binary-strings

Which one of the following regular expressions represents the set of all binary strings with an odd number of 1’s?

Which one of the following regular expressions represents the language: the set of all binary strings having two consecutive $$0s$$ and two consecutive $$1s?$$

Let $${x_n}$$ denote the number of binary strings of length $$n$$ that contains no consecutive $$0s$$. Which of the following recurrences does $${x_n}$$ satisfy?

Let $${x_n}$$ denote the number of binary strings of length $$n$$ that contain no consecutive $$0s$$. The value of $${x_5}$$ is

The number of binary strings of $$n$$ zeros and $$k$$ ones such that no two ones are adjacent is: