Upvote:1
The activities you mentioned (visiting potential graduate schools, having interviews, looking for potential projects, and sightseeing), and the length of 2.5 months, are all consistent with a B-2 visa. So there shouldn't be much chance of being rejected for wrong visa type.
The most common reasons for US visa denial are 214(b) failure to overcome the presumption of immigrant intent, or 221(g) incomplete application or supporting documentation. If you show strong ties to your home country and adequate documentation for your trip, including how you will pay for it, and your application doesn't raise other suspicions, it is likely that you would get the visa.