I have dropped my one year in graduation. Am I eligible to do MBA without any entrance exam?

Only if you have completed your graduation from a recognized university then you may apply at SCDL for the programs offered by SCDL.

Yes, you are eligible for MBA, but you have to qualify the MAT or GMAT test.

First of all, if you have dropped one year in graduation, you might get admission in a college for MBA, but you will have to appear for entrance exams provided you want to do a regular MBA.