Explanation:

This question requires us to choose the most appropriate determiner to complete the sentence 'They gave us ................. a form to fill in...'. The sentence implies that each individual within the group 'us' received a single form. Let's analyze each option: **Option (A): every** 'Every' is a determiner that refers to all the members of a group, considered individually. It is typically followed by a singular countable noun (e.g., 'every student', 'every day'). It cannot directly modify a pronoun like 'us' in this construction. While one might say 'They gave every one of us a form' or 'They gave a form to every student', 'They gave us every a form' is grammatically incorrect. **Option (B): some** 'Some' is a determiner used to refer to an unspecified quantity or number of something. It can be used with both countable and uncountable nouns. If used with 'a form', it would typically be 'They gave us some forms' (plural) or 'They gave some of us a form'. 'They gave us some a form' is grammatically incorrect and doesn't make sense, as 'some' and 'a' contradict each other when referring to the same item in this way. **Option (C): a few** 'A few' is a determiner meaning a small number of something. It is used with plural countable nouns (e.g., 'a few students', 'a few forms'). Similar to 'some', it cannot be used in the construction 'us ... a form'. 'They gave us a few a form' is grammatically incorrect. It would be 'They gave a few of us a form' or 'They gave us a few forms'. **Option (D): each** 'Each' is a determiner or pronoun that refers to every single one of two or more people or things, regarded separately. When 'each' is used after a pronoun like 'us' (or 'them', 'you'), it means that the action was performed individually for every person in that group. So, 'They gave us each a form' means 'They gave a form to each one of us'. This construction is grammatically correct and perfectly conveys the intended meaning that every student among 'us' received a form. This is the most appropriate choice. **Conclusion:** The determiner 'each' is correctly used after a pronoun (like 'us') to indicate that an action applies individually to every member of the group. This fits the context of distributing a single form to every student. Therefore, option (D) is the correct answer.