GATE CSE 2014 Set 3 | GATE CSE Year Wise Previous Years Questions

GATE CSE 2014 Set 3

MCQ (Single Correct Answer)

-0.6

Consider the following languages over the alphabet $$\sum { = \left\{ {0,\,1,\,c} \right\}:} $$
$$\eqalign{ & {L_1} = \left\{ {{0^n}\,{1^n}\,\left| {n \ge } \right.0} \right\} \cr & {L_2} = \left\{ {wc{w^r}\,\left| {w \in \left\{ {0,\,1} \right\}{}^ * } \right.} \right\} \cr & {L_3} = \left\{ {w{w^r}\,\left| {w \in \left\{ {0,\,1} \right\}{}^ * } \right.} \right\} \cr} $$

Here, $${w^r}$$ is the reverse of the string $$w.$$ Which of these languages are deterministic Context- free languages?

None of the languages

$$(B)$$ Only $${L_1}$$

Only $${L_1}$$ and $${L_2}$$

All the three languages.

GATE CSE 2014 Set 3

MCQ (Single Correct Answer)

-0.3

Let $$\sum \, $$ be a finite non - empty alphabet and let $${2^{\sum {{}^ * } }}$$ be the power set of $$\sum {{}^ * .\,} $$ Which one of the following is TRUE?

Both $${2^{\sum {{}^ * } }}$$ and $$\sum {^ * } $$ are countable

$${2^{\sum {{}^ * } }}$$ is countable and $$\sum {^ * } $$ is uncountable

$${2^{\sum {{}^ * } }}$$ is uncountable and $$\sum {^ * } $$ is countable

Both $${2^{\sum {{}^ * } }}$$ and $$\sum {^ * } $$ are uncountable

GATE CSE 2014 Set 3

MCQ (Single Correct Answer)

-0.6

Which one of the following problems is un-decidable?

Deciding if a given context-free grammar is ambiguous.

Deciding if a given string is generated by a given context-free grammar.

Deciding if the language generated by a given context-free grammar is empty.

Deciding if the language generated by a given context-free grammar is finite.

GATE CSE Papers

2024