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Mechanical engineering is known as the evergreen branch among all the other branches of engineering. Traditionally, mechanical engineers have to deal with concepts such as mechanics, Thermodynamics robotics, kinematics, structural analysis, fluid mechanics with their applications in Automotive Sector, Power Sector, Refrigeration and Air Conditioning Sector, Aerospace. Now I am sharing the list of top private Universities name which offers course :-
Geeta University, Panipat
SRM University
VIT
Manipal University
Chitkara University
Chandigarh University
Shoolini University
Sharda University
There are some key parameters that we should keep in mind before choosing any University, like, faculty, placements, international exposure, curriculum, alumni of that university.

You can go to Australia after applying under ELICOS because to study in Australia after 12th you need 5.5 bands with not less than 5 in each module. Since, you have 4.5 in one module you have 2 options i.e. either apply under ELICOS or else give the IELTS paper again. In ELICOS, besides studying your desire course, you have to study English in Australia to fulfill the language deficiency. The fee for studying English depends on college to college but don't expect it to be below 2 lacs. If you want to go for it, contact the agent. My cousin also deals in it. So, if you want I will give you the number. Her institute is in Amritsar.
But, my advice for you would be to reappear for IELTS again in spite of wasting your money and time in studying English there. Rest depends on you.