How many substrings of different lengths (non-zero) can be formed from a character string of length $$n$$ ?

Let $$L$$ be the set of all binary strings whose last two symbols are the same. The number of states in the minimum state deterministic finite-state automaton accepting $$L$$ is

Let $$L$$ be the set of all binary strings whose last two symbols are the same. The number of states in the minimum state deterministic finite-state automation accepting $$L$$ is

Which of the following statements is false?