The sentence with the correct determiner is: Do you have any information about the lost child? In this sentence, "any" is the correct determiner used to inquire about information.

Here's why:

• "Any" is the correct indefinite article to use before a singular noun when we are unsure or have no specific information.
• "How few sugar did you buy?" is incorrect because "few" is an adjective and should be preceded by an article like "a" or "the." Also, "sugar" is an uncountable noun, so it should not be used with "few."
• "The head is the much sensitive part of the body." is incorrect because "much" is an adjective and should be replaced with an adverb like "most" or "very" to modify the adjective "sensitive."
• "He had absolutely a few knowledge about the postponement of the examination." is incorrect because "absolutely" negates the need for "a few." It should be either "absolutely no knowledge" or "some knowledge."