General Instructions:

Read the following instructions very carefully and strictly follow them:

(i) This question paper comprises four Sections – A, B, C and D.

(ii) There are 37 questions in the question paper. All questions are compulsory.

(iii) Section A – Questions no. 1 to 20 are very short answer type questions, carrying one mark each.

(iv) Section B – Questions no. 21 to 27 are short answer type questions, carrying two marks each.

(v) Section C – Questions no. 28 to 34 are long answer type questions, carrying three marks each.

(vi) Section D – Questions no. 35 to 37 are also long answer type questions, carrying five marks each.

(vii) There is no overall choice in the question paper. However, an internal choice has been provided in 2 questions of 1 mark, 2 questions of 2 marks, 1 question of three marks and all the 3 questions of five marks.

You have to attempt only one of the choices in such questions.

(viii) In addition to this, separate instructions are given with each section and

question, wherever necessary.

(ix) Use of calculators and log tables is not permitted.

(x) You may use the following values of physical constants wherever necessary.

Mass of neutron = 1.675 × 10⁻²⁷ kg

Mass of proton = 1.673 × 10²⁷ kg

Avogadro’s number = 6.023 × 10²³ per gram mole

Boltzmann constant = 1.38 × 10⁻²³ JK^-1

 

Section A

 

Note: Select the most appropriate option from those given below each question:

 

Question 1:

If the net electric flux through a closed surface is zero, then we can infer

(A) no net charge is enclosed by the surface.

(B) uniform electric field exists within the surface.

(C) electric potential varies from point to point inside the surface.

(D) charge is present inside the surface.

 

Question 2:

An electric dipole consisting of charges + q and – q separated by a distance L is in stable equilibrium in a uniform electric field E.

The electrostatic potential energy of the dipole is

(A) qLE

(B) zero

(C) –qLE

(D) –2 qEL

 

Question 3:

A potentiometer can measure emf of a cell because

(A) the sensitivity of potentiometer is large.

(B) no current is drawn from the cell at balance.

(C) no current flows in the wire of potentiometer at balance.

(D) internal resistance of cell is neglected.

 

Question 4:

Two resistors R₁ and R₂ of 4 W and 6 W are connected in parallel across a battery. The ratio of power dissipated in them, P₁ : P₂ will be

(A) 4: 9

(B) 3: 2

(C) 9: 4

(D) 2: 3

 

Question 5:

The magnetic dipole moment of a current carrying coil does not depend upon

(A) number of turns of the coil.

(B) cross-sectional area of the coil.

(C) current flowing in the coil.

(D) material of the turns of the coil.

 

Question 6:

Larger aperture of objective lens in an astronomical telescope

(A) increases the resolving power of telescope.

(B) decreases the brightness of the image.

(C) increases the size of the image.

(D) decreases the length of the telescope.

 

Question 7:

A biconvex lens of glass having refractive index 1·47 is immersed in a liquid. It becomes invisible and behaves as a plane glass plate. The refractive index of the liquid is

(A) 1·47

(B) 1·62

(C) 1·33

(D) 1·51

 

Question 8:

For a glass prism, the angle of minimum deviation will be smallest for the light of

(A) red colour

(B) blue colour

(C) yellow colour

(D) green colour

 

Question 9:

Which of the following statements is not correct according to Rutherford model?

(A) Most of the space inside an atom is empty.

(B) The electrons revolve around the nucleus under the influence of coulomb force acting on them.

(C) Most part of the mass of the atom and its positive charge are concentrated at its centre.

(D) The stability of atom was established by the model.

 

Question 10:

Photons of energies 1 eV and 2 eV are successively incident on a metallic surface of work function 0·5 eV. The ratio of kinetic energy of most energetic photoelectrons in the two cases will be

(A) 1: 2

(B) 1: 1

(C) 1: 3

(D) 1: 4

 

Note: Fill in the blanks with appropriate answer:

 

Question 11:

The magnetic field and angle of dip at a place on the earth are 0·3 G and 30°, respectively. The value of vertical component of the earth’s magnetic field at the place is _____.

 

Question 12:

Laminated iron sheets are used to minimize ______ currents in the core of a transformer.

