The search engine’s business model __________ around the fulcrum of trust.

Answer: Revolves

'Revolves around' is the idiomatic phrase meaning to have something as the main focus or centre.

• Revolves — Correct. It indicates the business model has trust as its central focus.

• Plays — Incorrect. 'Plays around' suggests casual or experimental behavior; it does not convey that trust is the main focus.

• Sinks — Incorrect. 'Sinks around' is not a natural collocation; 'sink' typically pairs with prepositions like 'into' or 'in', not 'around'.

• Brust — Incorrect. 'Brust' is not a standard English word (likely a misspelling of 'burst'), and neither form fits the intended meaning with 'around'.

Therefore, 'Revolves' is the appropriate word to complete the sentence because it clearly expresses that trust is the central focus of the business model.