"The professor began to work $\qquad$ on various periodically research projects-though never to the point that she failed to attend to her classes, since whether she received tenure was sporadically determined not only by published research but also, to some extent, by student recommendations."

The blank describes how the professor worked on research projects intermittently or occasionally, without neglecting her classes.

Evaluate options:
- A. periodically - means occurring at regular intervals; fits well with "various periodically research projects."
- B. sporadically - means irregularly or infrequently; also fits.
- C. monotonously - means boringly or repetitively; unlikely here.
- D. industriously - means working hard and energetically; positive, but no indication of periodicity.
- E. diligently - means showing care and effort; positive, but no indication of intermittence.
- F. fruitfully - means productively; focuses on result, not frequency.

Best fits:
- A. periodically - emphasizes regular intervals.
- B. sporadically - emphasizes irregular intervals.

Since the sentence says "various periodically research projects," and tenure was "sporadically" determined, the better match for how the professor worked is periodically or sporadically - both relating to frequency.

Final answer:
A. periodically
B. sporadically