(A)
Many of them dug during the Greenwood copper boom a century ago, the hills to the east of Death Valley, Arizona, are dotted with hundreds of copper mines.
Incorrect.
Many of them dug during the Greenwood copper boom a century ago - acts as a modifier and modifies the noun that comes after the comma , i.e, hills. But as per context of sentence, hills were not dug , mines were dug.
(B)
Dug during the Greenwood copper boom a century ago, the hills to the east of Death Valley, Arizona, are dotted with many hundreds of copper mines.
Incorrect. Same error as (A).
Dug during the Greenwood copper boom a century ago - acts as a modifier and modifies the noun that comes after the comma , i.e, hills. But as per context of sentence, hills were not dug , mines were dug.
(C) Hundreds of copper mines, most of them dug during the Greenwood copper boom a century ago,
are dotting the hills to the east of Death Valley, Arizona.
Incorrect. This choice correctly uses the modifier to modify mines. But the use of present continuous tense is incorrect. We use the present continuous to talk about something temporary. But the mines have been in existence since a century and thus we cannot say that their existence is a temporary phenomenon.
(D) The hills to the east of Death Valley, Arizona, are dotted with hundreds of copper mines, most of them dug during the Greenwood copper boom a century ago.
Correct. This choice correctly uses simple present tense to describe a fact( Hills are dotted with hundreds of copper mines) and correctly places the modifier (copper mines, most of them dug during the Greenwood copper boom a century ago.)
(E) The hills to the east of Death Valley, Arizona, are dotted with hundreds of copper mines,
most of which are dug during the Greenwood copper boom
a century ago.Incorrect. This choice incorrectly uses present tense to describe something that has been completed in the past. For completed past events, past tense needs to be used.