The correct option is C As established by the Mars Exploration Program, the main scientific goals of the MSL mission are to help determine whether Mars could ever have supported life, as well as determining the role of water, and to study the climate and geology of Mars.
A. The Mars Exploration Program established that the main scientific goals of the MSL mission are to help determine whether or not Mars could ever have supported life, as well as determining the role of water, and to study the climate and geology of Mars. -- Whether or not is redundant and incorrect
B. The Mars Exploration Program established that the main scientific goals of the MSL mission are to help determine whether Mars could ever have supported life, as well as to determine the role of water, and to study the climate and geology of Mars. --- as well as determining is the correct verb when we join a verb; 'as well as to determine' is not
C. As established by the Mars Exploration Program, the main scientific goals of the MSL mission are to help determine whether Mars could ever have supported life, as well as determining the role of water, and to study the climate and geology of Mars. ---- The two things that are parallel here are 1. to help and 2. to study. Correct choice.
D. As established by the Mars Exploration Program, the main scientific goals of the MSL mission are to help to determine whether Mars could ever have supported life, as well as determining the role of water, and to study the climate and geology of Mars ------ to help 'to determine', especially because of the infinitive marker before determine is not to be taken as parallel 'to study'
E. As established by the Mars Exploration Program, the main scientific goals of the MSL mission is to help determine whether Mars could ever have supported life, as well as determining the role of water, and to study the climate and geology of Mars. --- Goals … is -- SV error