1. 재미있는공부하다 This one sounds most proper. 2. 재미있는공부하게다 Wrong. 재미있는 공부하겠다 is right in past meaning. 3. 재미있는공부하기다 We use -하기다. but in this context, very unnatural. 4. 재미있는공부하가 있다 Wrong. 공부하고 있다 is right in the meaning of present doing. 5. 재미있는공부하는 있다 Wrong. 6. 재미있는공부가 있다 There is a interesting study. 7. 재미있는공부는 있다 There is a interesting study. 6-7's is little different in nuance. 6 doesn't imply any meaning except that there is a interesting study. but 7 imply that other thinks there is no interesting study or someone already told that there isn't, so you wanna oppose it.

4. 재미있는공부하가 있다 5. 재미있는공부하는 있다 6. 재미있는공부가 있다 7. 재미있는공부는 있다 what is the difference meaning beetwen 45- and 6-7?