India

I answer this question contrary to what I've read in other answers. I gave MSE entrance exam in May 2016.
CUCET conducts an offline objective entrance test. It has two parts: Part A comprises of English and has 25 questions. Part B has 25 questions each from maths, statistics, economics (both theoretical and current affairs).
After the exam, an answer key is uploaded on the website and grievances of students regarding the answers are met. After this procedure, student's total marks and their category rank are uploaded and a cutoff score for different social/physical categories is announced.
All the selected students are then called to MSE, Chennai on a single day for counselling. Depending upon the number of seats in each course viz. General, financial etc (for students belonging to different categories); students are asked for their preferred course in the order of their ranks.
On the counselling day, hence, provisional admission is given to students in different courses along with the submission of other necessary documents.
There's also provision of upgradation i.e. within a specified time period if any student leaves MSE then candidate with the lower rank gets an option to migrate from his original course to the one where the seat is then vacant.

Hi Shalini,
For change of college you should have good academic marks. Also there will be availability of seat in the institution where you want to go and also your recent institution must permit you. For changing institution you should first contact with either your institution or your university, then will give you the information about this. You have to fill up one application form and you have to submit one to your institution and one to your university. Then after process they may allow you. But when you will take admission in other institution you have to pay again the admission fees and other fees and also you will not get back your admission fees from recent institution. They may return the caution money but it will be very difficult for you to get back.