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Obsequious describes a person who is excessively eager to please or obey someone, particularly a person in authority. Servile is the closest synonym because it suggests exaggerated submission and willingness to flatter. For example, an obsequious employee may agree with every opinion expressed by a superior, even when the opinion is incorrect. The word generally carries a negative meaning.

Profligate means recklessly extravagant or wasteful, especially in spending money. Thrifty describes someone who manages resources carefully and avoids unnecessary expenditure. Therefore, thrifty is the best antonym. A profligate person may spend beyond their means, whereas a thrifty person tries to save money and use resources efficiently.

In formal standard English, neither, when used as a singular pronoun referring to two alternatives, generally takes a singular verb. Therefore, 'Neither of the two explanations is satisfactory' is the expected examination answer. The noun following 'of the two' remains plural, but the subject of the verb is 'neither'.