To answer this question, let's go through each option to understand why it is correct or incorrect:
Option A) Methods cannot be overridden to be more private - This option is correct. In Java, when a method is overridden in a subclass, it must have the same or higher access level than the method it is overriding. Therefore, it is not possible to override a method to be more private.
Option B) static methods cannot be overloaded - This option is incorrect. In Java, static methods can be overloaded. Overloading refers to having multiple methods with the same name but different parameters in the same class.
Option C) private methods cannot be overloaded - This option is incorrect. In Java, private methods can be overloaded. Overloading refers to having multiple methods with the same name but different parameters in the same class.
Option D) An overloaded method cannot throw exceptions not checked in the base class - This option is incorrect. In Java, an overloaded method can throw exceptions that are not checked in the base class. The only restriction is that the overloaded method cannot throw checked exceptions that are not checked in the base class.
Therefore, the correct answer is A) Methods cannot be overridden to be more private. This option is correct because in Java, a method cannot be overridden to have a lower access level (more private) than the method it is overriding.