After a slave obtains his freedom from his master, he has his head shaved, and wears instead of his hair an undyed pileus.Option Elimination -
A. After a slave obtains his freedom from his master, he has his head shaved, and wears instead of his hair an undyed pileus. - "he" and "his" can refer to "slave" or "master." Ambiguous. Wrong.
B. After obtaining his freedom from his master and shaving his head, an undyed pileus has to be worn by the slave instead of his hair. - as if "undyed pileus" obtained the freedom. Wrong.
C. A slave has his head shaved after he obtains his freedom from his master and wears instead of his hair an undyed pileus. - ok.
D. A slave obtains his freedom from his master, shaving his head and wearing instead of his hair an undyed pileus. - Comma + ING modifies the verb in the preceding clause. So, "shaving" here modifies "obtains," meaning the "obtaining" and "shaving" are happening simultaneously, as against the intended meaning he is first he gets the freedom and then does the rest. Wrong.
E. A slave, when shaving his head and instead of his hair wearing an undyed pileus, obtains his freedom from his master. - meaning as if "when he shaves his head..." he gets freedom. Wrong.