(i) All questions are compulsory.

(ii) There are 29 questions in total. Question Nos. 1 to 8 are very short answer type questions and carry one mark each.

(iii) Questions Nos. 9 to 16 carry two marks each. Questions Nos. 17 to 25 carry three marks each and questions Nos. 27 to 29 carry 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 three questions of five marks each. You have to attempt only one of the choices in such questions.

(v) Questions No. 26 is value based question carries four marks.

(vi) Use of calculators is not permitted. However, you may use log tables if necessary.

Q1 :

Two charges of magnitudes −2Q and +Q are
located at points (a, 0) and (4a, 0) respectively. What is the
electric flux due to these charges through a sphere of radius
“3a”™ with its centre at the
origin? **(1)**

**Answer :**

Gauss’ theorem states that the electric flux
through a closed surface enclosing a charge is equal to
(1/Îµ_{0}) times the magnitude of the
charge enclosed.

The sphere encloses a charge of -2Q thus,

Q2 :

How does the mutual inductance of a pair of coils change when

(i) distance between the coils is increased and

(ii) number of turns in the coils is increased? **(1)**

**Answer :**

(i) As, Ï† = MI, with the increase in the distance between the coils the magnetic flux linked with the secondary coil decreases and hence the mutual inductance of the two coils will decrease.

(ii) Mutual inductance of two coils can be found out by, M =
Î¼_{o}n_{1}n_{2}Al, i.e. M âˆ n_{1}n_{2}, so, with the increase in number
of turns mutual inductance increases.

Q3 :

The graph shown in the figure represents a plot of current versus
voltage for a given semiconductor. Identify the region, if any,
over which the semiconductor has a negative resistance. **(1)**

**Answer :**

Resistance of a material can be found out by the slope of the curve V vs. I. Part BC of the curve shows the negative resistance as with the increase in current, voltage decreases.

Q4 :

Two identical cells, each of emf E, having negligible internal
resistance, are connected in parallel with each other across an
external resistance R. What is the current through this
resistance? **(1)**

**Answer :**

Q5 :

The motion of copper plate is damped when it is allowed to
oscillate between the two poles of a magnet. What is the cause of
this damping? **(1)**

**Answer :**

Q6 :

Define the activity of a given radioactive substance. Write its
S.I. unit. **(1)**

**Answer :**

Q7 :

Welders wear special goggles or face masks with glass windows to
protect their eyes from electromagnetic radiations. Name the
radiations and write the range of their frequency. **(1)**

**Answer :**

Q8 :

Write the expression for the de Broglie wavelength associated
with a charged particle having charge
“q”™ and mass
“m”™, when it is accelerated
by a potential V. **(1)**

**Answer :**

Q9 :

Draw typical output characteristics of an n-p-n transistor in CE
configuration. Show how these characteristics can be used to
determine output resistance. **(2)**

**Answer :**

Q10 :

A parallel beam of light of 500 nm falls on a narrow slit and the
resulting diffraction pattern is observed on a screen 1 m away.
It is observed that the first minimum is at a distance of 2.5 mm
from the centre of the screen. Calculate the width of the slit.
**(2)**

**Answer :**

Q11 :

A slab of material of dielectric constant K has the same area as
that of the plates of a parallel plate capacitor but has the
thickness d/2, where d is the separation between the plates. Find
out the expression for its capacitance when the slab is inserted
between the plates of the capacitor. **(2)**

**Answer :**

Q12 :

A capacitor, made of two parallel plates each of plate area A and
separation d, is being charged by an external ac source. Show
that the displacement current inside the capacitor is the same as
the current charging the capacitor. **(2)**

**Answer :**

Q13 :

Explain the term “drift
velocity”™ of electrons in conductor. Hence
obtain the expression for the current through a conductor in
terms of “drift velocity”™.
**(2)**

**OR**

Describe briefly, with the help of a circuit diagram, how a potentiometer is used to determine the internal resistance of a cell.

**Answer :**

Q14 :

A convex lens of focal length f_{1} is kept in
contact with a concave lens of focal length f_{2}. Find the focal length of the combination. **(2)**

**Answer :**

Q15 :

In the block diagram of a simple modulator for obtaining an AM
signal, shown in the figure, identify the boxes A and B. Write
their function. **(2)**

**Answer :**

Q16 :

In the circuit shown in the figure, identify the equivalent gate
of the circuit and make its truth table. **2**

**Answer :**

Q17 :

(a) For a given a.c., i = i_{m} sin Ï‰t, show that the
average power dissipated in a resistor R over a complete cycle is
R.

(b) A light bulb is rated at 100 W for a 220 V a.c. supply.
Calculate the resistance of the bulb. **(3)**

**Answer :**

Q18 :

A rectangular conductor LMNO is placed in a uniform magnetic
field of 0.5 T. The field is directed perpendicular to the plane
of the conductor. When the arm MN of length of 20 cm is moved
towards left with a velocity of 10 ms^{−1}, calculate the emf induced in the
arm. Given the resistance of the arm to be 5 Î© (assuming that other arms
are of negligible resistance) find the value of the current in
the arm. **(3)**

**OR**

A wheel with 8 metallic spokes each 50 cm long is rotated with a speed of 120 rev/min in a plane normal to the horizontal component of the Earth”™s magnetic field. The Earth”™s magnetic field at the place is 0.4 G and the angle of dip is 60Â°. Calculate the emf induced between the axle and the rim of the wheel. How will the value of emf be affected if the number of spokes were increased?

