Set of Binary Strings that do not contain 001 as Substring | DFA NFA Grammar | 021

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Set of Binary strings that do not contain 001 as substring, Automata Theory, in hindi, lectures, iit, tutorial, {0,1}* that does not contain the substring 001 w ∈ {0,1}* | w contains the substring 001
w does not contain the substring 110 regular expression
w does not contain two consecutive 0's
w ∈ {0,1}* | |w| is divisible by 2 or 3
Regular expression for a string not containing a set of substrings
w | w does not contain neither of the substrings 11 and 00.
Which one of the following regular expressions over {0,1} denotes the set of all strings not containing 100 as substring?
(a) 0∗(1+0)∗
(b) 0∗1010∗
(c) 0∗1∗01∗
(d) 0∗(10+1)∗
Consider the set of strings on {0,1} in which, every substring of 3 symbols has at most two zeros. For example, 001110 and 011001 are in the language, but 100010 is not. All strings of length less than 3 are also in the language. A partially completed DFA that accepts this language is shown below.
Let L1={w∈{0,1}∗∣w has at least as many occurrences of (110)′s as (011)′s}. Let L2={w∈{0,1}∗ ∣w has at least as many occurrences of (000)′s as(111)′s}. Which one of the following is TRUE?
(A) L1 is regular but not L2

(B) L2 is regular but not L1

(C) Both L1 and L2 are regular

(D) Neither L1 nor L2 are regular