Hello dear

You approximately rank will be near about 50-60 thousand and according to previous year trends you will get mechanical in any of them as you are from home state. As it's depend upon your interest , but I would suggest you to try for the IT or ECE branch as they are more demanding and you can go towards coding. But it is totally fine if you want to take mechanical.

You can see previous year cut off rank and have an idea about it.

Good luck