GATE CS Regular Expressions and Finite Automata questions

Let $w$ be any string of length $n$ in $\{0,1\}^*$. Let $L$ be the set of all substrings of $w$. What is the minimum number of states in non-deterministic finite automation that accepts $L$?

Let $L=\{ w \in \:(0+1)^* \mid w\text{ has even number of }1s \}$. i.e., $L$ is the set of all the bit strings with even numbers of $1$s. Which one of the regular expressions below represents $L$?

The above DFA accepts the set of all strings over $\{0,1\}$ that

Which one of the following languages over the alphabet $\{0,1\}$ is described by the regular expression: $(0+1)^*0(0+1)^*0(0+1)^*$?

Match the following NFAs with the regular expressions they correspond to: P Q R S $\epsilon + 0\left(01^*1+00\right)^*01^*$ $\epsilon + 0\left(10^*1+00\right)^*0$ $\epsilon + 0\left(10^*1+10\right)^*1$ $\epsilon + 0\left(10^*1+10\right)^*10^*$

Consider the following Finite State Automaton: The minimum state automaton equivalent to the above FSA has the following number of states:

Consider the following Finite State Automaton: The language accepted by this automaton is given by the regular expression

A minimum state deterministic finite automaton accepting the language $L=\{w\mid w \in \{0, 1\}^*,$ number of $0$s and $1$s in $w$ are divisible by $3$ and $5$, respectively $\}$ has

Consider the regular language $L=(111+11111)^{*}.$ The minimum number of states in any DFA accepting this languages is:

The following diagram represents a finite state machine which takes as input a binary number from the least significant bit. Which of the following is TRUE?

Let $N_f$ and $N_p$ denote the classes of languages accepted by non-deterministic finite automata and non-deterministic push-down automata, respectively. Let $D_f$ and $D_p$ denote the classes of languages accepted by deterministic finite automata and deterministic push-down automata respectively. Which one of the following is TRUE?

The following finite state machine accepts all those binary strings in which the number of $1$’s and $0$’s are respectively:

Consider the NFA $M$ shown below. Let the language accepted by $M$ be $L$. Let $L_1$ be the language accepted by the NFA $M_1$ obtained by changing the accepting state of $M$ to a non-accepting state and by changing the non-accepting states of $M$ to accepting states. Which of the following statements is true?

Consider the following deterministic finite state automaton $M$. Let $S$ denote the set of seven bit binary strings in which the first, the fourth, and the last bits are $1$. The number of strings in $S$ that are accepted by $M$ is

The regular expression $0^*(10^*)^*$ denotes the same set as

The smallest finite automaton which accepts the language $\{x \mid$ length of $x$ is divisible by $3\}$ has

The finite state machine described by the following state diagram with $A$ as starting state, where an arc label is $x/y,$ and $x$ stands for $1$-bit input and $y$ stands for $2$-bit output

Consider a DFA over $\Sigma=\{a,b\}$ accepting all strings which have number of a's divisible by $6$ and number of $b$'s divisible by $8$. What is the minimum number of states that the DFA will have?

Given an arbitrary non-deterministic finite automaton (NFA) with $N$ states, the maximum number of states in an equivalent minimized DFA at least

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