Hello dear aspirant
There are various engineering entrance exams in India,  the most important are JEE mains and JEE Advanced.

List of Engineering Exams in India
Joint Entrance Examination (Main) (JEE Main) ...
Joint Entrance Exam Advanced (JEE Advanced) ...
Birla Institute of Technology and Science Admission Test (BITSAT) ...
Graduate Aptitude Test in Engineering (GATE) ...
VIT Engineering Entrance Exam (VITEEE)
For complete list of engineering entrance exams,  visit the following link
https://engineering.careers360.com/exams

yes 

You can check them out in the website.also exams for other stream is also present.check them out too.

let me know in the comment box below if you are having any further doubt so that I can give you a clear and detailed information.

hope you find it helpful

Thanks 

good luck!