Shiv Nadar University (SNU)

You'll have to qualify a minimum gate score to apply to universities. If you qualify the basic merit criteria and the interview, you can successfully enroll for PhD.

It is basically a version of the SAT that's scaled down for an Indian student(the English part). It is found pretty easy though. It's neither too tough nor too easy. Just the right level of English and aptitude you are expected to have at this level.
Yes, definitely, if you do well you will get this college.

Private colleges do accept you for MBA without CAT or MAT scores

https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor?utm_source=connect&utm_medium=CR_JEECP&utm_campaign=7476690
Kindly visit this link.

Please check the chances by adding you rank in the link mentioned: https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor?utm_source=connect&utm_medium=CR_JEECP&utm_campaign=7476690.
Hope it helps. All the best!!

This place has it all, aesthetic buildings, multi - disciplinary approach, project oriented syllabus. I spent a wonderful year learning, looking forward to the rest. Learnt how to live life. Thanks to this amazing place. There can't be another university like SNU. It's not just an institute, it's a nursery for a new breed of world leaders. It's fulfilling the real needs of higher education by inculcating and nurturing critical thinking and providing avenues to explore hidden potentials of students.