Orchiectomy = ↓ testosterone production = ↓ DHT => prostate cells undergo apoptosis. (This mechanism is similar to using 5α-reductase blockers to treat BPH.)
Apoptosis is characterized by DNA fragmentation (pyknosis, karyorrhexis, karyolysis).
Alternatively, all the other options pointed to things that would actually increase testosterone production and its effects; orchiectomy would obviously not do that.
With the drop in testosterone (and therefore DHT), some of the prostate cells will undergo apoptosis. Apoptosis = DNA fragmentation (180 bp segments).