If a passage uses formal diction and logical reasoning to support a claim, the author's primary tone is likely:

The correct option is a.

When a passage uses formal diction (precise, academic language) and logical reasoning to support a claim, the author's primary goal is typically to present information or an argument in a clear, unbiased, and factual manner. This approach is characteristic of an objective tone. An objective tone avoids personal feelings, opinions, or emotional language, focusing instead on evidence and rational thought.

• b. A playful tone would involve humor and lightheartedness, which usually doesn't align with formal diction and strict logical reasoning.
• c. A sentimental tone expresses strong emotions like nostalgia or tenderness, which is subjective and contrasts with a logical, formal approach.
• d. An angry tone conveys displeasure or hostility, which is an emotional stance rather than a purely logical and formal one.

The final answer is $\boxed{\text{a. Objective}}$.