Hi, generally colleges give a number of criterion that should be followed in order to get admitted. As you said in the question, 1st is the cutoff marks. Then comes the score or percentage of boards,where you have to clear a cutoff percentage or percentile in individual subjects(PCM) as well as total. Then comes a factor called "domicile" factor. If you gave higher secondary exam in a state and the college where you are applying is in the same state, you are said to be in HS or Home State, otherwise you are said to be in OS or Other State.

Hello aspirant....
If you haven't qualified the entrance exam then you can take admission in many private college.There are many private college which take admission without qualifying the entrance exams.There are colleges which take admission on the basis of marks obtained in mains , Previous academic performance.Some private colleges also take admission through donation.But if you want to take admission in government or top private colleges then you must qualify the entrance exams.
Hope it is clear to you.
Best of luck.