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 defined 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.
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