**Answer :**

Q19 :

Define the current sensitivity of a galvanometer. Write its S.I.
unit. **(3)**

Figure shows two circuits each having a galvanometer and a battery of 3V.

When the galvanometers in each arrangement do not show any
deflection, obtain the ratio R_{1}/R_{2}.

**Answer :**

Q20 :

A wire AB is carrying a steady current of 12 A and is lying on
the table. Another wire CD carrying 5 A is held directly above AB
at a height of 1 mm. Find the mass per unit length of the wire CD
so that it remains suspended at its position when left free. Give
the direction of the current flowing in CD with respect to that
in AB. [Take the value of g = 10 ms^{−2}] **(3)**

**Answer :**

Q21 :

Draw V − I characteristics of a p-n junction diode. Answer the following questions, giving reasons:

(i) Why is the current under reverse bias almost independent of the applied potential up to a critical voltage?

(ii) Why does the reverse current show a sudden increase at the critical voltage?

Name any semiconductor device which operates under the reverse
bias in the breakdown region. **(3)**

**Answer :**

Q22 :

Draw a labelled ray diagram of a refracting telescope. Define its magnifying power and write the expression for it.

Write two important limitations of a refracting telescope over a
reflecting type telescope. **(3)**

**Answer :**

Q23 :

Write Einstein”™s photoelectric equation and point out any two characteristic properties of photons on which this equation is based.

Briefly explain the three observed features which can be
explained by this equation. **(3)**

**Answer :**

Q24 :

Name the type of waves which are used for line of sight (LOS) communication. What is the range of their frequencies?

A transmitting antenna at the tope of a tower has a height of 20
m and the height of the receiving antenna is 45 m. Calculate the
maximum distance between them for satisfactory communication in
LOS mode. (Radius of the Earth = 6.4 Ã—
10^{6} m) **(3)**

**Answer :**

Q25 :

(a) What is linearly polarized light? Describe briefly using a diagram how sunlight is polarised.

(b) Unpolarised light is incident on a polaroid. How would the
intensity of transmitted light change when the polaroid is
rotated? **(3)**

**Answer :**

Q26 :

One day Chetan”™s mother developed a severe stomach ache all of a sudden. She was rushed to the doctor who suggested for an immediate endoscopy test and gave an estimate of expenditure for the same. Chetan immediately contacted his class teacher and shared the information with her. The class teacher arranged for the money and rushed to the hospital. On realizing that Chetan belonged to a below average income group family, even the doctor offered concession for the test fee. The test was conducted successfully.

Answer the following questions based on the above information:

(a) Which principle in optics is made use of in endoscopy?

(b) Briefly explain the values reflected in the action taken by the teacher.

(c) In what way do you appreciate the response of the doctor on
the given situation? **(4)**

**Answer :**

Q27 :

(a) Using Biot − Savart”™s law, derive the expression for the magnetic field in the vector form at a point on the axis of a circular current loop.

(b) What does a toroid consist of? Find out the expression for the magnetic field inside a toroid for N turns of the coil having the average radius r and carrying a current I. Show that the magnetic field in the open space inside and exterior to the toroid is zero.

**OR**

(a) Draw a schematic sketch of a cyclotron. Explain clearly the role of crossed electric and magnetic field in accelerating the charge. Hence derive the expression for the kinetic energy acquired by the particles.

(b) An Î±-particle and a proton are released from the centre of the cyclotron and made to accelerate.

(i) Can both be accelerated at the same cyclotron frequency?

Give reason to justify your answer.

(ii) When they are accelerated in turn, which of the two will
have higher velocity at the exit slit of the does? **(5)**

**Answer :**

Q28 :

(a) Define electric dipole moment. Is it a scalar or a vector? Derive the expression for the electric field of a dipole at a point on the equatorial plane of the dipole.

(b) Draw the equipotential surfaces due to an electric dipole. Locate the points where the potential due to the dipole is zero.

**OR**

Using Gauss”™ law deduce the expression for the electric field due to a uniformly charged spherical conducting shell of radius R at a point

(i) outside and (ii) inside the shell.

Plot a graph showing variation of electric field as a function of r > R and r < R.

(r being the distance from the centre of the shell) **(5)**

**Answer :**

Q29 :

Using Bohr”™s postulates, derive the expression
for the frequency of radiation emitted when electron in hydrogen
atom undergoes transition from higher energy state (quantum
number n_{i}) to the lower state, (n_{f}).

When electron in hydrogen atom jumps from energy state
n_{i} = 4 to n_{f} = 3, 2, 1,
identify the spectral series to which the emission lines belong.
**(5)**

**OR**

(a) Draw the plot of binding energy per nucleon (BE/A) as a functino of mass number A. Write two important conclusions that can be drawn regarding the nature of nuclear force.

(b) Use this graph to explain the release of energy in both the processes of nuclear fusion and fission.

(c) Write the basic nuclear process of neutron undergoing Î²-decay.

Why is the detection of neutrinos found very difficult?

**Answer :**

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