Valid class declaration in Java:
A valid class declaration in Java consists of the keyword "class" followed by the class name and a pair of curly braces. Inside the curly braces, we can define variables, methods, and other members of the class.

Explanation of options:
a) class A { int x; };
This is a valid class declaration. It declares a class named A with a single variable x of type int.

b) class B { }
This is also a valid class declaration. It declares a class named B with no members inside the class.

c) public class A { }
This is a valid class declaration. It declares a public class named A with no members inside the class.

d) object A { int x; };
This is not a valid class declaration. The keyword "object" is not used to declare a class in Java. Instead, the keyword "class" is used.

Explanation of the correct answer:
The correct answer is option 'A' because it follows the syntax of a valid class declaration in Java. It declares a class named A with a single variable x of type int. The class declaration ends with a semicolon after the closing curly brace.

The other options (B, C, and D) are not valid class declarations for the following reasons:
- Option B is a valid class declaration but does not have any members inside the class.
- Option C is a valid class declaration but does not have any members inside the class and is declared as public.
- Option D is not a valid class declaration because it uses the keyword "object" instead of "class" to declare the class.

In summary, the valid class declaration is option 'A' because it follows the correct syntax and declares a class with a variable inside it.