Explanation:
Power factor is defined as the ratio of real power (P) to apparent power (S). It is a measure of how efficiently the electrical power is being used. A power factor of 1 means that all the electrical power being supplied is being used efficiently without any wastage. In the following cases, the power factor is not equal to 1:

Case b) XL XC:
In this case, the impedance of the circuit is given by Z = XL - XC. If XL > XC, then the circuit is said to be inductive and if XC > XL, then the circuit is said to be capacitive. In either case, the power factor is not equal to 1. For an inductive circuit, the power factor is lagging (less than 1) and for a capacitive circuit, the power factor is leading (greater than 1). This is because in an inductive circuit, the current lags behind the voltage and in a capacitive circuit, the current leads the voltage.

Case c) XL = XC:
If XL = XC, then the circuit is said to be in resonance. In this case, the impedance of the circuit is purely resistive and there is no reactive component. The power factor is equal to 1 in this case, as all the electrical power being supplied is being used efficiently without any wastage.

Case d) Z = R:
If the impedance of the circuit is purely resistive, then the power factor is equal to 1. This is because there is no reactive component and all the electrical power being supplied is being used efficiently without any wastage.

Case a) XC = XL = 0:
If both XC and XL are zero, then the circuit is purely resistive and the power factor is equal to 1. This is because there is no reactive component and all the electrical power being supplied is being used efficiently without any wastage.

Therefore, the correct answer is option b) XL XC, as the power factor is not equal to 1 in this case.