The trial balance would not expose the first option as an error, as the receipt of a payment debited and credited for the same amount, $2,000, maintains a balance in the accounts, despite the actual entry being correct in nature.
The trial balance is a check to ensure that the total debits equal total credits in a double-entry accounting system. However, there are certain types of errors that it cannot reveal. Specifically, the trial balance would not reveal transactions that are recorded with correct totals but in the wrong accounts, or transactions recorded at an incorrect amount but where the debit and credit sides still match.
The error that would not be revealed by the trial balance among the given options is the first one: a receipt of payment debited to accounts receivable for $2,000 and credited to cash for $2,000. This transaction is correctly balanced because the total amount debited is equal to the total amount credited, even though the entry itself is correct and there's no actual error present.
In summary, the trial balance would fail to identify errors that do not affect the equality of total debits and credits, such as posting to the wrong account, duplicating transactions, or mutual offsetting errors where debits equal credits.