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I will divide the answer in 2 parts, PGDM and MS:
MS cut offs are pretty high but at 96.93 you have a chance of admission AFTER the CAP rounds are over. Once the CAP rounds are over, all colleges come up with a list of vacant seats and Welingkar releases an advertisement in the leading newspapers inviting applications. You can apply then. Also there is a group on Facebook where all such MBA college details are shared which you should join. PGDM:
For PGDM, Welingkar has an exhaustive process which includes a psychometric test, GD and a PI. The scores of these determine your admission. I know of people with 98 percentile not getting through the PGDM but someone with 85 percentile getting through. It is all profile based. The applications close on 31st March for the PGDM so I recommend you apply fast. I would recommend you apply for the PGDM and accept admission if you are offered. Later around July-August, when the vacancy list comes out, you can internally apply and switch to MS based on your percentile. I know of people who have done that. Good luck and please don't hesitate to comment if you have any more questions.