equivalent gate for the following circuit and write its truth table.

VIEW SOLUTION

**Q14**Why does a galvanometer when connected in series with a capacitor show a momentary deflection, when it is being charged or discharged?

How does this observation lead to modifying the Ampere's circuital law?

Hence write the generalised expression of Ampere's law.

VIEW SOLUTION**Q15**In the given circuit in the steady state, obtain the expressions for (a) the potential drop (b) the charge and (c) the energy stored in the capacitor, C.

VIEW SOLUTION

**Q16**A circular coil of radius 10 cm, 500 turns and resistance 200 Ω is placed with its plane perpendicular to the horizontal component of the Earth's magnetic field. It is rotated about its vertical diameter through 180° in 0.25 s. Estimate the magnitude of the emf and current induced in the coil. (Horizontal component of the Earth's magnetic field at the place is 3.0 ✕ 10

VIEW SOLUTION^{−5}T)**Q17**Using Rydberg formula, calculate the longest wavelength belonging to Lyman and Balmer series. In which region of hydrogen spectrum do these transitions lie?

VIEW SOLUTION

[Given R = 1.1 ✕ 10^{7}m^{−1}]**Q18**Why cannot two independent monochromatic sources produce sustained interference pattern?

VIEW SOLUTION

Deduce, with the help of Young's arrangement to produce interference pattern, an expression for the fringe width.**Q19**Answer the following questions :

VIEW SOLUTION

(a) Define 'bandwidth' and describe briefly its importance in communicating signals.

(b) Distinguish between digital and analogue signals.

(c) Write the functions of transducer and repeater.**Q20**Four charges +

*q*, −*q*, +*q*and −*q*are to be arranged respectively at the four corners of a square ABCD of side 'a'.

(a) Find the work required to put together this arrangement.

(b) A charge q_{0}is brought to the centre of the square, the four charges being held fixed. How much extra work is needed to do this ?

**OR**

Three point charges +*q*each are kept at the vertices of an equilateral triangle of side '*l*'. Determine the magnitude and sign of the charge to be kept at its centroid so that the charges at the vertices remain in equilibrium. VIEW SOLUTION**Q21**(a) An electron moving horizontally with a velocity of 4 ✕ 10

VIEW SOLUTION^{4}m/s enters a region of uniform magnetic field of 10^{−5}T acting vertically upward as shown in the figure. Draw its trajectory and find out the time it takes to come out of the region of magnetic field.

(b) A straight wire of mass 200 g and length 1.5 m carries a current of 2 A. It is suspended in mid air by a uniform magnetic field*B*. What is the magnitude of the magnetic field?**Q22**A plane wavefront propagating in a medium of refractive index '

VIEW SOLUTION*μ*_{1}' is incident on a plane surface making the angle of incidence '*i*' as shown in the figure. It enters into a medium of refractive index '*μ*_{2}' (μ_{2}> μ_{1}). Use Huygens' construction of secondary wavelets to trace the propagation of the refracted wavefront. Hence verify Snell's law of refraction.

**Q23**Sushil is in the habit of charging his mobile and then leaving the charger connected through the mains with the switch on. When his sister Asha pointed it out to him, he replied there was no harm as the mobile had been disconnected. Asha then explained to him and convinced him, how the energy was still being wasted as the charger was continuously consuming energy.

Answer the following questions :

(a) What values did Asha display in convincing her brother?

(b) What measures, in your view, should be adopted to minimise the wastage of electric energy in your households?

(c) Imagine an electric appliance of 2 W, left connected to the mains for 20 hours. Estimate the amount of electrical energy wasted.

VIEW SOLUTION

**Q24**(a) A small conducting sphere of radius '

*r*' carrying a charge +*q*is surrounded by a large concentric conducting shell of radius*R*on which a charge +*Q*is placed. Using Gauss's law, derive the expressions for the electric field at a point '*x*'

(i) between the sphere and the shell (*r*<*x*<*R*),

(ii) outside the spherical shell.

(b) Show that if we connect the smaller and the outer sphere by a wire, the charge*q*on the former will always flow to the latter, independent of how large the charge*Q*is.

**OR**

(a) Consider a system of n charges*q*_{1},*q*_{2}, ...*q*_{n}with position vectors $\overrightarrow{{\mathrm{r}}_{1},}\overrightarrow{{\mathrm{r}}_{2},}\overrightarrow{{\mathrm{r}}_{3},}...\overrightarrow{{\mathrm{r}}_{\mathrm{n}}}$ relative to some origin 'O'. Deduce the expression for the net electric field $\overrightarrow{\mathrm{E}}$ at a point P with position vector $\overrightarrow{{\mathrm{r}}_{\mathrm{p}},}$due to this system of charges.

(b) Find the resultant electric field due to an electric dipole of dipole moment, 2*aq*, (2*a*being the separation between the charges $\pm $ q) at a point distant 'x' on its equator. VIEW SOLUTION**Q25**Draw a ray diagram showing the image formation of a distant object by a refracting telescope. Define its magnifying power and write the two important factors considered to increase the magnifying power.

Describe briefly the two main limitations and explain how far these can be minimized in a reflecting telescope.

**OR**

(a) Draw a ray diagram showing image formation in a compound microscope. Define the term 'limit of resolution' and name the factors on which it depends. How is it related to resolving power of a microscope ?

(b) Suggest two ways by which the resolving power of a microscope can be increased.

(c) "A telescope resolves whereas a microscope magnifies." Justify this statement. VIEW SOLUTION**Q26**Write any two important points of similarities and differences each between Coulomb's law for the electrostatic field and Biot-Savart's law of the magnetic field.

Use Biot-Savart's law to find the expression for the magnetic field due to a circular loop of radius '*r*' carrying current '*I*', at its centre.

**OR**

What are eddy currents? How are they produced?

Describe briefly three main useful application of eddy currents. VIEW SOLUTION

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