Class 12-science

Hi,
Belonging to a certain stream won't really hinder this aspiration of yours. If you have done your 12th, do your graduation from a recognized university. Prepare for civil service exams. It would be better if you could look for a coaching (HT's & Byju's classes offer this kind of coaching).
Prepare for it with full seriousness.

It depends on your interest. After 12th with maths, you can choose B.Sc or B.Tech in mechanical branch as it is having the best scope.

A general trend is to opt for B Tech/BE. You must clear state/national level entrance examinations to become eligible for B.Tech. B.Tech through lateral entry after a recognised polytechnic Diploma is not a bad idea and gives you an extra edge to compete in the job market. B.Sc in Science, Computer Science, Electronics, Mathematics, Animation and Multimedia, BBA and BCA are also good choices. If your ultimate aim is an MBA, then any graduation will do. Public Administration and Political Sciences may also be aimed at if you are determined for a career in Civil Services.

First, you should decide what you are interested in because maybe you can do it through science stream. If your field of interest is totally out of science subjects then you can always go for commerce because science students can shift to commerce but not the other way round. I would suggest you to search about actuarial science online.
All the best.

It's one of the good streams in engineering. Also, every stream is good in its own way.

Go for mechanical engineering, various institutions offer wide range of subjects like B.Tech in automobile engineering.
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Do visit shiksha again.

After completing class 12th in PCM, many courses are there. You can pursue B.Tech or you opt for B.sc if you want to become a scientist or researcher. You can also appear for government exams or join defense services.
According to me, you should opt for engineering or research program.

You cannot get admission in a government college. You should try to get admission in a private college.

If you belong to general or OBC category, you can get admission in a good government college. If you belong to SC or ST category, you can get admission in any of the NITs.