Dear Megha, this is a collobarated list of colleges offering courses on Automotive engineering in Karnataka and Kerala. Hope this helps.

 https://engineering.careers360.com/colleges/list-of-engineering-colleges-in-India?f%5B0%5D=sm_college_degree%3AB.Arch&f%5B1%5D=sm_college_degree%3AB.E%20/Btech&f%5B2%5D=sm_college_state%3AKarnataka&f%5B3%5D=sm_college_state%3AKerala&f%5B4%5D=sm_course_offered%3AAutomobile%20Engineering

Hello Megha

Automotive Engineering is a full time four year degree course. This branch of Engineering is meant for those who have a passion for cars. 
In this programme candidates are taught about the application of mechanical, thermodynamic, pneumatic, hydraulic and electrical principles with an aim to resolve engineering problems.

Good Luck!

HI, 

Yes , if you clear GATE in Mechanical with good marks and rank, you will be recruited for PSU jobs. There are few companies which are exceptional like BPCL and HPCL , who have restrictions on the degree and the course, where they take in only B.Tech/B.E degree holders for PSU jobs and Not Dual degree holder. Other than a handful of companies, most of them do recruit people who have completed their B.Tech, M.tech or Dual degree for PSU Jobs, Provided you should have been completed before the joining date. 

Hope it helps, 

Good Luck. :) 

Dear Student,

Yes, it offers the course.

Dear Sarang,

Yes MAIT has Automobile Engineering subject. You will get to learn this subject in Third Year in any one of the semester.

List of mechanical engineerin's college in Mumbai

IIT Bombay

Veermata jijabai technological institute, Mumbai

Kk somaiya college of engineering, Mumbai

Bhartiya vidya Bhavans, sadar patel college of engineering, Mumbai 

University of Mumbai

Mukesh patel school of technology management and engineering, Mumbai

Thakur college of engineering and technology

Don Bosco institute of technology

Rizvi college of engineering, Bandra

hi girish ,

• rajarambapu institute of technology
• amity university
• sinhgad college of engineering
• counsil of education and development programms
• dhole patil college of engineering
• nutan college of engineering and technology
• maharashtra institute of technology
• savitri bhai phule university
• veermata jijabai technological institute 
• kohinor technology institute
• dr.babasaheb ambedkar marathwada
• international institute of management and engineering

all the best