Panjab University

Every option is a good option but it completely depends on the student how he studies and how he looks forward with him to pursue his career. If you study well in any subject of course you will surely get a good package and you will surely have a good career in your life. University only can help you in studying but you have to study completely on yourself and BA LLB is quite good choice but remember that the government jobs are very less.

You should go with mechanical from PU as it has good placements as compared with production engineering.
But UCOE DEPT is in Panjabi University, Patiala, you should definitely go with production engineering in GNDEC.

Yes, you are eligible.

No, it's quite difficult, but mainly depends on Kurukshetra University.

You will go through the entrance exam. That is PUCET as PG test.

Admission is purely based on GATE score. But, there is less infrastructure for research and guidance.

No, it is compulsory to give PU , CET test.

Last year, Maths gen rank cutoff was 56. So, it is difficult for you.

Mention your course. Basically the bostel seats are based on the merit list. You have to fill hostel form. Each course given a valid no. Of hostel seats. Rest waiting list is formed. which is clear as course is going on. For eg. Waiting 1 is cleared with in one month.

Kindly mention the name of the course in which you want to take admission. However, your scores are pretty nice and I don't think that you will be facing any issues in getting admission.