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1

GATE CSE 2015 Set 2

Numerical
The number of states in the minimal deterministic finite automaton corresponding to the regular expression $${\left( {0 + 1} \right)^{\,\, * }}\left( {10} \right)$$ is ________________.
Your Input ________

Answer

Correct Answer is 3
2

GATE CSE 2015 Set 2

MCQ (Single Correct Answer)
Which of the following languages is/are regular?

$${L_1}:\left\{ {wx{w^R}|w,x\, \in \left\{ {a,b} \right\}{}^ * } \right.$$ and $$\left. {\left| w \right|,\left| x \right| > 0} \right\},\,{w^R}$$ is the reverse of string $$w$$
$${L_2}:\left\{ {{a^n}{b^m}\left| {m \ne n} \right.} \right.$$ and $$m,n \ge \left. 0 \right\}$$
$${L_3}:\left\{ {{a^p}{b^q}{c^r}\left| {p,q,r \ge 0} \right.} \right\}$$

A
$${L_1}$$ and $${L_3}$$ only
B
$${L_2}$$ only
C
$${L_2}$$ and $${L_3}$$ only
D
$${L_3}$$ only
3

GATE CSE 2015 Set 2

MCQ (Single Correct Answer)
Consider the alphabet $$\sum { = \left\{ {0,1} \right\},} $$ the null/empty string $$\lambda $$ and the sets of strings $${X_0},\,{X_1},$$ and $${X_2}$$ generated by the corresponding non-terminals of a regular grammar. $${X_0},\,\,{X_1},\,$$ and $${X_2}$$ are related as follows. $$$\eqalign{ & {X_0} = 1\,X{}_1 \cr & {X_1} = 0{X_1} + 1\,{X_2} \cr & {X_2} = 0\,{X_1} + \left\{ \lambda \right\} \cr} $$$
Which one of the following choices precisely represents the strings in $${X_0}$$?
A
$$10\left( {{0^ * } + {{\left( {10} \right)}^ * }} \right)1$$
B
$$10\left( {{0^ * } + \left( {10} \right){}^ * } \right){}^ * 1$$
C
$$1\left( {0 + 10} \right){}^ * 1$$
D
$$10\left( {0 + 10} \right){}^ * 1 + 110\left( {0 + 10} \right){}^ * 1$$
4

GATE CSE 2015 Set 2

MCQ (Single Correct Answer)
Which one of the following statements is NOT correct about $$HTTP$$ cookies?
A
A cookie is a piece of code that has the potential to compromise the security of an Internet user
B
A cookie gains entry to the user’s work area through an $$HTTP$$ header
C
A cookie has an expiry date and time
D
Cookies can be used to track the browsing pattern of a user at a particular site

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