Colleges in Rajasthan

The placements are not so dedicated. Hence, it is not recommended.
You can check the below mentioned link:
https://www.shiksha.com/mba/course/mba-dual-specialization-pacific-institute-of-management-pim-udaipur-259902

Yes, it is valid as per UGC act.

You should not judge a university by the report of news channel. It provide degree as per UGC norms.

Yes, as per UGC act it is a recognized university.

Yes, LLM course is valid.

Yes, you can do it as it is a recognized university.

No admission is offered on the basis of sports quota or any other quota at BITS. Admission is totally on the basis of merit and through BITSAT exam only.

The cutoff for mechanical engineering for BITS, Pilani is 346 and in BITS, Goa campus it is 322 for mechanical and 316 for Hyderabad.

BITS is one of the prestigious private colleges and provides ragging free environment so there are no major problem for girls and it doesn't matter which campus is it. So don't frightened of this and just prepare for BITSAT.
All the best.

It is a good one according to the previous data cutoff for admission to Pilani campus cutoff are given below. The cutoff for chemical is 319, for computer it is 284, for mechanical it is 346, for civil it is 314 and for electrical and electrical it is 362.