Mechanical Engineering

Hello Syed. 2 months is enough to keep yourself engaged in different activities related to your academics, hobbies or extra-curriculars. You can opt for doing some/all of the below as per your wish:-
1. Pursue a certification course(online or classroom mode) related to Mech engineering.
2. Join an NGO; always a great initiative.
3. Hone your hobbies by attending classes; playing guitar, singing, dancing, etc.
4. Any internship, if possible.

Sorry to say, there is no chance for you to get any govt. college. I hope you might have taken some other exams too. If yes then you should be dependent on that exam because that exam can only give you a good college and prepare hard for the same.
You can also try for good private colleges.

Hello,
You will require a Bachelor's degree in mechanical engineering and take the GRE to be eligible for the admissions. You should be giving TOEFL/IELTS and have good academics in your undergrad degree with least backlogs. Besides, you should have a strong statement of and letter of recommendation from your professors in support of your profile. Different universities have different admission requirements, universities in the US will typically require an all-round profile in addition to having good grades.

It clearly depends on what branch you prefer and in which institution, your class 12th marks to be more than the required minimum marks & at last, your score in the entrance exam.

Mechanical engineering have good scope. If you have a good goal, then IT will make you better.

There are no more good college for these branch except PES college of engineering, you can choose them or try some another place their are many colleges which have good rank in India.