PYQ Bank

Construct a digital circuit to add three bits A, B and C and provide their sum and carry as outputs. Show appropriate Boolean expressions and truth table to justify the outputs.

In an operational amplifier, the amplifier gain is 10000. The input series resistance is 100\text{ k}\Omega and the feedback resistance is 500\text{ k}\Omega. If the input voltage is 1\text{ volt}, find the exact output voltage and percentage error considering an infinite gain for the amplifier.

Starting with the expression for the density of states for electrons in a band, show that the Fermi energy of an intrinsic semiconductor is at the middle of the band gap. Use these results to estimate the electron density at 300 K (Assuming E_g=1\,\mathrm{eV} and the rest masses of electron and hole as m_e and m_h).

Draw and explain the collector characteristics of a bipolar junction transistor in common emitter configuration. Using the plot, explain how the transistor can be used as an ON-OFF switch.

Prove the following Boolean identity and draw its gates equivalent : Y = \bar{B}(A + C) + C(\bar{A} + B) + AC

Write down London second equation for superconductors. Explain how it accounts for the Meissner effect.

Show that the London equation \vec{\nabla} \times \vec{J} = -\frac{1}{\mu_0\lambda_L^2}\vec{B} or \vec{j} = -\frac{c}{4\pi n\lambda_L^2}\vec{A} leads to the Meissner effect.

\questiondiagram{
} Explain how the circuit shown above can be a source of oscillations. Use this circuit to construct a transistor oscillator and explain its working. What is the frequency of oscillations of this circuit?

\questiondiagram{
} A crystal plane is shown in the above figure. Find its Miller indices and interplanar spacing.

Can you comment from the above question whether you can use it to scan surface by microscopy?

A perfect conductor and a superconductor with T_c \sim 10\ \mathrm{K} are subjected to the following conditions:

(i) cooled under applied magnetic field to 4\ \mathrm{K}

(ii) cooled to 4\ \mathrm{K} and then magnetic field is applied with schematic diagrams, explain path of magnetic field lines in all these situations.

Explain parity violation in \beta-decay. Describe how parity violation was experimentally detected in the decay of {}^{60}\mathrm{Co}. Mention any other decay process in which the parity violation has been demonstrated.

Write down the nucleonic configuration of {}^{7}\mathrm{Li}, {}^{12}\mathrm{C}, {}^{17}\mathrm{O} and {}^{27}\mathrm{Al} in the ground state of the nuclear shell model and hence calculate the corresponding ground state angular momenta and parities. How do the observed ground state angular momenta and parities agree with those predicted on the basis of shell model?

What is the role of neutrino in the weak interaction of radioactive nuclides? Explain the experimental detection of neutrino.

The masses of hydrogen atom and neutron are 1 \cdot 007825\text{ u} and 1 \cdot 008665\text{ u} respectively. Calculate the binding energy per nucleon of ^{12}_6\text{C} nucleus.

What is solar neutrino problem and how the phenomenon of neutrino oscillations provides a solution for the problem?

What is the importance of the study of deuteron? Discuss the problem of ground state of deuteron and elicit information about nuclear forces from this study.

How many fissions take place per second in a 300\text{ MW} reactor? Assume that 200\text{ MeV} is the energy released per fission.

How magnetic moment and electric quadrupole moment of deuteron indicate the presence of non-central forces in deuteron?

Why was neutrino invoked upon by Fermi and how was it placed into experimental evidence?