Hi. I just finished working on a login/signup script using php and mysqli for a website which is similar to justdial.in.. Previously, I developed a similar system with full profile features for my own little startup, a taxi ordering web app, similar to ola cabs.
To carry out your requirement, two databases will be required, one for students and the other for colleges, for collection(registering) and verification(login).You will also require a functional admin area where you can manage, these students and colleges, delete and edit as needed.
I will also use Javascript and jquery for the design part of the website which your visitors and users can see.
Please feel free to contact me if you require further information
Kindest Regards,
David