PYQ Bank

Derive the relativistic length contraction using Lorentz transformation.

A satellite revolves in a circular orbit around the Earth at a certain height above it. Calculate the time period of revolution of the satellite, if the radius of the Earth is significantly higher than the height at which the satellite revolves.

A power supply using a full-wave rectifier is to provide 100\text{ mA} at 20\text{ V} with no more than 1\% ripple. Calculate the minimum value of smoothing capacitor used. Consider the diode resistance and the resistance of the secondary of the transformer as negligible. Also take ripple frequency as 50\text{ cycles per second}.

Metallic iron undergoes a structural phase transition from bcc to fcc at 910^\circ\mathrm{C}. At this temperature, the atomic radii of iron atoms in the bcc and fcc structures are 0.126 \times 10^{-9}\,\mathrm{m} and 0.129 \times 10^{-9}\,\mathrm{m} respectively. Calculate the volume change in percentage during this structural change.

For a simple cubic, a face centered cubic and a body centered cubic crystal, determine the atomic packing factor. How many atoms per \text{mm}^2 surface area are there in (100) plane for leads which has f.c.c. structure. The radius of the atoms is 0\cdot 174\text{ nm}.

Classify diamagnetic, paramagnetic and ferromagnetic materials in terms of their magnetic susceptibility \psi. Plot and explain the variation of \frac{1}{\psi} with temperature for the three materials.

Starting from an expression for the group velocity, arrive at an expression for the effective mass of an electron in a semiconductor. Explain the significance of sign of the effective mass.

(i) What is De Morgan's law ? (ii) Simplify the Boolean expression A + AB + ABC + ABCD

Explain the race problem encountered in an RS latch and how it can be avoided. Build a Mod-10 counter using JK flip-flops and explain its working.

Explain the variation of Magnetisation of Type I and Type II superconductors as a function of applied magnetic field.

A type I superconductor with T_c = 7\text{ K} has slope \frac{dB_c}{dT} = -25\text{ mT/K} at transition temperature T_c. Estimate its critical field at 6\text{ K}.

What is Meissner effect ? Determine the magnetic susceptibility of a superconductor. Explain whether a superconductor exhibits perfect ferromagnetism, paramagnetism or diamagnetism.

\questiondiagram{
} The above circuit exhibits a MOSFET with a source resistor. It has V_T = 1\text{ V} and \mu_n C_{ox} (W/L) = 2\text{ mA/V}^2. Calculate the drain voltage. Also determine whether the transistor is in saturation or in the triode region.

Construct an operational amplifier based analog computer to solve the differential equation \frac{d^2v}{dt^2}-\frac{dv}{dt}+2v=0.

What are the rules followed in biasing a bipolar junction transistor when it is used as an amplifier? Show how n-p-n and p-n-p transistors to be used as an amplifier are biased and the direction of flow of base, collector and emitter currents.

Calculate the recoil energy of ^{57}_{26}\mathrm{Fe} nucleus when it emits a gamma photon of energy 14\,\mathrm{keV}.

What are mirror nuclei? How does the charge independence of nuclear force emerges from this concept?

On the basis of binding energy curve explain why energy is released both in Fission and Fusion.

What is Q value of a nuclear reaction ? Obtain an expression for the Q-value in terms of mass and energy of the particles.

Discuss the four basic types of fundamental interactions in nature and compare them.