Correct option is A
The correct option is (a).
The error lies in the first segment: “The informations”. The noun information is an uncountable noun in English, so it does not take a plural form “informations.” Therefore, the correct phrase should be “The information”.
Option (a) correctly rectifies the error by changing “informations” to “information” and keeping the sentence grammatically correct: “The information given by the department about his whereabouts proved to be useless.”
Grammatical rule used: Uncountable nouns (information, advice, furniture, luggage, equipment) generally do not take plural “-s” and are not used with “many” or “few.” They are used with “much,” “a piece of,” “some,” etc.
Example: He gave me some information about the exam. (Not: informations)
Information booster: If you want to count such nouns, use counting expressions like a piece of information, two pieces of information.
So the correct answer is (a)