Colleges in Rajasthan

Hello Varun!
To get a college through JEE main exam, you need to get atleast 75% in your board exam. As you have got only 57% you cannot seek admission in any college under JEE. So, try to get a college that accepts both JEE Mains score and board exam marks.

I don't know about other colleges, but I can say SIESCOMS is very good college. Almost all 60% students of 2015-17 students are placed till know. With the highest package of 14 LPA offered by Amazon followed by 13 LPA offered by Asian Paints, Syntel 8 LPA, SBI Life 8 LPA, AC Nielson 6 LPA, Piramal 6.5 LPA, HDFC 7.2 LPA, etc. Mostly the companies in the campus were insurance, real estate and technology-based companies.
All the best.

I think you should choose CSE in Jaypee Noida SEC 62. Manipal Jaipur is not as good as it's main campus. Jaypee is best private engineeing college in Noida. Placement is also very good there.

BITS, Hyderabad or any other BITS campus is much better than VIT. I am not saying this because I am from BITS, but BITS Pilani has much more value as a private college than VIT. So, if you have a good BITSAT score and you are getting Computer Science branch in BITS, Hyderabad, don't hesitate to opt for the same.

Yes, they can as its recognized.

UEM, Kolkata is the best college you will get for CSE as it has good consistent placement record, get more information about the college by visiting the link:
https://www.shiksha.com/university/university-of-engineering-and-management-kolkata-47398

For pursuing law, there is an entrance exam conducted by Banasthali Vidyapith. You can register for the entrance online in www.banasthali.org (official website).