1

### GATE CSE 2015 Set 2

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
2

### GATE CSE 2015 Set 2

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
$10\left( {0 + 10} \right){}^ * 1 + 110\left( {0 + 10} \right){}^ * 1$
3

### GATE CSE 2015 Set 2

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

### Paper Analysis of GATE CSE 2015 Set 2

Subject NameTotal Questions
Algorithms5
Compiler Design3
Computer Networks6
Computer Organization4
Data Structures3
Database Management System4
Digital Logic3
Discrete Mathematics12
Operating Systems4
Programming Languages3
Software Engineering3
Theory of Computation4
Web Technologies1