 

Question 13:

The number of turns of a solenoid are doubled without changing its length and area of cross-section. The self-inductance of the solenoid will become ______ times.

 

Question 14:

According to Bohr’s atomic model, the circumference of the electron orbitis always an ______ multiple of de Broglie wavelength.

                                                                        OR

In β-decay, the parent and daughter nuclei have the same number of ______.

 

Question 15:

A ray of light on passing through an equilateral glass prism, suffers a minimum deviation equal to the angle of the prism. The value of refractive index of the material of the prism is ______.

 

Note: Answer the following:

 

Question 16:

Write the mathematical form of Ampere-Maxwell circuital law.

 

Question 17:

How does an increase in doping concentration affect the width of depletion layer of a p-n junction diode?

 

Question 18:

The nuclear radius of ₁₃AI²⁷ is 3·6 fermi. Find the nuclear radius of ₂₉Cu⁶⁴.

                                                            OR

A proton and an electron have equal speeds. Find the ratio of de Broglie wavelengths associated with them.

 

Question 19:

The variation of the stopping potential (V_o) with the frequency (v) of the light incident on two different photosensitive surfaces M₁ and M₂ is shown in the figure. Identify the surface which has greater value of the work function.

                                                                    

 

Question 20:

Why cannot we use Si and Ge in fabrication of visible LEDs?

 

SECTION B

 

Question 21:

Explain the principle of working of a meter bridge. Draw the circuit diagram for determination of an unknown resistance using it.

 

Question 22:

The space between the plates of a parallel plate capacitor is completely filled in two ways. In the first case, it is filled with a slab of dielectric constant K. In the second case, it is filled with two slabs of equal thickness and dielectric constants K₁ and K₂ respectively as shown in the figure. The capacitance of the capacitor is same in the two cases. Obtain the relationship between K, K₁ and K₂.

                       

 

Question 23:

Define the term ‘Half-life’ of a radioactive substance. Two different radioactive substances have half-lives T₁ and T₂ and number of undecayed atoms at aninstant, N₁ and N₂, respectively. Find the ratio of their activities at that instant.

 

Question 24:

Define wave front of a travelling wave. Using Huygens principle, obtain the law of refraction at a plane interface when light passes from a denser to rarer medium.

                                                                                  OR

Using lens maker’s formula, derive the thin lens formula   for a biconvex lens.

 

Question 25:

Two long straight parallel wires A and B separated by a distance d, carry equal current I flowing in same direction as shown in the figure.

                                                                         

(a) Find the magnetic field at a point P situated between them at a distance x from one wire.

(b) Show graphically the variation of the magnetic field with distance x for 0 < x < d.

 

Question 26:

Using Bohr’s atomic model, derive the expression for the radius of n^th orbit of the revolving electron in a hydrogen atom.

                                                                                   OR

(a) Write two main observations of photoelectric effect experiment which could only be explained by Einstein’s photoelectric equation.

(b) Draw a graph showing variation of photocurrent with the anode potential of a photocell.

 

Question 27:

Explain the terms ‘depletion layer’ and ‘potential barrier’ in a p-n junction diode. How are the (a) width of depletion layer, and (b) value of potential barrier affected when the p-n junction is forward biased?

 

Question 28:

(a) Two cells of emf E₁ and E₂ have their internal resistances r₁ and r₂, respectively. Deduce an expression for the equivalent emf and internal resistance of their parallel combination when connected across an external resistance R. Assume that the two cells are supporting each other.

(b) In case the two cells are identical, each of emf ԑ = 5V and internal resistance r = 2W, calculate the voltage across the external resistance R = 10 W.

 

Question 29:

(a) Write an expression of magnetic moment associated with a current (I) carrying circular coil of radius r having N turns.

(b) Consider the above-mentioned coil placed in YZ plane with its centre at the origin. Derive expression for the value of magnetic field due to it at point (x, 0, 0).

                                                                            OR

(a) Define current sensitivity of a galvanometer. Write its expression.

(b) A galvanometer has resistance G and shows full scale deflection for current Ig.

(i) How can it be converted into an ammeter to measure current up to I₀ (I₀ > I_g)?

(ii) What is the effective resistance of this ammeter?

