In a particular strain of E. coli , a mutation occurs in the i gene...

The $i$ gene of the $lac$ operon codes for the repressor protein. Normally, this repressor binds to the operator region and prevents RNA polymerase from transcribing the structural genes ($z$, $y$, and $a$).

In the given mutant strain, the repressor protein loses its affinity for the operator region. As a result, it can no longer bind to the operator to block transcription.

Since the operator is never blocked by the repressor, RNA polymerase will continuously bind to the promoter and transcribe the structural genes. This results in the constitutive (continuous) expression of the $lac$ operon, regardless of whether the inducer (lactose) is present or absent in the medium.

Answer: The operon will be transcribed continuously irrespective of the presence or absence of lactose.