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In a cash account, all transactions must be paid for in full at the time of the purchase. This means that certain types of transactions that rely on borrowing funds or leveraging investments are not allowed.

Initial Public Offerings (IPOs) can only be purchased in cash accounts because they involve a direct purchase of shares, and the buyer needs to have the full amount available at the time of purchase. Similarly, mutual funds can also only be purchased in cash accounts since they require the investor to pay the total investment amount using available cash when placing the order.

On the other hand, options and futures can be traded on margin accounts, allowing for greater flexibility and the possibility of leveraging positions. Short sales also necessitate a margin account since they involve borrowing securities to sell and then repurchasing them later. Cash-settled options are also permissible in margin accounts, allowing for similar leveraged trading opportunities.

Thus, the transactions that are exclusively allowed in a cash account align with the requirement that they be fully paid for at the time of purchase, making IPOs and mutual funds the correct answer.