Regulation of gene expression

The lac operon is a polycistronic unit in which the structural genes are regulated by a common promoter and regulatory gene.
It has one regulatory gene, the i gene (i for inhibitor), which codes for the repressor.
It has three structural genes: z codes for β-galactosidase, which hydrolyses lactose into galactose and glucose; y codes for permease, which increases the permeability of the cell to β-galactosides; a codes for transacetylase.
Hence the lac operon consists of one regulatory gene and three structural genes.

(a) is wrong: the inducer of the lac operon is lactose (allolactose); it binds to the repressor and inactivates it. Glucose and galactose cannot act as inducers.
(b) is correct: in the absence of the inducer (lactose), the repressor protein made by the i gene binds to the operator region and prevents RNA polymerase from transcribing the operon.
(c) is wrong: the z gene codes for β-galactosidase; permease is coded by the y gene and transacetylase by the a gene.
(d) is correct: the lac operon was elucidated by the geneticist Francois Jacob and the biochemist Jacque Monod.
Hence the correct statements are (b) and (d).