1

GATE CSE 2008

MCQ (Single Correct Answer)

+2

-0.6

Which of the following statements are true?

$$1.$$ Every left-recursive grammar can be converted to a right-recursive grammar and vice-versa

$$2.$$ All ε-productions can be removed from any context-free grammar by suitable transformations

$$3.$$ The language generated by a context-free grammar all of whose productions are of the form $$X \to w$$ or $$X \to wY$$ (where, $$w$$ is a string of terminals and $$Y$$ is a non terminal), is always regular

$$4.$$ The derivation trees of strings generated by a context-free grammar in Chomsky Normal Form are always binary trees

$$1.$$ Every left-recursive grammar can be converted to a right-recursive grammar and vice-versa

$$2.$$ All ε-productions can be removed from any context-free grammar by suitable transformations

$$3.$$ The language generated by a context-free grammar all of whose productions are of the form $$X \to w$$ or $$X \to wY$$ (where, $$w$$ is a string of terminals and $$Y$$ is a non terminal), is always regular

$$4.$$ The derivation trees of strings generated by a context-free grammar in Chomsky Normal Form are always binary trees

2

GATE CSE 2008

MCQ (Single Correct Answer)

+2

-0.6

Match the following List-$${\rm I}$$ with List - $${\rm II}$$

**List-$${\rm I}$$**

$$E)$$ Checking that identifiers are declared before their

$$F)$$ Number of formal parameters in the declaration of a function agrees with the number of actual parameters in a use of that function

$$G)$$ Arithmetic expression with matched pairs of parentheses

$$H)$$ Palindromes

**List-$${\rm II}$$**

$$P)$$ $$L = \left\{ {{a^n}{b^m}{c^n}{d^m}\,|\,n \ge 1,m \ge 1} \right\}$$

$$Q)$$ $$X \to XbX\,|\,XcX\,|\,dXf\,|g$$

$$R)$$ $$L = \left\{ {www\,|\,w \in \left( {a\,|\,b} \right){}^ * } \right\}$$

$$S)$$ $$X \to bXB\,|\,cXc\,|\,\varepsilon $$

3

GATE CSE 2007

MCQ (Single Correct Answer)

+2

-0.6

The language $$L = \left\{ {{0^i}{{21}^i}\,|\,i \ge 0} \right\}$$ over the alphabet $$\left\{ {0,1,2} \right\}$$ is

4

GATE CSE 2007

MCQ (Single Correct Answer)

+2

-0.6

Consider the $$CFG$$ with $$\left\{ {S,A,B} \right\}$$ as the non-terminal alphabet, $$\left\{ {a,b} \right\}$$ as the terminal alphabet, $$S$$ as the start symbol and the following set of production rules:

For the correct string of (earlier question) how many derivation trees are there?

Questions Asked from Push Down Automata and Context Free Language (Marks 2)

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