It will be easier if the sentence is rewritten to understand what exactly it is trying to say
Per the author:
Antitrust laws prevented companies from conspiring on restraining trade. Meaning large companies were not allowed to conspire to restrict trade(in other words to establish monopoly on trade and deprive other competiters from free trade) by the anti trust laws.
Large corporations are prevented from conspiracy on restraining trade by antitrust laws that were passed at the turn of the century, but they
A is wrong
- the use of "they" is ambiguous. It seems to refer to corporation but it actually is refering to the laws.
- The tense does not match in this case. The opening clause is a present perfect tense, which is ongoing, so when we say "but they needed the further support of Supreme Court decisions to be wholly effective", it should refere to something which is true even now,to be parallel to the present perfect tense in first clause.
Large corporations, prevented from conspiring to restrain trade by antitrust laws passed at the turn of the century, but the laws
B is wrong
- opening clause missing verb, and sounds as if large corporations are preventing something, where as it is the laws which is preventing something.
Conspiracy to restrain trade by large corporations was prevented by antitrust laws passed at the turn of the century, but they have
C is wrong
- problem with tense. "they have" , says it is still effective, where as the subject is in past.
Antitrust laws which were passed at the turn of the century, prevented large corporations from conspiring on restraining trade, but such laws have
D is wrong
- wrong idiom usage
Antitrust laws were passed at the turn of the century to prevent large corporations from conspiring to restrain trade, but such laws have
E is correct
- Here Voice is active, correct idiom is used, and the reference to "such laws have" would not depend on any tense since it is not refeing to a specific law in time.
