Q. You are given two converging lenses of focal lengths $1.25cm$ and $5cm$ to design a compound microscope. If it is desired to have a magnification of $30$, find out the separation between the objective and the eyepiece.

Q. Define the term 'self-inductance' of a coil. Write its S.I. unit.

Q. $I-V$ graph for a metallic wire at two different temperatures, $T_1$ and $T_2$ is a shown in the figure.
Which of the two temperature is lower and why?

Q. (a) Determine the value of phase difference between the current and the voltage in the given series $LCR$ circuit.
(b) Calculate the value of the additional capacitor which may be joined suitably to the capacitor C that would make the power factor of the circuit unity

Q. (a) Describe briefly three experimentally observed features in the phenomenon of photoelectric effect.
(b) Discuss briefly how wave theory of light cannot explain these features
OR
(a) Write the important properties of photons which are used to establish Einstein's photoelectric equation.
(b) Use this equation to explain the concept of (i) threshold frequency of (ii) stopping potential

Q. A uniform magnetic field B is set up along the positive x-axis. A particle of charge 'q' and mass 'm' moving with a velocity v enters the field at the origin in $X-Y$ plane such that it has velocity components both along and perpendicular to the magnetic field B. Trace, giving reason, the trajectory followed by the particle. Find out the expression for the distance moved by the particle along the magnetic field in one rotation

Q. Define modulation index. Why is its value kept, in practice, less than one?
A carrier wave frequency $1.5MHz$ and amplitude $50V$ is modulated by a sinusoidal wave of frequency $10kHz$ producing $50$% amplitude modulation. Calculate the amplitude of the AM wave and frequencies of the side bands produced.

Q. Write two factors which justify the need of modulating a low frequency signal into high frequencies before transmission

Q. Explain, using a labelled diagram, the principle and working of a moving coil galvanometer. What is the function of (i) uniform radial magnetic field, (ii) soft iron core?
Define the terms (i) current sensitivity and (ii) voltage sensitivity of a galvanometer. Why does increasing the current sensitivity not necessarily increase voltage sensitivity?

Q. A concave lens of refractive index $1.5$ is immersed in a medium of refractive index $1.65$. What is the nature of the lens?

Q. Calculate the potential difference and the energy stored in the capacitor $C_2$ in the circuit shown in the figure. Given potential at $A$ is $90V,C_1=20\mu F,C_2=30\mu F$ and $C_3=15\mu F$

Q. Which basic mode of communication is used for telephonic communication?

Q. Find the relation between drift velocity and relaxation time of charge carriers in a conductor. A conductor of length $L$ is connected to a d.c. The source of emf ${}^{\prime }{E}^{\prime }$. If the length of the conductor is tripled by stretching it, keeping ${}^{\prime }{E}^{\prime }$ constant, explain how its drift velocity would be affected.

Q. What is the electric flux through a cube of side $1cm$ which encloses an electric dipole?

Q. Calculate the shortest wavelength in the Balmer series of hydrogen atom. In which region (infra-red, visible, ultraviolet) of hydrogen spectrum does this wavelength lie?

Q. Graph showing the variation of current versus voltage for a material Ga As is shown in the figure, Identify the region of:
(i) negative resistance
(ii) where Ohm's law is obeyed

Q. A proton and an $\alpha -particle$ have the same de-Broglie wavelength. Determine the ratio of (i) their accelerating potentials (ii) their speeds

Q. One morning an old man walked bare-foot to replace the fuse wire in kit kat fitted with power supply mains for his house. Suddenly he screamed and collapsed on the floor. His wife cried loudly for help. His neighbour's son Anil heard the cries and rushed to the place with shoes on. He took a wooden baton and used it to switch off the main supply.
Answer the following questions :
(i) What is the voltage and frequency of mains supply in India?
(ii) These days most of the electrical devices we use require a.c. voltage. Why?
(iii) Can a transformer be used to step up d.c. voltage?
(iv) Write two qualities displayed by Anil by his action.

Q. Use Kirchhoff's rules to determine the potential difference between the points $A$ and $D$ when no current flows in the arm $BE$ of the electric network shown in the figure

Q. Identify the gates P and Q shown in figure. Write the truth table for the combination of the gates shown.
Name of equivalent gate representing this circuit and write its logic symbol

Q. (a) Write the characteristic properties of nuclear force.
(b) Draw a plot of potential energy of a pair of nucleons as a function of their separation. Write two important conclusions that can be drawn from the graph

Q. Answer the following questions:
(a) Define electric flux. Write its $SI$ unit.
(b) "Gauss's law in electrostatics is true for any closed surface, no matter what its shape or size is." Justify this statement with the help of a suitable example.

Q. Consider two coherent sources $S1$ and $S2$ producing monochromatic waves to produce interference pattern. Let the displacement of the wave produced by $S1$ be given by $Y_1=a\cos \omega t$ and the displacement by $S2$ and $Y_2=a\cos (\omega t+\varphi )$. Find out the expression for the amplitude of the resultant displacement at a point and show that the intensity at that point will be $I=4a^2{\cos }^2\varphi /2$. Hence establish the conditions for constructive and destructive interference.
(b) What is the effect on the interference fringes in Young's double slit experiment when (i) the width of the source slit is increased; (ii) the monochromatic source is replaced by a source of white light

Q. State clearly how an unpolarised light gets linearly polarised when passed through a polaroid.
(i) Unpolarised light of intensity $I_0$ is incident on a polaroid $P_1$ which is kept near another polaroid $P_2$ whose pass axis is parallel to that of $P_1$. How will the intensities of light, $I_1$ and $I_2$, transmitted by the polaroids $P_1$ and $P_2$ respectively, change on rotating $P_1$ without disturbing $P_2$?
(ii) Write the relation between the intensities $I_2$ and $I_1$

Q. Why does bluish colour predominate in a clear sky?

Q. Use Huygen's principle to show how a plane wavelength propagates from a denser to rarer medium. Hence verify $Snel{l}^{\prime }s$ $law$ of refraction

Q. When an electron in hydrogen atom jumps from the excited state to the ground state, how would the de-Broglie wavelength associate with the electron change? Justify your answer

Q. Define capacitor reactance. Write its S.I. units

Q. Draw a circuit diagram of a C.E. transistor amplifier. Briefly explain its working and write the expression for (i) current again, (ii) voltage gain of the amplifier

Q. Write the expression for the generalized form of Ampere's circuital law. Discuss its significance and describe briefly how the concept of displacement current is explained through charging/discharging of a capacitor in an electric circuit