Colleges in Bangalore

Hey,
Yes, you have BA in Psychology at Mount Carmel College Bangalore. The course for 3 years and 6 semesters. Visionand Mission and of this course is to facilitate a comprehensive understanding of human behavior, keeping abreast with the changing dynamics in the field of psychology.
To lay foundations that foster a research based approach.To sensitize students to psycho-social issues in order to catalyze a climate of social responsibility. I hope this was helpful.
All the best.

Yes, you can get in the first round itself. If not, don't worry, you will surely get in the 2nd round. If you have any reservation then you will surely get it in the first round itself.

https://www.shiksha.com/hospitality-travel/hotel-hospitality-management/ranking/top-hotel-management-colleges-in-india/98-2-0-0-0
You won't get direct admission to any IHMs without writing the JEE. So, Christ University in Bangalore, SRM in Chennai, Sikkim Manipal is also a good choice for direct BHM courses.

Yes, it is indeed mandatory to pass the JEE and get into the merit rank list for the college. Another way is when you are a district or state topper in your CBSE exams or equivalent exam. Then you can get a direct selection to the college. All other students who are not toppers have to apply for the JEE. For further details, just visit the NCHMCT website.

PGDM from SIBM is mostly for Working professionals who can add some skills and degrees and get some promotions in organizations. So, no placement scenario for PGDM. Go for full time MBA if you choose Symbiosis.
Best regards.

Yes, you can apply but you do B.Sc. It is best for you if you are interested in computer do BCA.

Yes, SJES College of Management studies offer MBA with Aviation and logistics management.

Admission are still open you can apply. You can download the form from the following link:
http://presidencycollege.ac.in/admissions/application-form/