What were the three types of colonies established by the english in north america? a) corporate b) democratic c) proprietary d) independent e) royal

Great question,

Let's quickly cancel out one answer, B)Democratic is not the correct answer. This is the United States modern day government system and would not be possible under monarch rule during that time when the King ruled everything.
D)independent could not be the answer because the King would have complete rule of everything. No colony could truly be independent.

Now that leaves us with the answers:
A) corporate- in order for a colony to have been corporate it would have had to have been run by a stockholder given that land by the King himself, however it still would have been run by the King. By doing this the King increased his revenue.
C)proprietary- a person or group was granted by the King to have complete governing rights of their colony. Think of this like a state today, it has a Governor ruling the state but it has Federal Government oversight.
E) royal- leaders chosen by the King and directly ruled by the King. They could pursue nothing other than what the King wanted them to.

I hope this helped!