The Logic: The "Belies" Pivot
The sentence centers on the word "belies," which means "to contradict" or "to give a false impression of."
- Public Reputation: In the academic world, Mannering is renowned for his "depth of thought" (intellectual, profound, complex).
- The Contrast: Because his diary belies (contradicts) this depth, the diary must contain the opposite: surface-level, ordinary, or trivial matters.
- The Clue: The phrase "domestic details" further supports the idea that the diary is about everyday, non-intellectual life (e.g., what he ate for breakfast or chores he did).
- The Goal: We need two synonyms that mean ordinary, commonplace, or trivial.

The Correct Answers:
B. mundane
C. petty
- Why they work: * Mundane means lacking interest or excitement; dull or of the earthly world (rather than the intellectual/spiritual). It perfectly matches "domestic details."
- Petty means of little importance; trivial. If a diary is full of petty preoccupations, it lacks the "depth of thought" he is famous for.
- Together, they create the same meaning: a diary focused on the small, unexciting parts of life.

Why the others fail:
- A. philosophical, D. weighty, and E. erudite: These are "opposite traps." They all mean profound, serious, or scholarly. If the diary were philosophical or erudite, it would confirm his academic reputation, not belie it.
- F. untoward: This means unexpected, inappropriate, or inconvenient. While a diary could be scandalous (untoward), it doesn't specifically contrast with "depth of thought" or align with "domestic details" as well as the correct pair.

Final Completed Sentence
Mannering's personal diary, a record of mundane / petty preoccupations and domestic details, belies the depth of thought for which he was renowned in the academic world.