I do not know what he is talking about but _________ he is an egoistic and self-centered person.  

The first part of the sentence contains a negative verb i.e “do not” and the second part of the sentence contains “but” which is a conjunction used to explain two different or opposite things. This means that the second part of the sentence will contain a positive verb. Option 1 is therefore eliminated. Option 4 is eliminated because a different be-verb is used i.e had when in fact the be-verb “do” is supposed to be used. Option 2 is further eliminated because an incorrect verb has been used which is “knew”. Since, the be-verb “do” is used only along with base form of the verbs which in this case is “know”.