Hi. All. Here  I would suggest some few top college in India.  Among them can also continue your education by enrolling in dual and integrated programmes. Few Best College in India  for pursuing MBA/PGDM programmes are :
1. GIBS B-School Bangalore (https://www.gibs.edu.in/)
2. Christ University
3. IIMs Bangalore
4. Jain University.

Some of the top law colleges accepting LSAT India scores are -

(1) Rajiv Gandhi School of Intellectual Property Law, Indian Institute of Technology, Kharagpur;

(2) Jindal Global Law School, Sonipat

(3) KLE Society's Law College, Bangalore

(4) College of Legal Studies, University of Petroleum and Energy Studies, Dehradun

(5) JSS Law College, Mysore

(6) The NorthCap University, Gurgaon

I would say most of the good institutes like IITs, NITs, IIIT-D etc accept Gate score and few universities/colleges which provide admission in M.Tech program without Gate are mentioned below -

BITs Pilani

Jamia Hamdard University, Kamdard Nagar, Delhi

Guru Gobind Singh Indraprastha University, Kashmere Gate, Delhi

Jawahral Nehru University(JNU), School of Environmental Sciences, New Delhi

Aligarh Muslim University, Zafarabad Road, Jaunpur

University of Rajasthan, Jaipur

Anna University, Guindy, Chennai

Bharathiar University, Coimbatore

Cochin University of Science and Technology, Kochi Tamil Nadu

GD Agricultural University, Coimbator

College of Science, GITAM University,Andhra Pradesh

Note : The eligibility criteria will not be the same of above mentioned colleges so kindly share what all exams you want to go for accordingly I would be providing you the further process.

Good Luck!!!

MAT is conducted by All India Management Association (AIMA). The test is conducted four time in a year. You can prefer the colleges under MAT in the range of tuition fees between 3-4 Lakh, given below: INDUS Business School

IPE Hyderabad

PES University Bangalore

For other participating colleges you can go through with given below link.

MAT Participating Institute

Good Luck!