Answer with explaination.

Dear student,

a) Lactose, allolactose and x-gal bind to beta galactosidase enzyme.
Lactose, Allolactose, and X-gal acts as substrate for beta galactosidase enzyme. Thus they bind to beta galactosidase and are metabolised into respective products.

b)Allolactose and IPTG acts as inducer of lac operon. It binds to the repressor of lac operon, thereby inhibiting it from binding to the operator sequence of lac operon. By this mechanism it induces gene expression in lac operon.
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Regards,

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