Q. Show diagramatically the behavior of magnetic field lines in the presence of (i) paramagnetic and (ii) diamagnetic substances. How does one explain this distinguishing feature.

Q. A cell of emf "E" and internal resistance 'r' is connected across a variable resistor 'R'. Plot a graph showing variation of terminal voltage 'V' of the cell versus the current 'I'. Using the plot, show how the emf of the cell and its internal resistance can be determined.

Q. Why is it experimentally difficult to detect neutrinos in nuclear $\beta$-decay?

Q. Using Rutherford model of the atom, derive the expression for the total energy of the electron in hydrogen atom. What is the significance of total negative energy possessed by the electron?

Q. (a) Deduce the expression for the torque acting on a dipole of dipole moment $\overrightarrow{p}$ in the presence of a uniform electric field $\overrightarrow{E}$.
(b) Consider two hollow concentric sphere, $S_1$ and $S_2$, enclosing charges 2Q and 4Q respectively as shown in the figure. (i) Find out the ratio of the electric flux through them. (ii) How will the electric flux through the sphere $S_1$ change if a medium of dielectric constant '${ϵ}_r$' is introduced in the space inside $S_1$ in place of air?
Deduce the necessary expression.

Q. A conducting loop is held above a current carrying wire 'PQ' as shown in the figure. Depict the direction of the current induced in the loop when the current in the wire PQ is constantly increasing.

Q. Two monochromatic rays of light are incident normally on the face AB of a isosceles right-angled prism ABC. The refractive indices of the glass prism for the two rays '1' and '2' are respectively 1.35 and 1.45. Trace the path of these rays after entering through the prism.

Q. A convex lens of focal length 20 cm is placed coaxially with a convex mirror of radius of curvature 20 cm. The two are kept at 15 cm apart from each other. A point object lies 60 cm in front of the convex lens. Draw a ray diagram to show the formation of the image by the combination. Determine the nature and position of the image formed.

Q. The electric current flowing in a wire in the direction from $B$ to $A$ is decreasing. Find out the direction of the induced current in the metallic loop kept above the wire as shown.

Q. Using Bohr's postulates of the atomic model, derive the expression for radius of n${}^{th}$ electron orbit. Hence obtain the expression for Bohr's radius.

Q. Explain, with the help of a circuit diagram, the working of a p-n junction diode as a half-wave rectifier.

Q. A resistance of R $\Omega$ draws current from a potentiometer as shown in the figure. The potentiometer has a total resistance $R_0\Omega$. A voltage V is supplied to the potentiometer. Derive an expression for the voltage across R when the sliding contact is in the middle of the potentiometer.

Q. Define intensity of radiation on the basis of photon picture of light. Write its S.I. unit.

Q. A parallel plate capacitor of capacitance C is charged to a potential V. It is then connected to another uncharged capacitor having the same capacitance. Find out the ratio of the energy stored in the combined system to that stored initially in the single capacitor.

Q. Estimate the average drift speed of conduction electrons in a copper wire of cross-sectional area $1.0\times {10}^{-7}{m}^2$ carrying a current of 1.5 A. Assume the density of conduction electrons to be $9\times {10}^{28}{m}^{-3}$

Q. Draw a labeled diagram of Van de Graff generator. State its working principle to show how by introducing a small charged sphere into a larger sphere, a large amount of charge can be transferred to the outer sphere. State the use of this machine and also point out its limitations.

Q. A biconvex lens made of a transparent material of refractive index $1.25$ is immersed in water of refractive index $1.33$. Will the lens behave as a converging or a diverging lens? Give reason.

Q. (a) In Young's double slit experiment, describe briefly how bright and dark fringes are obtained on the screen kept in front of a double slit. Hence obtain the expression for the fringe width.
(b) The ratio of the intensities at minima to the maxima in the Young's double slit experiment is 9:25. Find the ratio of the widths of the two slits.

Q. Considering the case of a parallel plate capacitor being charged, show how one is required to generalize Ampere's circuital law to include the term due to displacement current.

Q. Draw a circuit diagram n-p-n transistor amplifier, CE configuration. Under what condition does the transistor act as an amplifier?

Q. Define the term 'mutual inductance' between the two coils. Obtain the expression for mutual inductance of a pair of long coaxial solenoids each of length $l$ and radii $r_1$ and $r_2(r_2>>r_1)$. Total number of turns in the two solenoids are $N_1$ and $N_2$ respectively.

Q. (a) Deduce an expression for the frequency of revolution of a charged particle in a magnetic field and show that it is independent of velocity or energy of the particle.
(b) Draw a schematic sketch of a cylotron. Explain, giving the essential details of its construction, how it is used to accelerate the charged particles.

Q. What is the force between two small charges of $2\times {10}^{-7}C$ and $3\times {10}^{-7}C$ placed 30 cm apart in air?

Q. Two polaroids $P_1$ and $P_2$ are placed with their pass axes perpendicular to each other. Unpolarised light of intensity $I_0$ is incident on $P_1$. A third Polaroid $P_3$ is kept in between $P_1$ and $P_2$ such that its pass axis makes an angle of 30${}^o$ with that of $P_1$. Determine the intensity of light transmitted through $P_1,P_2$ and $P_3$.

Q. Write the functions of the following in communication systems:
i) Transducer
ii) Repeater

Q. Why do the electrostatic field lines not form closed loops?

Q. (a) Describe briefly how a diffraction pattern is obtained on a screen due to a single narrow slit illuminated by a monochromatic source of light. Hence obtain the conditions for the angular width of secondary maxima and secondary minima.
(b) Two wavelengths of sodium light 590 nm and 596 nm are used in turn to study the diffraction taking place at a single slit of aperture $2\times {10}^{-6}m$. The distance between the slit and the screen is 1.5 m. Calculate the separation between the positions of first maxima of the diffraction pattern obtained in the two cases.

Q. (a) Why are the connections between the resistor in a meter bridge made of thick copper strips?
(b) Why is it generally preferred to obtain the balance point in the middle of the meter bride wire?
(c) Which material is used for the meter bridge wire and why?

Q. A voltage $V=V_{0}sin\omega t$ is applied to a series LCR circuit. Derive the expression for the average power dissipated over a cycle.
Under what condition is (i) no power dissipated even though the current flows through the circuit, (ii) maximum power dissipated in the circuit?

Q. Using the concept of force between two infinitely long parallel current carrying conductors, define one ampere of current.