Here I am providing the list of few Engineering Entrance Exams in India

Joint Entrance Examination (Main) (JEE(Main))
Birla Institute of Technology (BITS)
COMEDK-UGET
DELHI CEE (Delhi Engineering College)
DTU
GGSIPU-Delhi
Graduate Aptitude Test in Engineering (GATE)
Indian Institute of Technology Joint Entrance Examination(IIT-JEE) as Joint Entrance Examination (Advanced) (JEE(Advanced))
Jamia Millia Islamia University Engg Entrance Exam
KIIT Entrance Examination (KIITEE)
OJEE
RPET
S.O.A. Entrance Examination (SAAT)
UPTU
VITEEE (VIT University)
WB-JEE

Top 40 Engineering Colleges Of India are given below :
1. Indian Institute of Technology (IIT), Delhi

2. Indian Institute of Technology (IIT), Kharagpur

3. Indian Institute of Technology (IIT), Kanpur

4. Indian Institute of Technology (IIT), Chennai

5. Indian Institute of Technology (IIT), Mumbai

6. Indian Institute of Technology (IIT), Roorkee

7. Birla Institute of Technology and Sciences (BITS), Pilani

8. Institute of Technology-BHU, Varanasi

9. Indian Institute of Technology (IIT), Guwahati

10. Vellore Institute of Technology (VIT), Vellore

11. National Institute of Technology (IIT), Surathkal

12. College of Engineering, Anna University, Chennai

13. National Institute of Technology (NIT), Warangal

14. PSG College of Technology, Coimbatore

15. Delhi College of Engineering, Delhi

16. International Institute of Information Technology (IIIT),
Hyderabad

17. National Institute of Technology (NIT), Tiruchirapalli

18. Netaji Subhash Institute of Technology (NSIT), Delhi

19. Motilal Nehru Institute of Technology (MNIT), Allahabad

20. National Institute of Technology (NIT), Calicut

21. National Institute of Technology (NIT), Rourkela

22. College of Engineering - New, Pune

23. Birla Institute of Technology (BIT), Mesra (Ranchi)

24. R.V. College of Engineering - New, Bangalore

25. Nirma Institute of Technology (NIT) - New, Ahmedabad

26. Harcourt Butler Technological Institute (HBTI), Kanpur

27. Thapar Institute Of Engineering & Technology, Patiala

28. Mumbai University Inst of Chemical Tech, Mumbai

29. Indian Institute of Information Technology (IIIT), Gwalior

30. Nirma Institute of Technology (NIT), Ahmedabad

31. University Inst of Engg and Tech, Chandigarh

32. P.E.S Institute of Technology, Bangalore

33. National Institute of Engineering (NIE), Mysore

34. Veermata Jijabai Technological Institute (VJTI), Mumbai

35. Madras Institute of Technology, Chennai

36. Indian School of Mines, Dhanbad

37. Osmania University College of Engineering, Hyderabad

38. SSN College of Engineering, Chennai

39. S.G.S. Institute of Technology & Science, Indore

40. Mepco Schlek Engineering College, Sivakasi