IIT

You need to work hard because if your basics (mechanics) are not clear then you cannot score good marks. You need to study mechanics from books like NCERT and HC Verma.

Well, the answer could include a spectrum of possibilities. I shall answer in general. If you have a rank of 57in JEE main, you pretty well-cleared Mains and are eligible for appearing in JEE Advanced. JEE Advanced is the basic requirement of getting into IIT. Appear for the test, score good, get a rank and Kudos, you can get admission into IITs but remember the very basic requirement is the rank in JEE Advanced given that you have already cleared the cutoff in Mains for it.

Hello Abhay,
For admission into IIT's, you need to take up JEE advance exam and score really well in that. However, based on your JEE Mains score, you will not get admission in IIT's.

Hi,
Yes, of course, petroleum is a good branch to pursue.
UPES is one of the best colleges to pursue a career in the petroleum sector.
Do check the various petroleum related programmes of UPES.

The books which are recommended are good but the main thing is to go through previous year JEE questions which will give you an idea and many of the questions will clear your misconceptions.

You should give MHT CET.

If by fund, you mean scholarship there is a relaxation in Tuition fee, and other expenses by the IITs to its students who are toppers in their field of study.