Colleges which are providing actuarial science courses are as follows

AMU
Amity
Manipur University
BIT
Bishop Herber College
University of Madras
University of Kalyani
Gurunanak  Dev University
Jaipuria Institute of Management
RNIS College of Insurance

You can get automobile engineering courses in below NITs

NIT Trichy
NIT Warangal
NIT Surathkal
MNIT Jaipur
VNIT Nagpur
MNIT Bhopal
NIT Delhi
MNIT Allahabad
NIT Hamirpur