Yes. I am sharing a list of colleges which take through MAT entrance.

Tapmi

DoMS, Pune

Nirma university

IPE Hyderabad

XIME, Bangalore

BIT Mesra, Bangalore

MAT participating colleges

You will find rating, ranking and each detail of the college in the link provided above for each college.

Good Luck!!

There are various criteria for shortlisting and selection after clearing CAT entrance exam with good score such as past academic records, Extra curricular activity, work experience etc. There are approximately 100 B-schools across the country accept CAT score except IIMs. It depends on your score to get admission in the best possible institutions for MBA. Here are some of the top B school name you can prefer Department of Management Studies, Indian Institute of Technology, Delhi Management Development Institute, Gurgaon SP Jain Institute of Management and Research, Mumbai TA Pai Management Institute, Manipal Faculty of Management Studies, University of Delhi, Delhi

You can also check further institute with given below link. 

Top B School

You can check the exam pattern & Syllabus with given below link.

CAT 2017

Aeronautical engineering is all about the science of aircraft, comprising the construction, research, development, testing, maintenance and design of military aircraft, civil aircraft, and missiles. It uses computer technology in every aspect of aircraft engineering, and is a field that also involves aerospace engineering (use of aerodynamics). 

Below are the some top colleges for Aeronautical Engineering

1- Indian Institute of Technology Bombay (IIT Bombay)

2- Indian Institute of Technology Kanpur (IIT Kanpur)

3- Indian Institute of Technology Kharagpur (IIT KGP)

4- Indian Institute of Technology Madras (IIT Madras)

5- PEC University of Technology

6- Bengal Engineering and Science University
7- Manipal Institute of Technology, Karnataka

8- Amrita Institute of Technology and Sciences - Tamil Nadu

9- Sathyabama University

10-Acharya Institute of Technology

To get admission in IIT's you have to qualify JEE Main and you have to appear for JEE Advanced. To get Top NITs you need to score more than 150 maks in JEE Main in other state quota and to get good college through MHT CET you need to score more than 150 marks in your exam.

To check the complete list of colleges you can refer below list

Aeronautical Engineering Colleges

Good Luck!!

The counselling procedure varies exam to exam. Please explain for which exam & programme you are asking accordingly I can help you about.