BHM

They are totally opposite streams and you need to decide your area of interest between computers or public relations.

Both the courses are from different fields and have their own importance in their respective areas. But then, also I will opine you that BHM will have a wider scope as it is an emerging field.
Now, it depends on your interest which field you will choose.
All the best.
Please feel free to revert.

Yes, there are, but these entrance exams are not conducted like in state level like CAT KCET etc. Some universities conduct an entrance exams in their college to select students. It will be having general questions, no need to worry.

It is approximately 2.39 lakhs/year.

B.Sc. in hotel management is traditional graduation, not a full-fledged hotel management course. It is the part of B.Sc. But, BHM is a full-fledged course and it is specially designed for hotel management. Of course, BHM has better scope as after doing it you can work in service industry, tourism sector and even airlines. There are institutes like IIHM, LPU, Amity, IHM that offer world class practical knowledge to their students, both on the campus as well as off the campus. Some of these institutes offer scholarships too. Check their websites for more information.