The correct option is A Yes, because the operator will not be bound by repressor and RNA polymerase can transcribe the lac operon
If the lac repressor is nonfunctional, it cannot bind the operator site and transcription of the lac operon will occur at all times, whether or not lactose is present.
When lactose is not available, the lac repressor binds tightly to the operator, preventing transcription by RNA polymerase. However, when lactose is present, the lac repressor loses its ability to bind DNA. It floats off the operator, clearing the way for RNA polymerase to transcribe the operon.
Similarly, mutations in the gene wncoding the lac repressor will lead to lower affinity for the repressor and hence less binding. Thus these mutations allow continued transcription (and thus expression) of the lac operon even in the absence of inducer.
Therefore, option (C) is correct.