CBSE 12th

Please check for your eligibility to pursue a course in BE Mechanical Engineering from the criteria mentioned below:
B.E. Mechanical Engineering: Eligibility
Candidates who have completed 10+2 or an equivalent examination with 55% of marks in physics, chemistry, and mathematics subjects from a recognised board are eligible for this course. The percentage may vary from one college to another. Candidates who have completed 3 years Diploma holders in any stream from a recognised board are eligible for B.E. Mechanical Engineering Lateral entry course. Eligible candidates may apply for this course through online/offline at official websites of the college or admission office. Regards.

Institutes to study cosmology in India:
Institute of Space Science and Technology, Trivandrum
Indian Institute of Astrophysics, Bangalore
Tata Institute of Fundamental Research, Pune
Raman Research Institute, Bangalore
Physical Research laboratory, Ahmedabad
Indian Institute of Sciences, Bangalore
Entrance exams for admission
After completion of 10+2 with Physics, Chemistry and Mathematics subjects you need to apply for entrance exams like JEE Main and Advanced. Clearing JEE Main is very important to GET the nod for JEE Advanced stage. Getting admission in top colleges is only possible if you clear the Advanced stage with a good rank. The above mentioned institutes are the best one and you need to have very good rank to GET admission. For Master's and Ph.D. programme you need to appear for exams like GATE/CSIR NET/JRF to GET admission in a top college.

There are many other entrance tests which you can apply to for admission to BCA. Some of these entrance tests are mentioned below. Top BCA Exams in India are mentioned at the link provided below:
https://www.shiksha.com/it-software/articles/top-bca-exams-in-india-blogId-13696
Application process for BCA entrance test usually starts in the month of May and June. Students have to apply to respective institutes in both online as well as offline modes. BCA Course: Selection Process
The selection for admission to BCA is generally based on the performance in the written test. Certain universities like the Christ University, Bangalore, also conduct a personal interview for selection to the programme. The final selection is based on the cumulative performance in written test, personal interview and qualifying examination. Regards.