(i) All questions are compulsory.

(ii) There are 30 questions in total. Question Nos. 1 to 8 are very short answer type questions and carry one mark each.

(iii) Question Nos. 9 to 18 carry two marks each, question 19 to 27 carry three marks each and question 28 to 30 carry five marks each.

(iii) 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 three questions of five marks each. You have to attempt only one of the choice in such questions.

(iv) Use of calculators is not permitted.

Q1 :

Why must electrostatic field be normal to the surface at every point of a charged conductor?

**Answer :**

In case of conductors the charge is present only on the outer surface. Inside the conductor the field is zero. And at the surface it has to be normal. If it is not normal to the surface, then it would have some non-zero component along the surface. The free charges on the surface would then experience a force and start moving. In a static situation, electrostatic field should not have tangential component, which in turn implies that the surface of a charged conductor must be normal to the surface at every point. If a conductor has no surface charge, then the field is zero.

Q2 :

Under what conditions does a biconvex lens of glass having a certain refractive index act as a plane glass sheet when immersed in a liquid?

**Answer :**

A biconvex lens will act like a plane sheet of glass if it is
immersed in a liquid having the same index of refraction as
itself. In this case, the focal length 1/*f* = 0 or
*f* → âˆž.

Q3 :

State de-Broglie hypothesis.

**Answer :**

de-Broglie Hypothesis states that—

Moving object sometimes acts as a wave and sometimes as a particle; or a wave is associated with the moving particle, which controls the particle in every respect. This wave associated with the moving particle is called matter wave or de Broglie wave, its wave length is given as

Where

*h* â†’
planck’s constant

*m* â†’ mass of the object

*v* â†’ velocity of the object

Q4 :

Name of physical quantity which remains same for microwaves of wavelength 1 mm and UV radiations of 1600 Ã… in vacuum.

**Answer :**

Q5 :

When electrons drift in a metal from lower to higher potential, does it mean that all the free electrons of the metal are moving in the same direction?

**Answer :**

Q6 :

Predict the direction of induced current in a metal ring when the
ring is moved towards a straight conductor with constant speed
*v*. The conductor is carrying current I in the
direction shown in the figure.

**Answer :**

Q7 :

The horizontal component of the earth”™s magnetic field at a place is B and angle of dip is 60Â°. What is the value of vertical component of earth”™s magnetic field at equator?

**Answer :**

Q8 :

Show on a graph, the variation of resistivity with temperature for a typical semiconductor.

**Answer :**

Q9 :

Draw a plot showing the variation of (i) electric field (E) and (ii) electric potential (V) with distance r due to a point charge Q.

**Answer :**

Q10 :

Derive the expression for the self inductance of a long solenoid
of cross sectional area A and length *l*, having
*n* turns per unit length.

**Answer :**

Q11 :

A ray of light, incident on an equilateral prism moves parallel to the base line of the prism inside it. Find the angle of incidence for this ray.

**Answer :**

Q12 :

The current in the forward bias is known to be more (~mA) than
the current in the reverse bias (~*Î¼*A). What is
the reason, then, to operate the photodiode in reverse bias?

**Answer :**

Q13 :

Distinguish between “Analog and Digital signals”™.

**OR**

Mention the function of any two of the following used in communication system:

(i) Transducer

(ii) Repeater

(iii) Transmitter

(iv) Bandpass Filter

**Answer :**

Q14 :

Define mutual inductance between two long coaxial solenoids. Find
out the expression for the mutual inductance of inner solenoid of
length *l* having the radius r_{1}
and the number of turns n_{1} per unit length
due to the second outer solenoid of same length and r_{2} number of turns per unit length.

**Answer :**

Q15 :

A cell of emf E and internal resistance r is connected to two
external resistance R_{1} and R_{2} and a perfect ammeter. The current in the circuit is
measured in four different situations:

(i) without any external resistance in the circuit

(ii) with resistance R_{1} only

(iii) with R_{1} and R_{2} in
series combination

(iv) with R_{1} and R_{2} in
parallel combination

The currents measured in the four cases are 0.42 A, 1.05 A, 1.4 A and 4.2 A, but not necessarily in the order. Identify the currents corresponding to the four cases mentioned above.

**Answer :**

Q16 :

Two identical circular loops, P and Q, each of radius r and carrying equal currents are

kept in the parallel planes having a common axis passing through O. The direction of current in P is clockwise and in Q is anti-clockwise as seen from O which is equidistant from the loops P and Q. Find the magnitude of the net magnetic field at O.

**Answer :**

Q17 :

A metallic rod of “L”™ length is rotated with angular frequency of “Ï‰”™ with one end hinged at the centre and the other end at the circumference of a circular metallic ring of radius L, about an axis passing through the centre and perpendicular to the plane of the ring. A constant and uniform magnetic field B parallel to the axis is present everywhere. Deduce the expression for the emf between the centre and the metallic ring.

