In the sentence "Rarely in the case of armed robbery do we hear a plea of no contest.", the word "do" serves as an auxiliary (helping) verb used for emphasis and inversion.

Explanation:

1. Inversion for Emphasis:

   • The sentence begins with the adverb "Rarely", which is a negative or restrictive adverb.
   • In English, when a negative or restrictive adverb (e.g., "never," "rarely," "seldom," "hardly") starts a sentence, subject-verb inversion is required.
   • Instead of saying "We rarely hear a plea of no contest in the case of armed robbery.", the sentence is rearranged for emphasis:
     "Rarely in the case of armed robbery do we hear a plea of no contest."

2. Use of "do" in Inversion:

   • Since the main verb in the sentence is "hear", which is not an auxiliary verb, we need "do" to form the correct structure in the inverted sentence.
   • This is similar to how we use "do" in questions:
     • Normal: You hear a plea of no contest.
     • Question: Do you hear a plea of no contest?
   • In the inverted sentence, "do" serves the same function, helping move the verb "hear" before the subject "we."

Conclusion:

The "do" in the sentence is used for grammatical correctness due to the inversion caused by starting with "Rarely." It helps maintain proper subject-verb order while emphasizing the rarity of the event.