DY Patil University School of Management

Congratulations on your good percentage.
The university is good. You should go ahead with your decision of doing BBA.

Yes, you can apply here for MBA after completion of B.Sc from IGNOU in 2014. And as there is no age limit for MBA, a 2014 graduation will not make any difference.
Go ahead. See the details at https://www.shiksha.com/mba-chp1 and https://www.shiksha.com/mba/course/mba-in-international-business-management-school-of-management-d-y-patil-university-navi-mumbai-211677

A candidate must have passed Bachelor's degree course of three years minimum duration from any recognized Indian university or its equivalent recognized university securing a minimum of 50% (45% for SC/ST) marks in aggregate.

Hello Divya,
The college you are willing to study is a very good college and the placements are also good. As per the reputation of the college, there is a very less chance to take direct admission without giving any entrance exam.