Final answer:
The variable declaration that would not compile in Java is 'int 1_var;' because it begins with a number, violating Java's variable naming conventions.
Step-by-step explanation:
In Java, variable names must follow certain rules for the code to compile correctly. A variable name can begin with a letter, an underscore (_), or a dollar sign ($). However, it cannot start with a number. Therefore, out of the options provided, the only variable declaration that would NOT compile in a Java program is (e) int 1_var;. This is because it begins with a number, which is against Java's variable naming rules. The rest of the options are all valid Java variable names, as they start with either a letter or an underscore.