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 because there is no requirement to enclose divisions in a try block. The try-catch block is used to handle exceptions, but it is not necessary for every division operation.
Option B) Compilation error: DivideByZeroException - This option is incorrect because there is no compilation error related to a divide-by-zero exception. In this case, a runtime exception will occur.
Option C) Runtime Exception - This option is correct. The division by zero operation is not allowed in mathematics, and it will result in a runtime exception called "ArithmeticException: Divide by zero". Therefore, executing the given code will result in a runtime exception.
Option D) No Error: a is NaN - This option is incorrect. NaN (Not a Number) is a special floating-point value that represents an undefined or unrepresentable result. However, dividing by zero does not result in NaN. It results in a runtime exception.
The correct answer is C. The code will result in a runtime exception.