**a)**

The frequency variable f can be defined by

For every fixed value of the frequency ‘F’. is periodic indeed. It can be represented.

It is the fundamental period of sinusoidal signal

So it is period with that period.

**b)**

The frequency variable f can be defined by

So, it is non periodic.

**c)**

The frequency variable ‘f’ can be defined by

So, it is non periodic. Because the frequency is not expressed in the ratio of two integers.

**d)**

In this the frequency variable can be define by

.

So, the product of the

It is non – periodic.

**e)**

In this the frequency variable , , can be defined by

, ,

So, so, so,

So, the is period.