Hello aspirant,
While there isn't a specific exam solely dedicated to UX Design, most M.Des programs with a UX specialization consider scores from general design entrance exams. but, here are some of the common examinations :

1. CEED (Common Entrance Examination for Design): Conducted by IIT Bombay, it's a highly regarded exam for design programs.

2. NID DAT (National Institute of Design Design Aptitude Test): Specific to NID, but often considered for other design programs.

3. UCEED (Undergraduate Common Entrance Examination for Design): Primarily for undergraduate programs, but sometimes accepted for postgraduate programs as well.

Many universities offering M.Des in UX Design have their own entrance exams. These exams usually assess design aptitude, creativity, and problem-solving skills. In addition to entrance exams, a strong portfolio showcasing your design work, especially in the UX domain, is crucial for admission.

I hope this information helps you.