Let $$L$$ denote the language generated by the grammar $$S \to 0S\left. 0 \right|00.$$ Which one of the following is true?

Let $$S$$ and $$T$$ be languages over $$\sum { = \left\{ {a,b} \right\}} $$ represented by the regular expressions $${\left( {a + {b^ * }} \right)^ * }$$ and $$\,{\left( {a + b} \right)^ * },$$ respectively. Which of the following is true?

Consider the regular expression $$(0+1)(0+1).......n$$ times. The minimum state finite automation that recognizes the language represented by this regular expression contains:

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