BCA

Hi Shivam.
Yes, you can do MBA after completing BCA. For the new 2020/21 academic year, the JMI 2020 entrance exam application forms will be released in the first week of February. The last date of submitting the application form is in the second week of March, 2020 and the JMI 2020 admit cards will be released in the second week of April, 2020.

Try visiting UEM Kolkata to get aware of eligibility options of BCA:
https://www.shiksha.com/university/university-of-engineering-and-management-kolkata-47398/courses/bca-bc

BCA is much better than B.Sc Computer Science because it includes the best part of BCA, i.e. the core technical part.

No it is better to do BCA only, then choose upto your interest.

Go for BCA as it is a core technical course instead of B.Sc in computer science.

The college have 60 seats through LUACMAT While 60 seats are college level seats. Because the total number of seats through LUMCMAT is very limited about 16 for BC category. Hence there is no surprise that seats has been filled up when you are approaching the college.

Better option is to go for B.Com instead of BCA and you will get more information on this context.

You can easily go for BCA here, as the gap will be considered after your higher secondary. So go and find the college suitable for you. as per the region and place.