UPSC Physics Optional PYQs (CSE & IFoS)PYQs

What are cyclic coordinates for a system of particles ? Discuss the significance of the Hamilton's principle. Show how Lagrange's equations can be derived from Hamilton's principle.

Using Euler's equations for a force free motion of a rigid body, show that the Kinetic energy remains constant throughout the motion of the rigid body.

A force field is given by \vec{F} = (2xy + z^3)\hat{i} + x^2\hat{j} + 3xz^2\hat{k} Is it a conservative field ? If so, what is the scalar potential ?

What is the significance of the null result of Michelson-Morley experiment ? In their experiment Michelson and Morley set l_1 = l_2 = 11\text{ metres}. The wavelength of light used was 5.5 \times 10^{-7}\text{ m}. The orbital velocity of the earth is taken to be 30\text{ kms/sec}. Estimate the fringe shift to be expected.

Explain the term critical magnetic field in a superconductor. How does the critical magnetic field vary with temperature in Type-I and Type-II superconductors ? What is Meissner effect ?

Construct the following function with logic gates : Y = (A + B) (C + D + E) (F + G + H + I) (JKL)

With a suitable circuit diagram and theory explain the use of OP-Amps as

(i) Adder, and

(ii) Integrator.

What are called intrinsic and extrinsic semiconductors ?

Describe an operational amplifier based integrator. Using operational amplifier integrators, design a circuit to solve the following differential equation: \frac{d^2v}{dt^2}+2\frac{dv}{dt}+3v=0

Simplify the logical expression [A\bar{B}(C+BD)+\bar{A}\bar{B}]C.

Distinguish between a superconductor and perfect conductor. Explain what is a Cooper pair.

Draw the device structure of a p-n junction solar cell and explain how light energy is converted into electrical energy. Draw and explain its I-V characteristics.

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

Differentiate between n-p-n and p-n-p transistors. Give their device structure and biasing circuits when used as an amplifier.

Show that any arbitrary rotation axis is not permitted in a crystal lattice.

Design a transistor based Colpitt oscillator which can oscillate at 9\,\mathrm{MHz}. Explain how the oscillations are created and sustained.

Describe the motion of an electron in one dimensional periodic potential and show that it leads to formation of bands of allowed and forbidden states in the electron energy spectrum. How are the conductors, semiconductors and insulators discriminated on the basis of band structure?

Explain the operation of NOR gate with a logical diagram and truth table. Show how NOR gate can be used as Universal gate.

Describe the quark model. Obtain the quark composition of baryons and mesons.

Describe grand unification theories (GUT).