Regular Expression

Question 1
Which of the following regular expressions represent(s) the set of all binary numbers that are divisible by three? Assume that the string \epsilon is divisible by three.
[MSQ]
A
(0+1(01^*0)^*1)^*
B
(0+11+10(1+00)^*01)^*
C
(0^*(1(01^*0)^*1)^*)^*
D
(0+11+11(1+00)^*00)^*
GATE CSE 2021 SET-2   Theory of Computation
Question 2
Which one of the following regular expressions represents the set of all binary strings with an odd number of 1's?
A
((0+1)^* 1(0+1)^*1)^*10^*
B
(0^*10^*10^*)^*0^*1
C
10^*(0^*10^*10^*)^*
D
(0^*10^*10^*)^*10^*
GATE CSE 2020   Theory of Computation
Question 3
In some programming language, an identifier is permitted to be a letter followed by any number of letters or digits. If L and D denote the sets of letters and digits respectively, which of the following expressions defines an identifier?
A
(L+D)^{+}
B
\text { (L.D)* }
C
L(L+D)^{*}
D
L(L . D)^{*}
ISRO CSE 2017   Theory of Computation
Question 4
Let L=\left\{w \in(0+1)^{*} \mid w \text { has even number of } 1 \text { 's }\right\}, i.e. L is the set of all bit strings with even number of 1's. Which one of the regular expression below represents L?
A
(0^*10^*1)^*
B
0^*(10^*10^*)^*
C
0^*(10^*1^*)^*0^*
D
0^*1(10^*1)^*10^*
ISRO CSE 2016   Theory of Computation
Question 5
Which one of the following regular expressions represents the language: the set of all binary strings having two consecutive 0s and two consecutive 1s?
A
(0+1)*0011(0+1)*+(0+1)*1100(0+1)*
B
(0+1)*(00(0+1)*11+11(0+1)*00)(0+1)*
C
(0+1)*00(0+1)*+(0+1)*11(0+1)*
D
00(0+1)*11+11(0+1)*00
GATE CSE 2016 SET-1   Theory of Computation
Question 6
The length of the shortest string NOT in the language (over \Sigma={a,b}) of the following regular expression is _________.
a*b* (ba)* a*
A
1
B
2
C
3
D
4
GATE CSE 2014 SET-3   Theory of Computation
Question 7
Let L = {w \in (0 + 1)*|w has even number of 1s}, i.e. L is the set of all bit strings with even number of 1s. Which one of the regular expressions below represents L?
A
(0 *10 *1) *
B
0 * (10 *10 *) *
C
0 * (10 *1) * 0 *
D
0 *1(10 *1) *10 *
GATE CSE 2010   Theory of Computation
Question 8
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)*?
A
The set of all strings containing the substring 00.
B
The set of all strings containing at most two 0's.
C
The set of all strings containing at least two 0's.
D
The set of all strings that begin and end with either 0 or 1
GATE CSE 2009   Theory of Computation
Question 9
Which of the following regular expressions describes the language over\{0, 1\} consisting of strings that contain exactly two 1's?
A
(0 + 1)^ * \ 11(0 + 1) ^*
B
0 ^* \ 110 ^*
C
0 ^* 10 ^* 10 ^*
D
(0 + 1) ^* 1(0 + 1) ^* 1 (0 + 1) ^*
GATE IT 2008   Theory of Computation
Question 10
Consider the regular expression R = (a + b)^* \ (aa + bb) \ (a + b)^*
Which one of the regular expressions given below defines the same language as defined by the regular expression R ?
A
(a(ba)^* + b(ab)^*)(a + b)^+
B
(a(ba)^* + b(ab)^*)^*(a + b)^*
C
(a(ba)^* (a + bb) + b(ab)^*(b + aa))(a + b)^*
D
(a(ba)^* (a + bb) + b(ab)^*(b + aa))(a + b)^+
GATE IT 2007   Theory of Computation
There are 10 questions to complete.

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