If you want to take admission in engineering you should appear for below entrance exams

1- JEE (Main+Advanced) - To take admission in prestigious IITs and NITs you have to appear for JEE exam. IIITs and GFTIs also consider admission through JEE.

In order to be eligible you should have 75% marks in your board exam or you should be in top 20 percentile.

For SC/ST you should have 65% marks.

In order to apply for the application form you can refer below link

https://engineering.careers360.com/articles/jee-main-application-form

2- BITSAT- BITS Pilani will conduct BITSAT 2018 in online mode, tentatively from the third week of May to the last week of May 2018.

In order to be eligible for this exam you should have 75% aggregate marks in Physics, Chemistry and Mathematics  in your 2th class. Also, in each of the 3 subjects, they must also secure 60% marks separately.

3- VITEEE- In order to be eligible for this exam you should have scored an aggregate of 60% in Maths, Physics and Chemistry in 10+2 and for SC, ST, J&K, North Eastern states you should have scored an average 50% marks in Physics, Maths and Chemistry in 10+2 or its equivalent exam.

To apply for the application form you can refer below link

https://engineering.careers360.com/articles/viteee-application-form

You should also appear for your state level entrance exam to take admission in state government colleges.

To know about all the entrance exam you can refer below link

https://engineering.careers360.com/exams

Good Luck!!