The answers are B (captious) and E (bellicose).

The "yet" is the hinge of the sentence - it sets up a turn between how the magistrate appeared (austere reserve, read as judicious, i.e., fair-minded and even-tempered) and what people actually found once they appeared before her. That turn requires a word with a sharply negative judicial temperament, something at odds with "judicious."
- Captious means quick to find fault or raise petty objections - exactly the kind of disposition litigants would discover the hard way once arguing a case in front of her.
- Bellicose means inclined toward hostility or conflict - also consistent with a judge whose rulings reveal a combative rather than even-handed nature.

Both function as the "reveal" the sentence is building toward: not judicious after all, but contentious.

The other four don't fit that turn: conciliatory (placating) and phlegmatic (calm, even-tempered) would actually reinforce the initial impression of judiciousness rather than contrast with it, so they break the "yet." Obsequious (servile, eager to please) doesn't suit a magistrate ruling from the bench at all-it's the wrong power dynamic. Histrionic (theatrical, melodramatic) describes a style of self-presentation rather than a judicial temperament, so it doesn't cleanly fit "cast of mind" in this context.