 

Question 30:

A resistance R and a capacitor C are connected in series to a source V =  V₀ sin wt. Find:

(a) The peak value of the voltage across the (i) resistance and (ii) capacitor.

(b) The phase difference between the applied voltage and current. Which of them is ahead?

 

Question 31:

What is the effect on the interference fringes in Young’s double slit experiment due to each of the following operations? Justify your answers. 

(a) The screen is moved away from the plane of the slits.

(b) The separation between slits is increased.

(c) The source slit is moved closer to the plane of double slit.

 

Question 32:

(a) Write the expression for the speed of light in a material medium of relative permittivity  and relative magnetic permeability .

(b) Write the wavelength range and name of the electromagnetic waves which are used in (i) radar systems for aircraft navigation, and (ii) Earth satellites to observe the growth of the crops.

 

Question 33:

The nucleusnucleus  , initially at rest, decays into  by emitting an 

The binding energies per nucleon of the parent nucleus, the daughter nucleus and a-particle are 7·8 MeV, 7·835 MeV and 7·07 MeV, respectively. Assuming the daughter nucleus to be formed in the unexcited state and neglecting its share in the energy of the reaction, find the speed of the emitted a-particle. (Mass of a-particle = 6.68 * 10^–27 kg)

 

Question 34:

(a) Draw circuit diagram and explain the working of a Zener diode as a dc voltage regulator with the help of its I-V characteristic.

(b) What is the purpose of heavy doping of p- and n-sides of a Zener diode?

 

Section-D

 

Question 35:

(a) Using Gauss law, derive expression for electric field due to a spherical shell of uniform charge distribution s and radius R at a point lying at a distance x from the centre of shell, such that (i) 0 < x < R, and (ii) x > R.

(b) An electric field is uniform and acts along + x direction in the region of positive x. It is also uniform with the same magnitude but acts in – x direction in the region of negative x. The value of the field is E = 200 N/C for x > 0 and E = – 200 N/C for x < 0. A right circular cylinder of length 20 cm and radius 5 cm has its centre at the origin and its axis along the x-axis so that one flat face is at x = +10 cm and the other is at x = – 10 cm. Find: 

(i) The net outward flux through the cylinder.

(ii) The net charge present inside the cylinder.

 

Question 36:

(a) Derive the expression for the torque acting on the rectangular current carrying coil of a galvanometer. Why is the magnetic field made radial?

(b) An  is accelerated through a potential difference of 10 kV and moves along x-axis. It enters in a region of uniform magnetic field

B = 2 ´ 10^–3 T acting along y-axis. Find the radius of its path. (Take mass of  = 6·4 ´ 10^–27 kg)

                                                                                         OR

(a) With the help of a labelled diagram, explain the working of a step-up transformer. Give reasons to explain the following:

(i) The core of the transformer is laminated.

(ii) Thick copper wire is used in windings.

(b) A conducting rod PQ of length 20 cm and resistance 0·1 W rests on two smooth parallel rails of negligible resistance AA' and CC'. It can slide on the rails and the arrangement is positioned between the poles of a permanent magnet producing uniform magnetic field B = 0·4 T. The rails, the rod and the magnetic field are in three mutually perpendicular directions as shown in the figure. If the ends A and C of the rails are short circuited, find the

(i) external force required to move the rod with uniform velocity v = 10 cm/s, and

(ii) power required to do so.

                                                                   

 

Question 37:

(a) Draw the ray diagram of an astronomical telescope when the final image is formed at infinity. Write the expression for the resolving power of the telescope.

(b) An astronomical telescope has an objective lens of focal length 20 m and eyepiece of focal length 1 cm.

(i) Find the angular magnification of the telescope.

(ii) If this telescope is used to view the Moon, find the diameter of the image formed by the objective lens. Given the diameter of the Moon is 3·5 ´ 10⁶ m and radius of lunar orbit is 3·8 ´ 10⁸ m.

                                                                                                  OR

(a) An object is placed in front of a concave mirror. It is observed that a virtual image is formed. Draw the ray diagram to show the image formation and hence derive the mirror equation .

(b) An object is placed 30 cm in front of a plano-convex lens with its spherical A’ surface of radius of curvature 20 cm. If the refractive index of the material of the lens is 1·5, find the position and nature of the image formed.

 

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