Exam

You can apply online on their official website for admission request and your preference, then if your rank comes under the college required list then you might get a call from the college to admission.

Uttar Pradesh Engineering College get the admission through UPTU and JEE score basis. All private and government colleges get the admission through these entrance so you can choose according to your rank and branch preferences.

Contact the college authority, they might better answer you this question.

Hello Yuva Kiran,
Yes, you can get a seat at Sastra University. Your chances are high. They consider your board exam percentage and JEE scores (97.8&62). Your percentile will be 97.8(0.75)+62(0.25)= 88.85. On this basis, you will be placed on a rank.
Apply if you have not and the last date is June 10

BIT, Mesra doesn't take admission via BITSAT. BITS Pilani and BIT Mesra are different.

CMAT will do. Rest, you can check on www.ibsindia.org for more details.