Ranchi

Hi,
Visit this link to check the colleges based upon your rank:
https://www.shiksha.com/b-tech/resources/upsee-college-predictor

https://www.shiksha.com/college/st-xavier-s-college/xavier-s-bms-entrance-exam-syllabus
Check The link to know about the syllabus and more. Good luck.

I would suggest Amity Noida because of its proximity to NCR. You have options to do internship in most of the law firms in Delhi.

Please visit this link. This is a college predictor by Shiksha and I hope this will help you to choose the right college-
https://www.google.com/url?sa=t&source=web&rct=j&url=https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor&ved=2ahUKEwie-7mvrITiAhWz73MBHYuID8oQFjAAegQIAxAB&usg=AOvVaw1N9BzFtyUCP4JU-2UQHQ0H.

Can't find out in Ranchi but yes for different cities are available
National Institute of Event Management, Mumbai, Vile Parle West
Mumbai University, Mumbai
Impact Institute of Event Management - [IIEM], Delhi
Apeejay Institute of Mass Communication, New Delhi
Pacific University, Udaipur.

Your JEE rank is good, and you will get NIT college. To know which college, you may get use Shiksha JEE college predictor tool. Here is the link. https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor.

College does not offer BCA (Bachelor in Computer Application) course. A very similar and equivalent Bachelor's degree course is offered here. It is B.Sc in Computer Application. There is no cut-off declared officially. Cut-off varies every year. It depends on the performance of the candidates in the entrance exam that year.

Refer the below links :
https://www.shiksha.com/accounting-commerce/colleges/b-com-hons-colleges-Kolkata
https://www.shiksha.com/accounting-commerce/colleges/b-com-colleges-Ranchi.

You can refer Guide for BBA/BBS/BBM 2019 (English, Paperback, Arihant Expert), BBA entrance complete book paperback 2018-By Chandresh Agrawal (author), Chandresh Agrawal & Nandini books (editor), BBA/BCA/BHM/Integrated MBA Exam Guide by RPH Editorial Board Paperback, etc.