The correct option is A 1 and 4 alone are correct
The lac operon
The lac operon is an inducible operon system that remains usually in a repressed condition and gets activated only when the substance to be metabolised (lactose) is present.
Statement 1
The inducer binds with a repressor, the repressor is prevented from binding to the operator region. This allows RNA polymerase to carry out the transcription by binding to the promoter region. Hence, the operon is switched on. When the inducer is absent, the operon is switched off. Hence, statement 1 is correct.
Statement 2
When the repressor protein dissociates from the operator region due to the presence of an inducer (here, lactose or allolactose), it allows the RNA polymerase to transcribe the operon. Hence, statement 2 is incorrect.
Statement 3
Lactose or allolactose acts as an inducer in lac operon. In the presence of an inducer, the repressor protein is not allowed to bind to the operator due to its interaction with the inducer. Hence, statement 3 is incorrect.
Statement 4
When the repressor is inactivated by lactose, the promoter region becomes available for RNA polymerase to bind to. This allows transcription to occur. Hence, statement 4 is correct.