(a) Derive the mathematical expression for law of radioactive decay for a sample of radioactive nucleus.

(b) How is the mean life of a given radioactive nucleus related to the decay constant?

(i) Distinguish between a conductor and a semiconductor on the basis of energy band diagram.

(ii) The following figure shows the input waveforms (A, B) and the output waveform (Y) of a gate. Identify the gate, write its truth table and draw its logic symbol.

What is space propagation? State the factors which limit its range of propagation. Derive an expression for the maximum line of sight distance between two antennas for space wave propagation.

(i) A screen is placed at a distance of 100 cm from an object. The image of the object is formed on the screen by a convex lens for two different locations of the lens separated by 20cm. calculate the focal length of the lens used.

(ii) A converging lens is kept coaxially in contact with a diverging lens- both the lenses being of equal focal length. What is the focal length of the combination?

Seema’s uncle was advised by his doctor to have an MRI (Magnetic Resonance Imaging) scan of his brain. Her uncle felt it to be expensive and wanted to postpone it.

When Seema learnt about this, she took the help of her family and also approached the doctor, who also offered a substantial discount. She then convinced her uncle to undergo the test to enable the doctor to know the condition of his brain. The information thus obtained greatly helped the doctor to treat him properly.

Based on the above paragraph, answer the following question:

(a) What according to you are the values displayed by Seema, her family and the doctor?

(b) What could be the possible reason for MRI test to be so expensive?

(c) Assuming that MRI test was performed using a magnetic field of 0.1T, find the minimum and maximum values of the force that the magnetic field could exert on a proton (charge= 1.6× 10^-19C) moving with a speed of 10⁴m/s.