UPSC Physics Optional PYQs (CSE & IFoS)PYQs

State the basic conditions for oscillations in a feedback amplifier. What are the primary requirements to obtain steady oscillations at a fixed frequency?

(i) Prove the following using De Morgan's theorems : A \cdot B + C \cdot D = \overline{\overline{A \cdot B} \cdot \overline{C \cdot D}} (ii) Simplify the following expression : Y = A \cdot B \cdot \bar{C} \cdot D + \bar{A} \cdot B \cdot \bar{C} \cdot \bar{D} + B \cdot \bar{C} \cdot D

Compare the dependence of resistance on temperature of a superconductor with that of a normal conductor. Describe briefly the formation of Cooper pairs.

Describe briefly the functions of the basic segments of a microprocessor. Draw a block diagram of the registers in the 8085 microprocessor.

Why is the Field Effect Transistor (FET) called Unipolar Transistor? Discuss how it is superior than Bipolar Junction Transistor.

Show that for an n-type semiconductor, the Fermi level lies midway between the donor states and the conduction band edge at low temperature (assuming E_v=0).

The wavelength of a prominent X-ray line from a copper target is 0.1512\,\mathrm{nm}. The radiation, when diffracted with (111) plane of a crystal with fcc structure, corresponded to a Bragg angle of 20.2^\circ. If the density of the crystal is 2698\,\mathrm{kg/m^3} and atomic weight is 26.98\,\mathrm{kg/kmol}, calculate the Avogadro number.

Explain why each of the following particles cannot exist according to the quark model.

(i) A Baryon of spin 1

(ii) An anti-Baryon of electric charge +2

Which of the following decays are allowed and which are forbidden? If the decay is allowed, state which interaction is responsible. If it is forbidden, state which conservation law its occurrence would violate.

(i) n\to p+e^{-}+\bar{\nu}_e

(ii) \Lambda^{0}\to\pi^{+}+\pi^{-}

(iii) \pi^{-}\to e^{-}

(iv) \pi^{0}\to e^{-}e^{+}+\nu_e+\bar{\nu}_e

(v) \pi^{+}\to e^{+}e^{-}+\mu^{+}+\nu

Show that for a specific value (n,l), there exists a large degeneracy relative to the energy characterized by the quantum number (N). Find the shell closures and the magic numbers predicted by harmonic oscillator potential.

Write down the Weizsäcker semi-empirical mass formula and explain each term. Explain why {}^{238}_{92}\mathrm{U} nuclide is an \alpha-emitter and not a \beta^--emitter?

A neutron and a proton can undergo radiative capture at rest: n+p \longrightarrow d+\gamma Find the energy of the photon emitted in this capture. Is the recoil of the deuteron important?

(i) Show that pion decay, muon decay and pair production conserve lepton numbers L_e and L_\mu. (ii) Which of the following reactions is/are possible? Justify with reason : \bar{\nu}_e + p = n + \mu^+ \bar{\nu}_e + p \rightarrow n + e^+

Write the semi-empirical mass formula. Establish the relation A \approx 2Z, where A is mass number and Z is atomic number of the light nuclei, using this semi-empirical mass formula. [Given : good fitting coefficients for Coulomb energy (a_c) = 0\cdot 71\text{ MeV}, for asymmetry energy (a_n) = 22\cdot 7\text{ MeV}]

A reactor is developing nuclear energy at a rate of 3\cdot 2 \times 10^7\text{ watts}. How many atoms of \text{U}^{235} undergo fission per second? How many kg of \text{U}^{235} would be used up in 1000 hours of operation? Assume that an average energy of 200\text{ MeV} is released per fission. Take Avogadro number as 6 \times 10^{23} and 1\text{ MeV} = 1\cdot 6 \times 10^{-13}\text{ joule}.

(i) What is Q-value and how does it help to study the kinematics of a nuclear reaction? (ii) Prove that {}^{252}\text{Cf} can undergo spontaneous fission as under : {}^{252}\text{Cf} = {}^{98}\text{Zr} + {}^{145}\text{Ce} + 9 {}^{1}\text{n} Given : \begin{aligned} M(^{252}\text{Cf}) &= 252\cdot 081621\text{ a.m.u.}\\ M(^{98}\text{Zr}) &= 97\cdot 912735\text{ a.m.u.}\\ M(^{145}\text{Ce}) &= 144\cdot 917230\text{ a.m.u.}\\ M(^{1}\text{n}) &= 1\cdot 008665\text{ a.m.u.} \end{aligned}

What do you mean by strength of interaction among the elementary particles? Calculate the dimensionless coupling constants of gravitational and electromagnetic interactions.

Explain how the nuclear shell model predicts the existence of magic numbers. Using shell model, predict the spin parity or characteristics of ground state of {}^{15}_8\text{O}, {}^{16}_8\text{O} and {}^{17}_8\text{O}.

(i) The radius of a nucleus is given to be 3\cdot 46\text{ fermi}. Estimate the mass number A of the nucleus and identify the nucleus. (ii) What is Bohr magneton? Find out the ratio of nuclear magnetic moment to Bohr magneton.

If the nuclear force is charge independent and a neutron and proton form a bound state then why is there no bound state for two neutrons? What information does this provide on the nucleon-nucleon force?