I wrote my 12th board exams last week. Can I pursue BBA in event management?

Yes, you can pursue BBA from any government. Recognised university. BBA is a three year undergraduate course which teaches basics in business and management and students who have passed their 12th standards are eligible to pursue this course irrespective of what subjects they studied in their 12th s

Yes, you can apply to most of the colleges. You can lock your seat in college by paying the some amount of fees. You can also apply for Delhi University and IIMs. IIM are well known In India for the placements and quality of education they provide.