There are several competitive exams students aim for, after class 10th, few of them include

1.

National Talent Search Examination or NTSE :

This has always been an influential and prestigious program of India conducted by NCERT at the high school level to identify and recognize students with high intellect and academic talent. It’s a national-level scholarship program (https://digital.aakash.ac.in/foundations/national-talent-search-examination) that requires students to go beyond books and explore different options to prepare thoroughly to score high in the exam.

2.

Indian National Mathematical Olympiad (INMO):

The INMO is conducted by the MO CELL (Mathematical Olympiad Cell) which is held on the third Sunday of January at 30 centers across the country. It is a High School Mathematics Competition held annually in India, since 1989. This program aims at promoting excellence in science and mathematics among students at school level.

3.

Science Olympiad Foundation (SOF):

This Olympiad is for the students of class I to XII, having different exam paper for each class. The question paper consists 35 multiple choice questions of 40 marks, for classes I to IV, and 50 multiple choice questions, for classes V to XII of 60 marks, to be answered in given time of an hour

There are many more exams but the important ones are listed above .

After 12th you have  vast options to choose a field you want to pursue your career in ,