JEE Main

You need to score a minimum of 40 percent marks in JEE Mains get admission in NIT.

You can check the link mentioned below:
http://www.result24.co.in/jee-main-2015-syllabus-download-pdf.html

Can I get the details of your academic performance?

JEE Mains is an all India entrance exam, so it is going to be tough. If you have to score high, you have to be good in physics. Chemistry consists of similar reaction, so it helps to score high. You need to be good in mathematics to score or crack the logic.
To prepare for JEE Mains, you must solve at least 50 MCQs per day per subject. Time management is the most important thing for any competitive exam. Usage of the shortcut is required to save time and score high.
In mathematics, don't prepare half section. You should study every section completely and then move on to the next section.

I think Allen is the best coaching institute for the preparation of JEE Mains and Advanced exam.

According to me, it is from CET but I will suggest you to prepare for JEE because the news is that CET is going to be cancelled for all engineering and medical students. If you will prepare for JEE and then there will be CET, it will not be difficult for you because JEE has little higher level then CET.
All the best.

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.

Its cut-off varies every year like it was 105 for JEE Mains (General category) in 2015 and was 100 this year for the same.

Yes, it is possible as there are many other entrance exams that you can give to get admission into petrochemical engineering. You can also get admission into it through JEE Mains.