To get into NIts, IITs, IIITs etc you have to crack JEE mains/JEE advance however there are many government engineering colleges whose intake is based on exams such as JKCET (Jammu and Kashmir Common Entrance Exam) TNCET (Tamil Naidu Common Entrance Exam), BITSAT,VITEEE, AIEEE, etc

Here are list of engineering exams that allows admission in different universities and take different courses in India -

JEE MAIN

JEE ADVANCED

BITSAT

VITEEE

WBJEE

MHTCET

KCET

AP EAMCET

UPSEE

KIITEE

You can clear the entrance exams and take admission to colleges based on your score.