Hotel / Hospitality Management

Yes, there are multiple entrance exams conducted by various institutes for admission to hotel management courses. The most popular is NCHMCT JEE. This entrance is for admission to 21 Central IHM, state IHM and some Private IHM. They offer 3 year B.Sc.
AIHMCT- Army Institute of Hotel Management and Catering Technology.
Common Hotel Admission Test by IIHM (e-chat).
Maharashtra Hotel Management Common Entrance Test.
Punjab University Tourism and Hospitality Aptitude Test.

Kindly visit this link:
https://www.shiksha.com/hospitality-travel/hotel-hospitality-management/ranking/top-hotel-management-colleges-in-Lucknow/98-2-0-138-0

You will have the option of lateral entry if you are a topper in your state or district for 12th. But for that you would have to personally contact the institute with your marks-list in original and proof of your qualification as the topper in the state.

Admission for Diploma courses in IHMs are conducted by the institute itself. You can apply at the institute. You will get the application form at the college or from the college website.

IIMs do not provide specialisation in Hotel Management. They offer general management mostly. However, if you are convinced about HM, you can google about IHM.

Yes, you can study MBA after completing your Hotel Management and especially I would recommend you to study MBA in Hotel & Hospitality Management which is very beneficial for Hospitality Students.

If you don't have much interest in study, then you can take BBA as it is what you can do. But at some point, you have to give time for study to clear any degree. So, you make your interest in study. Try to take interest in study.
Good luck.