To solve this question, the user needs to understand the syntax and rules for declaring methods within an interface in Java.

In Java, an interface is a collection of abstract methods, which means the methods declared within an interface do not have a body. The purpose of an interface is to define a contract that classes can implement, specifying the methods they must provide.

Now, let's go through each option and explain why it is right or wrong:

A. public double methoda(); This option is a valid declaration within an interface definition. It declares a public method named "methoda" that returns a double value. Since interfaces only contain abstract methods, there is no need to provide a method body.

B. public final double methoda(); This option is not a valid declaration within an interface definition. The "final" keyword cannot be used to modify a method declaration within an interface. The "final" keyword is used to indicate that a method cannot be overridden by a subclass.

C. static void methoda(double d1); This option is not a valid declaration within an interface definition. The "static" keyword cannot be used to modify a method declaration within an interface. Static methods belong to the class itself, not an instance of the class.

D. protected void methoda(double d1); This option is not a valid declaration within an interface definition. The "protected" keyword cannot be used to modify a method declaration within an interface. Protected methods are accessible within the same package and by subclasses.

Therefore, the valid declaration within an interface definition is:

The Answer is: A. public double methoda();