Step 1: Understand the meaning of the underlined word.
The word eloquent means able to express thoughts and ideas clearly, effectively, and persuasively.
Step 2: Interpret the sentence.
The sentence says that the Chairman delivered an eloquent speech which inspired the employees. This indicates that the speech was clear, impressive, and persuasive.
Step 3: Analyse the options.
• (A) inspiring -- Incorrect. An inspiring speech is often eloquent rather than opposite to it.
• (B) lengthy -- Incorrect. A speech may be long or short regardless of being eloquent.
• (C) inarticulate -- Correct. It means unable to express ideas clearly, which is the opposite of eloquent.
• (D) formal -- Incorrect. Formal refers to style, not clarity of expression.
Step 4: Final conclusion.
\[
\boxed{\text{Eloquent} \longleftrightarrow \text{Inarticulate}}
\]
Hence, the correct option is \(\boxed{(C)}\).