India

Hello Simran,
NIFT, Delhi is providing Continuing Education Programme after 12th to students which are interested in short-term courses. Following courses with their time period are as follows-
One-year programmes:
Fashion & Clothing Technology (FCT)
Fashion Integration for Apparel Industry (FIAI)
Entrepreneur Development in Fashion Leather Accessories
Footwear Designing & Production Technology (FDPT)
Jewellery Design & Handcraft Technology (JDHT)
Luxury Product Design (LPD)
Fashion Knitwear & Production Technology (FKPT)
Fashion Integration & Marketing Application for Textiles (FIMAT)
Textile Development for Fashion (TDF)
Graphics Desigh & Communication
Fashion retail Management (FRM)
Garment Export Merchandising Management (GEMM)
Clothing Production Technology (CPT)
Garment Production Technology & Apparel Design (GPTAD)
Fashion Designing and Apparel Technology (FDAT)
Six-month programmes:
Introduction to Design & Fashion
Computer Aided Designing for footwear
Leather goods designing & production technology
Visual merchandising & Retail store Design
CAD for knits
Fashion art & Illustration
CAD for Textiles
Fashion Communication and Journalism
Fashion Stlying and Photography
Fashion Photography
Visual Merchandising
Multimedia and Web Design
Fashion Brand Management
Marketing and Mercahandizing for Fashion Industry (MMFI)
Apparel Merchandising & Retail Operations
Apparel Costing & Fashion Merchandising Management (ACFMM)
Fabric Knowledge for Garment Manufacturers
Sewing Machine Engineering (some)
Apparel Production Management
Design Process Thinking
Design & Pattern Making for Ethnic Apparel
Industrial Pattern Making
Three-month programmes: Fashion Merchandising Management (FMM)

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.