Concept:The word "invaluable" means extremely useful or priceless, so its opposite must mean "having no use or value."
Explanation:The underlined word is "invaluable."
In English, "invaluable" does not mean "not valuable"; it actually means "so valuable that it is impossible to measure."
Thus, we need an antonym that expresses the complete lack of usefulness or worth.
Option A "insincere" refers to being dishonest, which is not related to value or usefulness.
Option C "impossible" means something cannot happen, not something that is worthless.
Option D "preposterous" means absurd or ridiculous, which is also unrelated.
Option B "useless" means having no value or benefit, which is the exact opposite of "invaluable."
Therefore, the correct word to fill the gap is "useless."
Answer:B. useless