Let M be the 5-state NFA with ε-transitions shown in the diagram below.
![GATE CSE 2024 Set 2 Theory of Computation - Finite Automata and Regular Language Question 2 English](https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1lwug14iu/097d303e-8a05-4f40-a6d1-704bb307186d/beef5c60-1f2a-11ef-b236-4f75b99a7f02/file-6y3zli1lwug14iv.png?format=png)
Which one of the following regular expressions represents the language accepted by M?
Let L1 be the language represented by the regular expression b*ab*(ab*ab*)* and L2 = { w ∈ (a + b)* | |w| ≤ 4 }, where |w| denotes the length of string w. The number of strings in L2 which are also in L1 is __________.
Consider the 5-state DFA $M$ accepting the language $L(M) \subseteq (0+1)^*$ shown below. For any string $w \in (0+1)^*$ let $n_0(w)$ be the number of 0's in $w$ and $n_1(w)$ be the number of 1's in $w$.
![GATE CSE 2024 Set 1 Theory of Computation - Finite Automata and Regular Language Question 5 English](https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1lwudgsa3/5967e0f4-529b-4f25-a913-7a26e7bb4b18/b7094fb0-1f20-11ef-b5e1-abf5eb713f23/file-6y3zli1lwudgsa4.png?format=png)
Which of the following statements is/are FALSE?
Consider the following two regular expressions over the alphabet {0,1} :
$$r = 0^* + 1^*$$
$$s = 01^* + 10^*$$
The total number of strings of length less than or equal to 5, which are neither in r nor in s, is ________