1
GATE CSE 2001
MCQ (Single Correct Answer)
+2
-0.6
Consider the following program
Program P2
      var n:int;
      procedure W(var x:int)
      begin
          x=x+1;
          print x;
      end

      procedure D
      begin
          var n:int;
          n=3;
          W(n);
      end
begin     \\begin P2
      n = 10;
      D;
end
If the language has dynamic scooping and parameters are passed by reference, what will be printed by the program?
A
10
B
11
C
3
D
None of the above
2
GATE CSE 2001
MCQ (Single Correct Answer)
+2
-0.6
Consider the following problem $$X.$$ Given a Turing machine $$M$$ over the input alphabet $$\sum , $$ any state $$q$$ of $$M$$ And a word $$w\,\,\varepsilon \,\,\sum {^ * ,} $$ does the computation of $$M$$ on $$w$$ visit the state $$q''$$

Which of the following statements about $$X$$ is correct?

A
$$X$$ is decidable
B
$$X$$ is undecidable but partially decidable
C
$$X$$ is undecidable and not even partially decidable
D
$$X$$ is not a decision problem
3
GATE CSE 2001
MCQ (Single Correct Answer)
+1
-0.3
Consider the following two statements;
$${S_1}\,\,:\,\,\left\{ {{0^{2n}}\left| {n \ge 1} \right.} \right\}$$ is a regular language
$${S_2}\,\,:\,\,\left\{ {{0^m}{1^n}{0^{m + n}}\left| {m \ge 1} \right.\,\,and\,\,n \ge \left. 1 \right\}} \right.$$ is a regular language

Which of the following statements is correct?

A
Only $${S_1}$$ is correct
B
Only $${S_2}$$ is correct
C
Both $${S_1}$$ and $${S_2}$$ are correct
D
None of $${S_1}$$ and $${S_2}$$ is correct
4
GATE CSE 2001
MCQ (Single Correct Answer)
+1
-0.3
Given an arbitrary non-deterministic finite automaton $$(NFA)$$ with $$N$$ states, the maximum number of states in an equivalent minimized $$DFA$$ is at least
A
$${N^2}$$
B
$${2^N}$$
C
$$2N$$
D
$$N!$$
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