1
GATE CSE 2008
+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-$${\rm II}$$
$$P)$$ $$L = \left\{ {{a^n}{b^m}{c^n}{d^m}\,|\,n \ge 1,m \ge 1} \right\}$$
$$Q)$$ $$X \to XbX\,|\,XcX\,|\,dXf\,|g$$
$$R)$$ $$L = \left\{ {www\,|\,w \in \left( {a\,|\,b} \right){}^ * } \right\}$$
$$S)$$ $$X \to bXB\,|\,cXc\,|\,\varepsilon$$

A
$$E - P,\,F - R,\,G - Q,\,H - S$$
B
$$E - R,\,F - P,\,G - S,\,H - Q$$
C
$$E - R,\,F - P,\,G - Q,\,H - S$$
D
$$E - P,\,F - R,\,G - S,\,H - Q$$
2
GATE CSE 2007
+2
-0.6
The language $$L = \left\{ {{0^i}{{21}^i}\,|\,i \ge 0} \right\}$$ over the alphabet $$\left\{ {0,1,2} \right\}$$ is
A
Not recursive.
B
is recursive and is a deterministic $$CFL$$.
C
is a regular language.
D
is not a deterministic $$CFL$$ but a $$CFL$$.
3
GATE CSE 2007
+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?

A
$$1$$
B
$$2$$
C
$$3$$
D
$$4$$
4
GATE CSE 2007
+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:

Which of the following strings is generated by the grammar?

A
$$aaaabb$$
B
$$aabbbb$$
C
$$aabbab$$
D
$$abbbba$$
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