After graduation, can I take admission in MBA without any competitive exam? If yes, then what is the procedure to take admission?

I am afraid most colleges give admission in MBA based on the CAT / open test score. Even if you manage to get admission into a college based on trustee / paid quota it may not benefit you from a career perspective, as the college will not be a reputed one.

Well, you will get admission directly in some colleges that were not that famous and average colleges, so it is recommended that you should give entrance exams next year and get admission in one of the top colleges for MBA.