Which of the following classes will not allow unsynchronized read operations by multiple threads?

To answer this question, the user needs to have knowledge of Java's synchronized collections and multithreading.

Option A: Vector is a synchronized collection class, which means that multiple threads can read and write from it but only one thread can access it at a time. Therefore, unsynchronized read operations are not allowed by multiple threads in Vector.

Option B: TreeMap is not a synchronized collection class, and therefore, it does not provide thread-safety. Multiple threads can read and write to it at the same time, which means that unsynchronized read operations are allowed by multiple threads in TreeMap.

Option C: TreeSet is not a synchronized collection class, and therefore, it does not provide thread-safety. Multiple threads can read and write to it at the same time, which means that unsynchronized read operations are allowed by multiple threads in TreeSet.

Option D: HashMap is not a synchronized collection class, and therefore, it does not provide thread-safety. Multiple threads can read and write to it at the same time, which means that unsynchronized read operations are allowed by multiple threads in HashMap.

Option E: HashSet is not a synchronized collection class, and therefore, it does not provide thread-safety. Multiple threads can read and write to it at the same time, which means that unsynchronized read operations are allowed by multiple threads in HashSet.

Therefore, the answer is: A. Vector