India

IIM Indore is the best option for integrated MBA program. It is called IPM Integrated Program in Management. You may refer to list of top BBA colleges in India: https://www.shiksha.com/bba/articles/top-10-bba-colleges-in-india-blogId-7797

You are eligible for BCA at IGNOU.

Dear Nirupam Sharma, rankings are not stable. Some agencies, organizations provide rankings. Birla Global University is one of the best university in India. You can pursue courses over there. All the best.

Every branch has its own importance. But keeping the future in mind. Computer Science and IT have a lot of scope. Mechanical seems to be an evergreen branch. Robotics Engineering could be a good option.

Maharshi Dayanand University
Tolani Maritime Institute
St. Stephen's College
Lady Shri Ram College for Women
Hans Raj College
Ramjas College
Shri Ram College of Commerce
HR college of Commerce and Economics
Delhi College of Arts and Commerce
Ethiraj College

You are quiet close to the dark horse. Do not spoil your score by choosing an average B-school in hurry. Probably, you are investing last time to choose a right career not just a degree with uncertain job profile of 100percent placement show off.
You can chase SIMSREE-Mumbai, PUMBA-Pune, XIME-Banglore, Great lakes Chennai, IFMR-Chennai,
If you are unable to get into above all, then think of XIME-Kochi, IIRM -Hyderabad, IPE- Hyderabad.

Yes, surely you can try for it.