As per the VIT affidavit the student has to submit, it is clearly mentioned that the students aren't allowed to operate any motor vehicle but bicycles are allowed.

To know more you can visit the pdf below:

https://chennai.vit.ac.in/files/Hostel_Affidavit_Boys%20chennai%20campus.pdf

For KIIT there are no official mentions, but in general no such private motor vehicles can't be associated with any hosteler.

I hope my answer helps. All the very best for your future endeavors!