Petroleum Engineering

If you want to pursue petroleum engineering then I would suggest applying in UPES, Dehradun. It is one of the best college in India and it also has better placements.

Yes, if you confident about it, then take a drop. Prepare well for it. Otherwise, drop is not a good idea. Go for some good coaching institutes that provide good notes about engineering entrance exam. And they also keep you up to date about exams pattern, old papers, syllabus etc. Best of luck.

No, You cannot get any NIT. But there are chances to get Any government college. And you can also try for private college.

Top Petroleum and Energy Engineering Colleges in India are mentioned at the link provided below:
https://www.shiksha.com/engineering/articles/top-petroleum-and-energy-engineering-colleges-in-india-blogId-14466.

Trust me when I say you'll get in very easily. Although non-exam merit seats are reportedly 20% of total seats, with the University accepting more than 200 students per branch (according to recent trends) that makes it a total of 40 seats for the non-exam category and of course, if there are 40 students ahead of you, and you're the 41st, you will still get in, simply because one more student means more money and it seems this college wants only that.

Through these marks, you cannot get good government college.
There are no chances of you getting a government college, but there are chances that a private college takes you with this score through your good academic performance.

Petroleum Engineering placements are scarce. The government sector is worth mentioning for this field. Petrochemical firms and gas plants recruit petroleum engineers.