Explanation:

The given word pair is "Sorrow : Black", and we need to find a related word pair from the given options.

Relation between Sorrow and Black:
Sorrow is an emotion that is often associated with sadness, grief, or a feeling of loss. Black, on the other hand, is a color that is often associated with darkness, mourning, or a lack of light. In this word pair, black is used to convey a sense of darkness or sadness, which is related to the emotion of sorrow.

Applying the same logic to the options:

a) Red : Green
Red and green are both colors, but they do not have a direct relationship. They are not related in terms of emotions or meanings. Therefore, this option can be eliminated.

b) Rank : Star
Rank and star are unrelated terms. They do not have a clear connection in terms of their meanings or associations. Therefore, this option can be eliminated.

c) Danger : Green
Danger and green are both unrelated terms. Danger is associated with a sense of risk or harm, while green is a color associated with nature or freshness. There is no clear relationship between these two terms. Therefore, this option can be eliminated.

d) Pink : Pencil
Pink and pencil are unrelated terms. Pink is a color, while pencil is an object. There is no direct relationship between these two terms in terms of their meanings or associations. Therefore, this option can be eliminated.

Conclusion:

After analyzing all the given options, the only related word pair is "Rank : Star". Both rank and star are terms that can be associated with positions or levels of achievement. A rank can refer to a position or level of authority, while a star can represent excellence or recognition. Therefore, "Rank : Star" is the correct answer.