Mark each statement if it is an example of charlemgne's achievments choose all the answers that are correct, a) was crowned pope on christmas day, a. d. 800. b) united a vast realm under the christian faith. c) became the first emperor of the holy roman empire.

For sure, choose these two:
A) Was crowned pope on Christmas day, A.D. 800.
C) Became the first emperor of the Holy Roman Empire.

Item B has some vagueness and difficulty to it.  Depending on your teacher's point of view, it could be marked true or not.  How "vast" is vast?  How unified must an empire become to be termed "united"?   One biography report of Charlemagne states, "Charlemagne attempted to create unity and harmony" within his realm -- that's probably a better way to put it.  In his ongoing battles with the Saxons, getting them to accept Christianity was a great difficulty.  

A and C i am sure                                  

If he breaks the law then he had to resign from his post and so he'll lose his/her powers.