UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Using OP-AMPs design an analog circuit to solve the following differential equation : \frac{d^2 v}{dt^2} + k_1 \frac{dv}{dt} + k_2 v = v_1(t) with \frac{dv_{(0)}}{dt} = 1\cdot 5\text{ V}; v_{(0)} = 2\cdot 0\text{ V}.

Explain the basic structure and operation of an n-channel FET. How FET acts as an amplifier ? Explain.

Simplify the logical expression AB + \bar{A}\bar{B} + ABC using a Karnaugh map.

Derive Bragg diffraction condition in vectorial form using incident and diffracted wave vectors and reciprocal lattice vector.

Explain the origin of energy band formation in solids. Show that in nearly free electron approximation, the energy band gap is 2|V_G|, where V_G is Fourier transform of periodic potential seen by the valence electrons.

Find an expression for lattice specific heat of solids, and its low and high temperature limits. What is Debye temperature?

Describe the characteristic properties of a superconductor. Derive London equation for a superconductor and hence explain Meissner effect.

Distinguish between intrinsic and extrinsic semiconductors. Show that in a semiconductor, the product of concentrations of the two types of charge carriers is constant at a given temperature.

Simplify the logical expression \overline{(A+B)}B(A+\bar{C}) and draw the logical circuit to implement it.

How are the band structures of insulators and semiconductors similar ? How are they different ?

What type of interaction takes place in the following reactions and justify your answer. (i) \mu^- \longrightarrow e^- + u_e + \bar{\nu}_\mu (ii) p + \mu^- \longrightarrow n + u_\mu

What are quarks ? Give any four properties. Give quark composition of the following particles : p,\quad n,\quad \Lambda^\circ,\quad \Pi^+,\quad K^+

What do you mean by non-central forces?

Find the total kinetic energy of electron and antielectron neutrino emitted in beta decay of free neutron. (The neutron-proton mass difference is 1.30\,\mathrm{MeV} and mass of electron is 0.51\,\mathrm{MeV})

Show that nucleus is a quantum system.

Find the density of {}^{12}_6 C nucleus. (Given, nuclear radius of carbon = 2\cdot 7 \times 10^{-15} \text{ m})

Explain the source of energy in stars using proton-proton thermonuclear reaction cycles.

What are magic numbers in an atomic nucleus and why are they so called ? How is it explained using nuclear shell model ?

Explain conservation of Baryon Number. Comment on the stability of proton.

What are the reactor materials used in design and construction of a nuclear reactor and their important functions ?