Read the following sentence carefully and select the pair of words from the given choices that appropriately fills the two blanks to render the statement grammatically correct and meaningful.

Invaluable ______________ of the past lie ______________ alongside the ancient shipwreck deep within the ocean floor.

The correct option is relics, submerged.

Step-by-Step Explanation:

1. Analyzing the First Blank:
The first blank requires a noun that agrees grammatically with the plural verb "lie" and makes contextual sense when referring to objects "of the past".
- "Relics" refers to historical objects or artifacts that have survived from an earlier period. Since "relics" is a plural noun, it correctly agrees with the plural verb "lie" (i.e., "Invaluable relics... lie").

2. Analyzing the Second Blank:
The second blank describes the condition or state of these historical objects near an ancient shipwreck at the bottom of the ocean.
- "Submerged" is a participial adjective meaning covered with water or existing underwater, which logically describes objects situated "deep within the ocean floor."

3. Evaluating the Incorrect Options:
- evidences, under: "Evidence" is typically uncountable in this context, making "evidences" improper, and "lie under alongside" creates awkward phrasing.
- antiques, floats: "Floats" contradicts the setting of being "deep within the ocean floor" (floating implies being at or near the surface) and is grammatically incorrect following the verb "lie".
- item, sink: "Item" is a singular noun and fails to agree with the plural verb "lie" (which would require a plural noun like "items").
- facets, skyward: "Facets" (aspects or sides of a concept/gem) does not refer to physical artifacts found near a shipwreck, and "skyward" (towards the sky) directly opposes being at the ocean floor.

Conclusion:
Inserting relics and submerged renders the sentence grammatically accurate and meaningful:
"Invaluable relics of the past lie submerged alongside the ancient shipwreck deep within the ocean floor."