Appearance of antibiotic-resistant bacteria is an example of 

1. adaptive radiation

2. transduction 

3. pre-existing variation in the population

4. divergent evolution 

(c) Appearance of antibiotic-resistae bactria is an example of pre-existing variation

the populaton. When a bacterial popuaion encounters a parcular antbac, those antibiotic, those sensitive to die.
But some bacteria having mutations become resistant ot the antibiotic. Soon, the resistance providing genes become widespread and the entire population becomes resistant.

lt is not due to adaptive radiation because adaptive radiation is development of different functional structures from a common ancestral form. Which is also known as divergent evolution.

Transduction is process whereby, foreign DNA is notroduced into another call via a viral vector.