Choice "C" is correct. Illegality of the services to be performed always results in a discharge of duties. This assumes that the services were legal at the time the contract was formed. If the services had been illegal at the time of attempted formation, there would be no contract.
Choice "a" is incorrect. The death of the party who is to receive the services does not usually result in discharge of duties under a personal services contract. However, death might make performance impossible therefore causing a discharge (e.g., if doctor contracts to perform a bypass operation on patient and patient dies before the operation can be performed, doctor is discharged from performing).
Choice "d" is incorrect. A party can be discharged from a contract for impossibility or commercial impracticability, but a mere increase in costs does not make a performance impossible or impracticable.
Choice "b" is incorrect. Mere bankruptcy of the party to receive the services will not result in a discharge, although discharge is possible if the bankruptcy constitutes anticipatory repudiation, such as when it makes it very unlikely that the person receiving the services will be able to pay.