As such you dont have any PSU Jobs particularly for Automobile Engineering. However you have many Jobs for Mechanical Engineering. Sometimes what happens is, PSU and Public Research Organizations like BHEL, HAL, ONGC, ISRO, DRDO, BARC they accept Automobile or Manufacturing Engineers under Mechanical Engineering Specializations, however this isnt the case every year. You have a lot of scope however in the Private Sector, especially in the Western and Southern Part of India, with most of the Automobile and Components Industry located there.