Business Management Studies

CAT score above 95 is required to get calls from top Iims. And you definitely need a CAT score above 85 to get seen top 30 b schools. Not even 100 percentile is a security if you don't have that IIM factor. You need to qualify for the minimum cut off to get shortlisted for What/PI. The qualifying cut-off is fixed before CAT result. There are also some sectional cut off
Factor considered by IIM to shortlist candidate- 10th, 12th, graduation, CAT score, interview score, extracurricular. Cutt off trends of few Iims during previous years-
IIM Ahmedabad : 99 -100
IIM Bangalore :99-100
IIM Calcutta :98 -99
IIM Lucknow : 97 -98
FMS Delhi : 97-98
XLRI : 93-95
Top 200/300 scorer of CAT get IIM A, B, C or L. Cut off vary for category and courses. Try to get above 85 and top 30 b school. Minimum of 6 months of preparation is enough to score a good CAT score. Your profile is suitable for IIM shortlisting. Best wishes.

Because you are from an Engineering background, So you need to complete the LLB first, then LLM in order to become eligible for Ph.D. in Law. The eligibility criteria of Ph.D. of NLSIU Bangalore is given below for an idea. Eligibility criteria of Ph.D. of NLSIU Bangalore : The Candidate shall have an LL. M. Degree (regular mode) from recognised University securing an aggregate of 55% marks or its equivalent grade (50% of marks or its equivalent grade in case of SC/ST/SAP). Admission criteria : There shall be a written test. The test shall consist of the following:
a) Objective type questions on Research Aptitude : 50 marks
b) Contemporary developments in the field of law and society : 50 marks
c) Specific questions in Law /MBL/Public Policy/other disciplines: 50 marks
Candidate securing not less than 50% marks on the aggregate will qualify for making an oral presentation before the panel of experts on the date specified by the University. A separate Admission Test shall be conducted to the candidates who have qualified for UGC NET / JRF, SLET, M.Phil and Foreign Nationals. The eligibility criteria of LPU for Ph.D in Law is also given below. Eligibility : Masters degree with 55% aggregate marks in a relevant discipline or equivalent, subject to qualifying LPUNEST and Interview; Other conditions as prescribed in the Guidelines for Degree of Doctor of Philosophy (Ph.D. ) programmes.

The eligibility criteria is:
Students pursuing or having completed a minimum of three-year graduate programme in any discipline with minimum 50% aggregate marks from any University recognised by Association of Indian Universities (AIU)/AICTE are eligible for Post Graduate Studies in Management. Students applying for their final exams in April-May 2021 can also apply. However, they should produce documentary evidence of having passed the graduation examination with minimum aggregate marks as specified above, on or before 31 August 2021, failing which the student will forfeit the admission. The student must have completed the graduation examination process before joining the institute.