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Following is the list of a few entrance exams:
AIIMS Entrance Exam- The All India Institute of Medical Sciences Delhi is one of the best medical colleges in the country. It conducts entrance exams for its B.Sc. Nursing and B.Sc. Nursing post basic course. The exam is usually conducted in June.
AFMC Entrance Exam- Armed Forces Medical College conducts an entrance exam for its B.Sc. Nursing course.
JIPMER Entrance Exam- Jawaharlal Institute of Post Graduate Medical Education and Research is considered to be one of the best institutes in the country.
Lady Harding's Medical College- This College situated in Delhi also conducts entrance exams for admission to its B.Sc. (Hons) Nursing course. There are other entrance exams conducted by each state for admissions to their affiliated colleges.

You have named three of the best colleges in the country. But being an alumni of IMI Kolkata, and having made a career in a reputed organisation, I would say IMI Kolkata would be my pick. The location of IMI Kolkata is one of the best things about the institute. Kolkata is a beautiful city. It was the capital of the country in the British Raj and it is proof that it is strategically one of the best business places. IMI Kolkata is not just located at a very important place, it is also the home to the country most intelligent people as faculty. These people have their papers published in journals of national and international repute. Some might say that IMI Kolkata is best because of its placements, and that is one of the reasons. TOI says, the highest package offered was 20.7 LPA which was made by JSW. The average package of top 50 percentile students stood at 8.55 LPA The great lab facilities, ICT classrooms, a vast library, with more than 6100 books are great perks too. When it comes to Finance, skilling and reskilling are of utmost importance. You can choose to specialize in Finance or take a course in PGCFM. Post Graduate Certificate in Financial Markets (PGCFM) is a joint initiative by International Management Institute, Kolkata and NSE Academy Ltd. This is an 11 months executive weekend programme. So, you have two very good options when it comes to Finance at IMI Kolkata.