It is necessary to have HR & Admin department in small companies?

No need in small companies just one admin with good experience can handle HR and administration also work 

It is not really important to have H.R. and Administration Department in small companies because this will be additional expenditure for the company and since company is small the work will not be much but the expenditure will increase which matters a lot to small companies. Therefore hiring few but best people will make do your work.

well you can't call it a small company it's not alone in the universe but still (5-) employees there must be an H.R and admin Department if it was a solely small  company there's no need for one even a partnership must head to consultancy as HR's

It depends on the number of employees in the organization. Usually in a office with less than people,1 experienced personnel can handle all the requirements of HR and Admin. Some companies even outsource these services. However, once the size of your company grows it is best to have a HR and admin to keep it professional and make sure that all your policies are being implemented correctly. 

Thanks for the Invite. I don't see the use of having both departments for small companies. Admin departments at initial stages can include the function of Human resources. It's just a matter of having a qualified person that can multi task.

Thanks for invite , I agreed with Rania Hafez , one person with profitionals experinces can managing the works