Q. Two metallic spheres $A$ and $B$ kept on insulating stands are in contact with each other. A positively charged rod $P$ is brought near the sphere $A$ as shown in the figure. The two spheres are separated from each other, and the rod $P$ is removed. What will be the nature of charges on spheres $A$ and $B$?

Q. A metal sphere is kept on an insulating stand. A negatively charged rod is brought near it, then the sphere is earthed as shown. On removing the earthing, and taking the negatively charged rod away, what will be the nature of charge on the sphere? Give reason for your answer.

Q. A carbon resistor is shown in the figure. Using colour code, write the value of the resistance.

Q. State the condition under which a large magnification can be achieved in an astronomical telescope.

Q. On the basis of the graphs shown in the figure, answer the following question:
(a) Which physical parameter is kept constant for the three curves?
(b) Which is the highest frequency among $v_1,v_2$ and $v_3$?

Q. The figure shown a network of five capacitors connected to a $100V$ supply. Calculate the total energy stored in the network.

Q. A $0.5m$ long solenoid of $10turns/cm$ has area of cross-section $1c{m}^2$. Calculate the voltage induced across its ends if the current in the solenoid is charged from $1A$ to $2A$ in $0.1s$.

Q. A small flat search coil of area $5c{m}^2$ with $140$ closly wound turns is placed between the poles of a powerful magnet producing magnetic field $0.09T$ and then wuickly removed out of the field region. Calculate
(a) charge of magnetic flux through the coil, and
(b) emf induced in the coil.

Q. For paraxial rays, show that the focal length of a spherical mirror is one-half of its radius of curvature.

Q. Obtains Bohr's quantisation condition for angular momentum of electron orbiting in $n^{th}$ hydrogen atom on the basis of the wave picture of an electron using de Broglie hypothesis.

Q. Plot a graph showing the variation of undecayed nuclei $N$ versus time $t$. From the graph, find out how one can determine the half-life and average life of the radioactive nuclei.

Q. Write two distinguishing feature of nuclear forces.

Q. Complete the following nuclear reaction for $\alpha$ and $\beta$ decay:
(i) ${}_{92}^{238}U⟶?+{}_2^{4}He+Q$
(ii) ${}_{11}^{22}Na⟶{}_{10}^{22}Ne+?+v$

Q. Explain briefly, using a paper diagram, the difference in behaviour of a conductor and a dielectric in the presence of external electric field.

Q. Define the term polarization of a dielectric and write the expression for a linear isotropic dielectric in terms of electric field.

Q. Twelve wire each having a resistance of $3\Omega$ are connected to form a cubical network. A battery of $10V$ and negligible internal resistance is connected across the diagonally opposite corners of this network. Determine its equivalent resistance and current along each edge the cube.

Q. A student uses the circuit diagram of a potentiometer as shown in the figure (a) For a steady current $l$ passing through the potentiometer wire, he gets a null point for the cell $e_1$ and not for $e_2$. Give reason for this observation and suggest how this difficulty can be resolved? (b) What is the function of resistance $R$ used in the circuit? How will the change in its value affect the null point? (c) How can the sensitivity of the potentiometer be increased?

Q. Show that the time period (T) of socillations of a freely suspended magnetic dipole of magnetic moment (m) in a uniform magnetic field (B) is given by $T=2\pi \sqrt{\frac{I}{mB}}$, where $I$ is a moment of inertia of the magnetic dipole.

Q. Identify the following magnetic materials:
(i) A material having susceptibility $\left(x_m\right)=-0.00015$.
(ii) A material having susceptibility $\left(x_m\right)={10}^{-5}$.

Q. (a) How are eddy currently generated in a conductor which is subjected to n magnetic field?
(b) Write two examples of their useful applications.
(c) How can the disadvantages of eddy currents be minimized?

Q. (a) An ac circuit as shown in the figure has an inductor of inductance $L$ and a resistor of resistance it connected in series. Using the phasar diagram, explain why the voltage in the circuit will lead the current in phase.
(b) The potential difference across the resistor is $160V$ and that across the inductor is $120V$. Find the effective value of the applied voltage. If the effective current in the circuit be $1.0A$. calculate the total impedance of the circuit.
(c) What will be the potential difference in the circuit when direct current is passed through the circuit?

Q. An ac circuit consist of a series combination of circuit elements $X$ and $Y$. The Current is ahead of the voltage in phanse by $\frac{\pi }{4}$. If element $X$ is a pure resistor of $100\Omega$.
(a) name the circuit element $Y$.
(b) calculate the rms value of current, if rms value of voltage is $141V$.
(c) what will happen if the ac source is replaced by a dc source?

Q. Which constituent radiation of the electromagnetic spectrum is used
(i) In RADAR,
(ii) To photograph internal parts of a human body, and
(iii) For taking photographs of the sky during night and foggy conditions?
Give one reason for your answer in each case.

Q. A converging beam of light travelling in air converges at a point P as shown in the figure. When a glass sphere of refractive index $1.5$ is introduced in between the path of the beam, calculate the position of the image. Also draw the ray diagram for the image formed.

Q. A point '$O$' marked on the surface of a glass sphere of diameter $20cm$ is viewed through glass from the position directly opposite to the point '$O$'. If the refractive index of the glass is $1.5$, find the position of the image formed. Also, draw the ray diagram for the formation of the image.

Q. Explain how an unpolarised light gets polarised when incident on the interface separating the two transparent media.

Q. Green light is incident at the polarising angle on a certain transparent medium. The angle of refraction is ${30}^o$. Find
(i) polarising angle, and
(ii) refractive index of the medium.

Q. Plot a graph to show the variation of stopping potential with frequency of incident radiation in relation to photoelectric effect.

Q. Use Einstein's photoelectric equation to show how from this graph, (i) Threshold frequency, and (ii) Planck's constant can be determined.

Q. (i) Write the truth tables of the logic gates marked $P$ and $Q$ in the given circuit.
(ii) Write the truth table for the circuit.