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(a) Find the value of fourier series coefficient

`b`

for

`f(x)=x^(2)`

in the interval

```
=0.04979-\pi .
[b] Prove that the function coshz is analytic and find its derivative.
(c)Out of 100 bulbs sample, the probability of a bulb to be defective is 0.03 . Using Polsson distribution, obtain that in a sample of 100 bulbs, none is defective. { Given e-3 =0.04979 }.
(d) Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Find the probability distribution of number of queens.
(e) Write the Cauchy - Reimann equations in polar co ordinates
```