JEE Main:In NITs,GFITs and other government engineering colleges
JEE Advanced:Admission in UG programmes in IITs and ISM Dhanbad
BITSAT: Admission in Integrated First Degree programmes in BITS Pilani, Goa & Hyderabad campuses
COMED-K: For many engineering colleges in Karnataka.The names of the colleges you can get in the folowing link:
https://engineering.careers360.com/colleges/list-of-engineering-colleges-in-india-accepting-comedk-uget

IPU-CET(B.Tech): For admission in colleges under GURU GOBIND SINGH INDRAPRASTHA UNIVERSITY
VITEEE    :Admission in B.Tech in VIT
AMU(B.Tech): For admission in colleges under Aligarh Muslim University
Manipal: For admission in Manipal University
SRM: For admission in SRM University

State Level Engineering Entrance Exams

Andhra Pradesh - https://apeamcet.nic.in/Default.aspx

Karnataka - http://kea.kar.nic.in/cet_2017.htm

Kerala - http://www.cee-kerala.org/

Maharashtra - http://www.dtemaharashtra.gov.in/

West Bengal - http://www.wbjeeb.in/

Chattisgarh - PET - Chattisgarh - PET

Gujarat - CET (B.Tech) - http://dte.gswan.gov.in/edte/

Jammu and Kashmir - CET (B.Tech) - http://www.jakbopee.org/index.aspx 

Odisha - JEE (B.Tech) - http://ojee.nic.in/publicinfo/Public/View.aspx?page=71

Uttar Pradesh - JEE - http://www.jeecup.org/

These will help you get into the engineering colleges present in the respective state.

Generally everyone appears for JEE exam,for admission into NITs/IITs.

BITS exam is also one of the finest for B.E. try for it.

VITEEE(vellore institute of technology) conducts its own exam , you can apply for it.

If you are from gujarat,You can appear for GUJCET for state colleges(like GECs )