Obtain the Boolean expression for the output Y in the given logic circuit :

Simplify the expression and show that the circuit is equivalent to an AND gate with inputs A and B.

A superconducting material has a critical temperature of 3\cdot 7~\text{K} and a magnetic field of 0\cdot 0306~\text{tesla} at 0~\text{K}. Find the critical field at 2~\text{K}.

A transistor having \alpha = 0\cdot 975 and a reverse saturation current I_{\text{CO}} = 10~\mu\text{A} is operated in CE configuration. What is \beta for this configuration? If the base current is 250~\mu\text{A}, calculate the emitter current and the collector current.

Explain the Meissner effect in superconductivity. Obtain an expression for London penetration depth of magnetic field for a superconductor.

A silicon semiconductor sample is doped with 6\times10^{16}\,\mathrm{cm^{-3}} of aluminium and 7\times10^{15}\,\mathrm{cm^{-3}} of phosphorus atoms. Given at T=300\,\mathrm{K}, the intrinsic carrier concentration, n_i=1.5\times10^{10}\,\mathrm{cm^{-3}}; the band gap, E_g=1.1\,\mathrm{eV}; the electron mobility, \mu_n=1250\,\mathrm{cm^2\,V^{-1}\,s^{-1}} and the hole mobility, \mu_p=480\,\mathrm{cm^2\,V^{-1}\,s^{-1}}. Determine in the sample of the following:

(i) The type of the semiconductor, n or p

(ii) The hole carrier concentration

(iii) The electron carrier concentration

(iv) The position of the Fermi level in the sample with respect to the bottom of the conduction band

(v) The conductivity of the sample

Assuming equal masses for up (u) and down (d) quarks, find the ratio (\mu_n/\mu_p) of the magnetic moments of neutron and proton.

Given that the single particle energy separation between 1d_{5/2} and 1d_{3/2} in ^{17}\mathrm{O} is 5\,\mathrm{MeV}. Calculate the strength of spin-orbit interaction. It is observed that 1d_{5/2} level is lower than 1d_{3/2} level.

Stable light nuclei have equal number of protons and neutrons, whereas heavy nuclei have excess of neutrons. Explain why.

In the following nuclear reactions, what particles are possible for the unknown particle X?

(i) \pi^- + p \rightarrow K^0 + X

(ii) p + p \rightarrow \pi^+ + n + \Lambda^0 + X

Explain the various methods of finding the size of the nucleus. How will you determine the nuclear radius from the observation of beta rays resulting from nuclear transition when the initial and final nuclei are mirror nuclei?

What do you understand by the reproduction factor of a fission reactor? What is the maximum value of the reproduction factor in a uranium fission reaction?

What are the properties of the particles made up of the following quarks? Also write the names of particles :

(i) u\bar{d}

(ii) \bar{u}d

(iii) dds

(iv) uss

For a system consisting of one proton and one neutron (not necessarily a deuteron), write down the various possible states specifying clearly its isospin, spin and orbital quantum numbers.

On the basis of liquid-drop model, write the semi-empirical mass formula for the total binding energy. Also explain their each term.

By applying the conservation laws, state about the following decay equations, whether they are allowed or not allowed :

(i) \Sigma^+ \rightarrow p + \pi^0

(ii) \Sigma^0 \rightarrow \Lambda^0 + \gamma

(iii) \Lambda^0 \rightarrow n + \pi^0

Explain the origin of the nuclear magnetic moment. Deduce expression for the magnetic dipole moment with the help of the Schmidt single particle model.

Calculate the decay rate of ^{14}\text{C} per gram of carbon in a living organism, assuming the ratio ^{14}\text{C} / ^{12}\text{C} = 1\cdot 35 \times 10^{-12}. The half-life of ^{14}\text{C} is 5730 years.

Why is it not possible to detect the parity violation in weak interaction by observing only the beta decay rate? Justify your answer.

Explain the salient features of nuclear shell model. What are the magic numbers? Write the experimental facts in support of shell model of nuclei.

Discuss the anomalous magnetic splitting of sodium D-lines with necessary illustration (no deduction is required). Identify the polarization of each component line. What condition needs to be satisfied for this splitting to take place?