The instructor added the restriction that all projects had to be __________ no student could research an area that had been investigated previously by anyone else.

Original is the correct word.
Option 1: 'Acceptable' means 'moderately good or satisfactory'.
Option 2: 'Useful' means 'something that is of good use or function'.
Option 3: 'Extensive' means 'large in amount or scale'.
Option 4: 'Original' means 'created personally by someone'.
The word 'original' is the most appropriate among these because it completes the meaning of the sentence: the instructor had added the restriction that the projects shouldbe created by the students personally, and no student could conduct research on something that had already been touched on by someone else (making it unoriginal). As a result, option 4 is right. The other words, 'acceptable,' 'useful,' and 'extensive,' do not add meaning to the phrase.