Hello dear aspirant,
If you want to pursue mechanical engineering the there are a number of exams which you can give to get admission to prominent institutions.
Here is a list of entrance exams:
1. JEE MAINS: Conducted at National level with over 10 lakh+ applicants. You can visit jeemain.nta.nic.in
2. JEE-ADVANCE: Conducted at national level. Only those candidates who qualify jee mains are eligible for it.
If you pass this then you may get admission in IITs.
3. WBJEE:Conducted by the government of West Bengal. It is a state level examination and if you clear this then you can get admission into engineering colleges of West Bengal
4 COMEDK: Conducted by the Karnataka government to get admission into engineering colleges of Karnataka. It is also a state level exam
5. MHT-CET: Entrance exam for getting admission into colleges of Maharashtra. It is also a state level exam.
6. BITSAT: Entrance exam to get into the BITS Colleges. The colleges are private but a very good exposure is given to students.
Hope this helps