To answer this question, let's go through each option to understand why it is correct or incorrect:
Option A) Compilation error: Divisions must be in a try block - This option is incorrect. Divisions do not need to be in a try block. The try-catch block is used to handle exceptions that may occur during the execution of a program, but it is not necessary for all divisions.
Option B) Compilation error: DivideByZeroException - This option is incorrect. The code will compile without any errors.
Option C) Runtime Exception - This option is correct. When dividing an integer by zero, a runtime exception called "ArithmeticException" is thrown. In this case, the code will throw a "ArithmeticException: divide by zero" runtime exception.
Option D) No Error: a is NaN - This option is incorrect. NaN (Not a Number) is a special value in some programming languages that represents an undefined or unrepresentable value. However, in Java, dividing an integer by zero does not result in NaN. It throws an exception instead.
The correct answer is C) Runtime Exception. This option is correct because dividing an integer by zero will result in a runtime exception.