Rationale
Ambivalent and decisive are antonyms.
Antonyms are words that have opposite meanings. Ambivalent means having mixed feelings or contradictory ideas about something or someone, whereas decisive means settling an issue or producing a definite result.
A) Unfettered - loosened
These two words do not represent antonyms as they both have similar meanings. Unfettered means free, unrestricted, or liberated, while loosened also implies being free or relaxed. So, these words are synonyms, not antonyms.
B) Ambivalent - decisive
As mentioned, these two words have opposite meanings. Ambivalent is when one has mixed feelings or is unsure, while decisive implies certainty or conclusiveness. Therefore, they are antonyms.
C) Ambitious - determined
Ambitious and determined cannot be considered as antonyms since they both have positive connotations and similar meanings. Being ambitious means having a strong desire for success, achievement, or distinction, and being determined refers to having made a firm decision and being resolved not to change it. Hence, these words are more synonymous than antonymous.
D) Lucrative-profitable
Lucrative and profitable both suggest yielding a favorable or useful result, especially in terms of earning money. Therefore, these words are synonyms, not antonyms.
Conclusion
In summary, antonyms are words with opposite meanings. Among the given pairs, only ambivalent (having mixed feelings or contradictory ideas) and decisive (settling an issue or producing a definite result) are antonyms. The other pairs are more synonymous in nature, expressing similar rather than opposite meanings.