Here I am giving you name of some best entrance examination are organized for admission in various course offered by reputed colleges in India below :

Engineering entrance exams :
BITSAT - Birla Institute of Technology and Science Exam
GATE - Graduate Aptitude Test in Engineering
JEE - Joint Entrance Exam
JEE Advanced - Joint Entrance Exam (Advanced)
JEE Main - Joint Entrance Exam (Main)
AMIETE - Associate Membership of Institute of Electronics and Telecommunication Engineers Exam
AMIE - Associate Membership of Institution of Engineers Exam
AEEE - Avinashilingam University for Women Engineering Entrance Exam
BEEE - Bharath University Engineering Entrance Exam
BU-DRDO - Bharathiar University - Defense Research and Development Organization entrance exam
BVP Pune CET - Bharati Vidyapeeth Engineering Entrance Exam
DET - Diploma Entrance Test
D Y Patil AIET-B.Tech - Dr. D.Y.Patil Institute All India Entrance Test
EAMCET - Engineering Agriculture and Medical Common Entrance Test
ECET FDH - Engineering Common Entrance Test for Diploma Holders
HP PAT - Himachal Pradesh Polytechnic Admission Test
ICAR AIEEA - Indian Council of Agricultural Research - All Indian Entrance Exam for Admission
JET - Joint Entrance Test
ATIT - Admission Test for ICFAI Tech
AICE - All India Competitive Examination for Admissions to Master's Degree Programmes
AEEE - Amrita Engineering Entrance Exam
AUEEE - Annamalai University Engineering Entrance Exam
IICPT Entrance Exam - Indian Institute of Crop Processing Technology Entrance Exam
IIMS - Indian Institute of Maritime Studies Entrance Exam
ISTC Entrance Exam - Indo Swiss Entrance Exam
IIIT PGEE - International Institute of Information Technology - Post Graduate Entrance Exam
JMI EEE - Jamia Millia Islamia Engineering Entrance Exam
JNU EEE - Jawaharlal Nehru University Engineering Entrance Exam
KIITEE - Kalinga Institute of Industrial Technology Entrance Exam
KCET - Karnataka Combined Entrance Test
KEE - Karunya University Entrance Exam
MP PET - Madhya Pradesh Pre Engineering Test
MT CET - Maharashtra Technology Common Entrance Test
MERI - Marine Engineering & Research Institute Entrance Exam
NMAT UG - Narsee Monjee Aptitude Test for Under Graduates
NATA - National Aptitude Test in Architecture
NERIST - (NEE) - NERIST Entrance Exam
NSIT CEE - Netaji Subhas Institute of Technology Entrance Exam
Odisha DET - Odisha Diploma Entrance Test
OJEE - Orissa Joint Entrance Exam
JNTU PACET - Planning and Architecture Common Entrance Test
RPET - Rajasthan Pre Engineering Test
SPA - School of Planning and Architecture Entrance Exam
SRM EEE - SRM Engineering Entrance Exam
TMI BITS - Tolani Maritime Institute - Birla Institute of Technology and Science
VITEEE - Vellore Institute of Technology Engineering Entrance Exam
VMU-EEE - Vinayaka Missions University Engineering Entrance Exam
BEE - Bureau of Energy Efficiency Entrance Exam
CIPET JEE - Central Institute of Plastic Engineering & Technology Entrance Exam
DA-IICT - Dhirubhai Ambani Institute of Information and Communication Technology Entrance Exam

MBBS entrance exams list :
AIPGMET - All India Post Graduate Medical Entrance Test
AIPMT- All India –Pre Medical/ Pre Dental Entrance Exam
AIPVT - All India Pre Veterinary Test
NEET - National Eligibility cum Entrance Test (NEET)
All India Common Entrance Exam, Vinayaka Mission University
AIPGMEE - All India Post Graduate Medical/Dental Entrance Exam
BLDE University under graduate entrance Test
DUMET - Delhi University Medical/ Dental Entrance test
DUPGMET - Delhi University Post Graduate Medical Entrance Test
DUSET- Delhi University Super- speciality Entrance Test
Haryana PMT -Haryana Pre- Medical Test
HP CPMT - Himachal Pradesh Combined Pre Medical Entrance Test HP CPMT Medical Entrance Exam
JIPMER - Jawaharlal Institute of Post-graduate Medical Education and Research
KEAM- Kerala Entrance Exam (MBBS, BDS, BV.Sc AND AH)
KLE UGAIET / PGAIET - KLE University Under Graduate/Post Graduate All India Entrance Test
Medical entrance examinations in Andhra Pradesh
Medical Entrance Exams in Delhi
MP DMAT - All India Dental & Medical Admission Test - Madhya Pradesh
PGIMER - Post Graduate Institute of Medical Education and Research
SRM Institute of Science and Technology Medical Entrance Exam.
UPCAT/ UPCMET/UPCPMT – Uttar Pradesh Medical Entrance Exams
CMC Vellore Common Entrance Test
Gujarat Common Entrance Test (GUJCET)
Consortium of Medical, Engineering and Dental Colleges of Karnataka (COMEDK) UGET
BHU All India PMT (BHU-PMT)
Punjab Medical Entrance Test (PMET)
All India common Entrance test, Dr. DY Patil Medical College.
AMU Medical Entrance Exam
AFMC- Armed Forces Medical College exam
AIIMS Entrance Exams – All India Institute of Medical Science Entrance Exam
AIMS- Amrita Institute of Medical Sciences
AIPGDET - All India Post Graduate Dental Entrance Test