Select the most appropriate option that can substitute the underlined segment in the given sentence.
He lived on the bank of a mighty river, broad and deep, that have always silently rolling on to a vast undiscovered ocean.

The correct answer is which was always silently rolling.

Step-by-step Explanation:

1. Subject-Verb Agreement: The underlined relative clause refers to the singular noun "a mighty river". Therefore, a singular verb ("was") must be used instead of the plural verb ("have" or "were").

2. Relative Pronoun Usage: The relative pronoun "which" or "that" is appropriate for referring to non-human entities like a river. However, looking at the options and standard continuous past usage for describing an ongoing background action in the past ("lived"), "was... rolling" correctly aligns in tense.

3. Grammatical Tense and Structure: "which was always silently rolling" correctly uses the past continuous tense ("was rolling") modified by the adverbs "always" and "silently", matching the past simple tense of the main verb ("He lived...").

Thus, the correct substituted sentence is:
"He lived on the bank of a mighty river, broad and deep, which was always silently rolling on to a vast undiscovered ocean."