Hello,
You can definitely study  and prepare for the entrance examinations where ever you want to go like engineering or medical.
In case of engineering you can apply for the JEE main examination for three consecutive years after your 12th. You have to justify why was there a gap of 2 years when you face an interview during placements. If you can justify with conviction and proper reasoning, they should not be any problem. However, having a 2-year gap between your class XII and engineering will not act in your favor. You have to get very good marks in 3rd and 4th year, to nullify this drawback.