Atype of mutation in the repressor results in a molecule known as a super-repressor because it represses the lac operon permanently. which of these would characterize such a mutant?

I believe the answer for the above question is that it cannot bind to the inducer. An inducer molecules regulates gene expression, it can bind to protein repressors or activators. The binding of the inducer to the repressor prevents the repressor from binding to the operator.  A super repressor is a repressor that binds to an operator and is non-iducible so it can not be removed. These are dominant because they will bind and never be removed, even if the wild type is attached to one, once it is removed the lac IS may attach and never be removed.