Yes sure, here I am suggesting you the names of engineering entrance exams for an average student:

WBJEE
BCECE
UPTU engineering entrance exam
PTU engineering entrance exam
CET, maharastra
SRM,Chennai engineering entrance exam
Sikkim manipal engineering entrance exam

For your reference here I am also giving you the list of some other Engineering Entrance Exams in India:

Indian Institutes of Technology Joint Entrance Examination
Joint Entrance Examination Main
All India Engineering Architecture Entrance Examination
Birla Institute of Technology and Science Admission Test
EPSI National Admission Test
Vellore Institute of Technology Engineering Entrance Exam
National Aptitude Test
Graduate Aptitude Test in Engineering
Planning and Architecture Common Entrance Test
Admission Test for ICFAI Science and Technology
IIST Admission Test
Written Admission Test
Marine Engineering & Research Institute Entrance Exam
Associate Membership of Institution of Engineers
National Engineering Aptitude Test
National Aptitude Test in Architecture
Engineering Common Entrance Test for Diploma Holders ECET
Maharashtra's Common Entrance Test
Karnataka's Common Entrance Test
Tamil Nadu Engineering Admissions
Uttar Pradesh State Entrance Exam
Consortium of Medical, Engineering and Dental Colleges of Karnataka
Engineering, Agriculture and Medicine Common Entrance Test
Kerala Engineering Architecture Medical Examination
Assam Joint Admission Test
Pondichery Centralised Admission Committee Joint Entrance Test
Bihar Common Entrance Test
Karnataka Religious & Linguistic Minority Professional Colleges Association Common Entrance Test
Jammu and Kashmir Board of Professional Entrance Examinations Common Entrance Test
Punjab Technical University Combined Entrance Test
Orissa Joint Entrance Examination
Rajasthan Pre Engineering Test
Madhya Pradesh Professional examination Test
West Bengal Joint Entrance Examinations Board
Guru Gobind Singh Indraprastha University Common Entrance Test
Combined Pre-Entrance Test
Puducherry Joint Entrance Test