I am a junior undergraduate student in China majoring in (computational) mathematics. Just right before the year of grad school application and graduation, I want to spend my summer vacation in USA to go for a tour visiting several grad schools, have interviews with professors and look for potential grad positions and projects. The summer vacation is about 2.5 months long so I plan to go sightseeing to fill up the blanks.
Some friends of mine go for this kind of tour during their summer intern, with which they apply for J visas. However, some including me failed to find that kind of research opportunity this year and I want to plan my own tour with sightseeing since no schools will provide me materials for J visas. Is this a appropriate reason to apply for a B2 visa? What is my chance not being rejected with the reason on wrong visa type? Is the length of 2.5 months too long to be plausible?