Final answer:
A cervical swab would be used for the DNA test for gonorrhea in Mrs. Mills.
Step-by-step explanation:
The instrument that would be used for the DNA test for gonorrhea in Mrs. Mills would be a cervical swab. A cervical swab is a medical instrument that is used to collect a sample of cells from the cervix, which can then be sent to a medical lab for testing. In the case of gonorrhea, the cervical swab would be used to collect a sample of cervical cells that can be tested for the presence of the Neisseria gonorrhoeae bacterium, which is the causative agent of gonorrhea.