The underlined portion of the sentence contains the final two items in a three-item list. Items in a list must be in parallel form. Here, however, the first two items, "conducting," and "diagnosing," are in gerund form (-ing form being used as a noun), while the third item, "to administer," is in the infinitive. Since the first item of the list appears before the underlined portion, the other items must match it in form. Thus, the correct answer will change the third item in the list.

Focusing on the third item, (A) and (D) use "to administer," (B) uses "administering," (C) uses "administer," and (E) uses "administration of."

(A) can be eliminated because it uses the non-parallel "conducting ... diagnosing ... and to administer."

(C) is incorrect because it uses the non-parallel "conducting ... diagnose ... and administer." Remember, the list begins before the underlined portion, so the items must match "conducting."

(D) can be eliminated because it uses the non-parallel "conducting ... to diagnose ... and to administer." Again, the list begins before the underlined portion, so the items must match "conducting."

(E) is incorrect because it uses the non-parallel "conducting ... diagnosis of ... and administration of."

(B) uses the correct parallel form and is the answer. It reads, "conducting ... diagnosing ... and administering."