I have taken a year drop after the 12th. Am I eligible to apply for the PGDBA program offered by IIM Calcutta?

That is perfectly acceptable. This should not be an issue. You are eligible to apply for IIM Calcutta's PGDBA program even if you have taken a year drop after the 12th. The only thing you should be prepared for is a valid reason for taking a year's leave.

Your response must be convincing, and you must not appear to have wasted your gap year. Whatever the reason, you must be prepared to provide a confident response. You can be comfortable knowing that it will have no effect on your selection process.