**Answer :**

Q18 :

When an ideal capacitor is charged by a dc battery, no current flows. However, when an ac source is used, the current flows continuously. How does one explain this, based on the concept of displacement current?

**Answer :**

Q19 :

In the figure a long uniform potentiometer wire AB is having a
constant potential gradient along its length. The null points for
the two primary cells of emfs Îµ_{1}
and Îµ_{2} connected in the manner
shown are obtained at a distance of 120 cm and 300 cm from the
end A. Find (i) Îµ_{1}/
Îµ_{2} and (ii) position of null
point for the cell Îµ_{1}.

How is the sensitivity of a potentiometer increased?

**OR**

Using Kirchhoff”™s rules determine the value of unknown resistance R in the circuit so that no current flows through 4 Î© resistance. Also find the potential difference between A and D.

**Answer :**

Q20 :

The figure shows a series LCR circuit with L = 10.0 H, C = 40
*Î¼*F, R = 60 Î© connected to
a variable frequency 240 V source, calculate

(i) the angular frequency of the source which drives the circuit at resonance,

(ii) the current at the resonating frequency,

(iii) the rms potential drop across the inductor at resonance.

**Answer :**

Q21 :

(a) Why are coherent sources necessary to produce a sustained interference pattern?

(b) In Young”™s double slit experiment using
monochromatic light of wavelength *Î»*, the
intensity of light at a point on the screen where path difference
is *Î»*, is K units. Find out the intensity
of light at a point where path difference is *Î»*/3.

**Answer :**

Q22 :

A rectangular loop of wire of size 2 cm Ã— 5 cm carries a steady current of 1 A. A straight long wire carrying 4 A current is kept near the loop as shown. If the loop and the wire are coplanar, find (i) the torque acting on the loop and (ii) the magnitude and direction of the force on the loop due to the current carrying wire.

**Answer :**

Q23 :

Write Einstein”™s photoelectric equation. State clearly how this equation is obtained using the photon picture of electromagnetic radiation.

Write the three salient features observed in photoelectric effect which can be explained using this equation.

**Answer :**

Q24 :

(a) Using Bohr”™s second postulate of
quantization of orbital angular momentum show that the
circumference of the electron in the *n*^{th} orbital state in hydrogen atom is *n*
times the de Broglie wavelength associated with it.

(b) The electron in hydrogen atom is initially in the third excited state. What is the maximum number of spectral lines which can be emitted when it finally moves to the ground state?

**Answer :**

Q25 :

Use Huygens”™s principle to explain the formation of diffraction pattern due to a single slit illuminated by a monochromatic source of light.

When the width of the slit is made double the original width, how would this affect the size and intensity of the central diffraction band?

**Answer :**

Q26 :

(i) What characteristic property of nuclear force explains the constancy of binding energy per nucleon (BE/A) in the range of mass number “A”™ lying 30 < A < 170?

(ii) Show that the density of nucleus over a wide range of nuclei is constant-independent of mass number A.

**Answer :**

Q27 :

Name the three different modes of propagation of electromagnetic waves. Explain, using a proper diagram the mode of propagation used in the frequency range from a few MHz to 40 MHz.

**Answer :**

Q28 :

Explain the principle of a device that can build up high voltages of the order of a few million volts.

Draw a schematic diagram and explain the working of this device.

Is there any restriction on the upper limit of the high voltage set up in this machine? Explain.

**OR**

(a) Define electric flux. Write its S.I. units.

(b) Using Gauss”™s law, prove that the electric field at a point due to a uniformly charged infinite plane sheet is independent of the distance from it.

(c) How is the field directed if (i) the sheet is positively charged, (ii) negatively charged?

**Answer :**

Q29 :

Define magnifying power of a telescope. Write its expression.

A small telescope has an objective lens of focal length 150 cm and an eye piece of focal length 5 cm. If this telescope is used to view a 100 m high tower 3 km away, find the height of the final image when it is formed 25 cm away from the eye piece.

**OR**

How is the working of a telescope different from that of a microscope?

The focal lengths of the objective and eyepiece of a microscope are 1.25 cm and 5 cm respectively. Find the position of the object relative to the objective in order to obtain an angular magnification of 30 in normal adjustment.

**Answer :**

Q30 :

Draw a simple circuit of a CE
transistor amplifier. Explain its working. Show that the
voltage gain,
A_{V}, of the
amplifier is given by where Î²_{ac}is the current gain, R_{L}is the load resistance and r_{i}is the input resistance of the transistor. What is the
significance of the negative sign in the expression for the
voltage gain?

**OR**

(a) Draw the circuit diagram of a full wave rectifier using p-n junction diode.

Explain its working and show the output, input waveforms.

(b) Show the output waveforms (Y) for the following inputs A and B of

(i) OR gate (ii) NAND gate

**Answer :**

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