What type of contract requires both parties to perform certain duties for enforceability?

The correct choice is a conditional contract, as it is characterized by requiring performance from both parties based on specified conditions. In a conditional contract, the obligations of each party depend on the occurrence or non-occurrence of a particular event or condition. The enforceability of the contract is contingent upon these conditions being met.

For instance, in a conditional life insurance contract, the insurer's obligation to pay a death benefit is dependent on the occurrence of the event of the insured’s death, while the policyholder's obligation to pay premiums triggers the insurer’s duty to provide coverage. This mutual responsibility is a hallmark of conditional contracts.

In contrast, unilateral contracts involve one party making a promise in exchange for performance by another party, leaving the promise unfulfilled until the action is taken. Bilateral contracts represent mutual agreements where both parties make promises to each other, which does seem similar but doesn't capture the conditional aspect inherent in the context of this question. Exempt contracts generally refer to agreements that may not be enforceable under law and are not a recognized type in this context. Thus, conditional contracts uniquely encapsulate the concept of duties that must be performed for enforceability.