Solution
Based on the given passage, the relationship between Assertion (A) and Reason (R) is that Assertion (A) is correct but (R) is not correct.
Assertion (A) states: "The passage presents a rationale behind the great writers' flight to the solitude of their thoughts and silent companionship of immortals." This assertion is supported by the passage, which explains that great thinkers seek solitude because of their intellectual nature and the "habitual meditation on the vast problems that underline human life." The passage clearly describes why these thinkers "fly to the solitude of their own thoughts, or the silent companionship of the immortals."
However, Reason (R) states: "They do so because they are melancholic and naturally averse to ordinary humanity and disgust of unregenerated masses." This explanation is not accurate according to the passage. While the passage mentions that great thinkers become "impatient of mere men," it attributes this to their "habit of intercourse with the gods" and the "spiritual or intellectual pride that is engendered on the high plane of intellectual life." The passage suggests their solitude stems from their intellectual depth and contemplative nature, not from melancholy or disgust toward humanity.
Hence, the correct answer is Option 3: Assertion (A) is correct but (R) is not correct.