Show that nuclear density in a given nucleus is independent of mass number A.

(a) Why Photoelectric effect can not be explained on the basis of wave nature of light? Give reasons.
(b) Write the basic features of photon picture of electromagnetic radiation on which Einstein's photoelectric equation is based.

A metallic rod of length 'l' is rotated with a frequency v with one end hinged at the centre and the other end at the circumference of a circular metallic ring of radius r, about an axis passing through the centre and perpendicular to the plane of the ring. A constant uniform magnetic field B parallel to the axis is present everywhere. Using Lorentz force, explain how emf is induced between the centre and the metallic ring and hence obtain the expression for it.

Output characteristics of an n-p-n transistor in CE configuration is shown in the figure.
Determine:
(i) dynamic output resistance
(ii) dc current gain and
(iii) ac current gain at an operating point Vᴄᴱ = 10 V, when Iᴮ = 30 𝜇A.

Using Bohr's postulates, obtain the expression for the total energy of the elctron in the stationary states of the hydrogen atom. Hence draw the enrgy level diagram showing how the line spectra corresponding to Bamer series occur due to transition between enerygy levels.

(i) In what way is diffraction from each slit related to the interference pattern in a double slit experiment?
(ii) 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 x10⁻⁴ m. The distance between the slit and the screen is 1.5 m. Claculate the separation between the positions of the first maxima of the diffraction pattern obtained in the two cases.

In a series LCR circuit connected to an ac source of variable frequency and voltage v = vm sinωt, draw a plot showing the variation of the current (I) with angular frequency (ω) for two different values of resistance R₁ and R₂ ( R₁ > R₂). Write the condition under which the phenomenon of resonance occurs. For which value of the resistance out of the two curves, a sharper resonance is produced? Define Q-factor of the circuit and give its significance.

While travelling back to his residence in the car, Dr. Pathak was caught up in a thunderstorm. It became very dark. He stopped driving the car and waited for thunderstorm to stop. Suddenly he noticed a child walking alone on the road. He asked the boy to come inside the car till the thunderstorm stopped. Dr. Pathak dropped boy at his residence. The boy insisted that Dr. Pathak should meet his aprents. The parents expressed their gratitude to Dr. Pathak for his concern for safety of the child.
Answer the following question based on the above information:
(a) Why it is safer to skit inside a car during a thunderstorm?
(b) Which two values are displayed by Dr. Pathak in his actions

Draw a ray diagram showing the image formation by a compound microscope. Hence obtain expression for total magnnification when the image is formed at infinity.

Distinguish between myopia and hypermetropia. Show diagrammatically how these defects can be corrected.