The Kleene Star operation accepts the following string of finite length over set A = {0,1} | where string s contains even number of 0 and 1. 

The correct answer is ε, 0011, 11001100

Key PointsThe Kleene Star operation (*) is used to represent the set of all possible concatenations of zero or more instances of a given set of strings. In the context of regular expressions, the Kleene Star applied to a set of strings means any combination (including none) of those strings.

• ε,0011,11001100 - This set contains strings with an even number of 0s and 1s, so it satisfies the given condition.
• 0011,11001100 - This set contains strings with an even number of 0s and 1s, but it is not contain Null value, so it not fully correct the given condition.
• 01,0011,010101 - This set contains strings with an odd number of characters, so it does not satisfy the requirement of having an even number of 0s and 1s.
• ε,0011,11001101 - The empty string ε has an even number of 0s and 1s. However, the last string 11001101 has an odd number of characters, violating the condition.