Answer:

The correct answer is option 'C', the method used to determine the length of a string in Java is length(). Here is an explanation of why this is the correct answer:

1. Introduction:
In Java, the length of a string can be determined using the length() method. This method is a member of the String class and returns the number of characters present in the string.

2. Syntax:
The syntax to use the length() method is as follows:
```java
int length = str.length();
```
where str is the string for which we want to determine the length, and length is the variable that stores the length of the string.

3. Example:
Let's consider an example to understand how the length() method works:
```java
String str = "Hello, World!";
int length = str.length();
System.out.println("The length of the string is: " + length);
```
Output:
```
The length of the string is: 13
```
In the above example, the length() method is called on the string "Hello, World!" and the returned value (13) is stored in the variable length. The value is then printed to the console.

4. Explanation:
The length() method in Java calculates the length of a string by counting the number of characters present in the string. It does not include any whitespace or special characters in the count, only the actual characters in the string are considered.

5. Comparison with other options:
Let's compare option 'C' (length()) with the other given options:
- Option 'A' (count()): There is no built-in method called count() in Java for determining the length of a string.
- Option 'B' (size()): The size() method is used to determine the number of elements in a collection or container, such as an ArrayList. It is not applicable to strings.
- Option 'D' (getSize()): There is no built-in method called getSize() in Java for determining the length of a string.

Therefore, the correct option for determining the length of a string in Java is length().