GATE CSE 2015 Set 2 | GATE CSE Year Wise Previous Years Questions

GATE CSE 2015 Set 2

MCQ (Single Correct Answer)

-0.6

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 $${X_0}$$?

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

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

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

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

GATE CSE 2015 Set 2

MCQ (Single Correct Answer)

-0.3

Consider the following statements.

$$\,\,\,$$ $${\rm I}.\,\,\,\,\,\,\,\,\,$$ The complement of every Turing decidable language is Turing decidable
$$\,$$ $${\rm II}.\,\,\,\,\,\,\,\,\,$$ There exists some language which is in $$NP$$ but is not Turing decidable
$${\rm III}.\,\,\,\,\,\,\,\,\,$$ If $$L$$ is a language in $$NP,$$ $$L$$ is Turing decidable

Which of the above statements is/are true?

Only $${\rm I}$$$${\rm I}$$

Only $${\rm III}$$

Only $${\rm I}$$ and $${\rm II}$$

Only $${\rm I}$$ and $${\rm III}$$

GATE CSE 2015 Set 2

MCQ (Single Correct Answer)

-0.3

Which one of the following statements is NOT correct about $$HTTP$$ cookies?

A cookie is a piece of code that has the potential to compromise the security of an Internet user

A cookie gains entry to the user’s work area through an $$HTTP$$ header

A cookie has an expiry date and time

Cookies can be used to track the browsing pattern of a user at a particular site

GATE CSE Papers

2025