Need help answering these homework questions for a Theory of Computation class. Got them all wrong the first time I attempted them

Question 1

Design a DFA to recognize a*b* what is the minimum number of states you need?

A	2
B	3
C	4
D	none of the above

Question 2

Let D = {w| w contains an odd number of as and an even number of bs and does not contain the substring ab}. what is the minimum number of states for a DFA that recognizes D.

A	3
B	4
C	5
D	none of the above

Question 3

Which of the following is/are true. (There may be multiple answers)

A	There is unique DFA for every regular language
B	Every regular language is also a context-free language
C	If A is regular, then the reverse of A is also regular.
D	Every subset of a regular language is regular

Question 4

S -> 0S0 | 1S1 | 0 | 1 | epsilon ; The language generated by the above grammar over the alphabet {0,1} is the set of

A	All palindromes
B	All even length palindromes
C	All odd length palindromes
D	Strings that begin and end with the same symbol

Question 5

Consider the CFG with {S,A,B) as the non-terminal alphabet, {a,b) as the terminal alphabet, S as the start symbol and the following set of production rules

S --> 1B S --> 0A

B --> 0 A --> 1

B --> 0S A --> 1S

B --> 1BB A --> 0AA

Which of the following strings is generated by the grammar?

A	100001
B	110000
C	111100
D	110010

Question 6

Suppose the alphabet is {a, b}, which of the following regular expression accepts accepts all strings that have odd number of a and reject otherwise? (multi-select question)

A	(b*ab*a)*b*ab*
B	ab*(ab*ab*)*
C	b*a(b*ab*ab*)*
D	(b*ab*ab*)*ab*

Question 7

Given the language L = {ab, aa, baa}, which of the following strings are in L*? (Note: this is a multi-select question, you may choose more than one option)

A	abaabaaabaa
B	aaaabaaaa
C	baaaaabaaaab
D	baaaaabaa

Question 8

Which of the following is/are context free? (multi-select question)

A	{0^n1^n}
B	A language {a^i b^j c^k} such that either i is not equal to j or j is not equal to k. The alphabet is {a, b, c}. That is, the set of strings of as followed by bs followed by cs, such that there are a different number of as and bs or a different number of bs and cs.
C	the set of strings over 0 and 1 with odd length.
D	all positive integer numbers

Question 9

Which of the CFL can generate exactly the following language {w: w=w^R}, the alphabet is {0, 1}. (there may be more than one correct answer)

A	S -> 0S0 | 1S1 | 0 | 1
B	S -> T T-> 0T0 | 1T1 | 0 | 1 |
C	S -> 0S0 | 1S1 | 0 | 1 |
D	S -> 0T0 | 1T1 | T-> 0T0 | 1T1 | 0 | 1 |