Yes, he/she can. The requirement is for acting as director or shareholder, he/she should have attained age of majority.
As you fulfill this condition, you are clear for the company registration primarily.
With respect your query on registered office address, registration is probably not allowed at the hostel.
However, you may provide your residential address or any other place, say even a virtual office address, as registered office address.
We have answered widely asked question ‘Can I use my Residential place as Registered Office Address?’ here.
If you are looking for professional’s assistance for company registration in India, you can rely on quality services offered by LegalWiz.in.