1
GATE CSE 2016 Set 1
Numerical
+1
-0
Consider the following C program.
#include < stdio.h >
void mystery(int *ptra, int *ptrb) {
int *temp;
temp = ptrb;
ptrb = ptra;
ptra = temp;
}
int main() {
int a=2016, b=0, c=4, d=42;
mystery(&a, &b);
if (a < c)
mystery(&c, &a);
mystery(&a, &d);
printf("%d\n", a);
}
The output of the program is _____________.
2
GATE CSE 2016 Set 1
+1
-0.3
Which of the following languages is generated by the given grammar? $$S \to aS|bS|\varepsilon$$\$
A
$$\left\{ {{a^n}{b^m}|n,m \ge 0} \right\}$$
B
$$\left\{ {w \in \left\{ {a,b} \right\}{}^ * |w} \right.$$ has equal number of $$a’s$$ and $$\left. {b's} \right\}$$
C
$$\left\{ {{a^n}|n \ge 0} \right\} \cup \left\{ {{b^n}|n \ge 0} \right\} \cup \left\{ {{a^n}{b^n}|n \ge 0} \right\}$$
D
$${\left\{ {a,b} \right\}^ * }$$
3
GATE CSE 2016 Set 1
+1
-0.3
Which of the following decision problems are undecidable?

$$\,\,\,\,\,\,\,\,\,\,{\rm I}.\,\,\,\,\,\,\,\,\,\,$$ Given $$NFAs$$ $${N_1}$$ and $${N_2},$$ is $$L\left( {{N_1}} \right) \cap L\left( {{N_2}} \right) = \Phi ?$$
$$\,\,\,\,\,\,\,\,{\rm I}{\rm I}.\,\,\,\,\,\,\,\,\,\,$$Given a $$CFG\,G = \left( {N,\sum {\,,P} ,S} \right)$$ and string $$x \in \sum {^ * } ,$$ does
$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$$ $$x \in L\left( G \right)?$$
$$\,\,\,\,\,\,{\rm I}{\rm I}{\rm I}.\,\,\,\,\,\,\,\,\,\,$$ Given $$CFGs\,\,{G_1}$$ and $${G_2},$$ is $$L\left( {{G_1}} \right) = L\left( {{G_2}} \right)?$$
$$\,\,\,\,\,\,{\rm I}V.\,\,\,\,\,\,\,\,\,\,$$ Given a $$TM$$ $$M,$$ is $$L\left( M \right) = \Phi ?$$

A
$${\rm I}$$ and $${\rm IV}$$ only
B
$${\rm II}$$ and $${\rm I}$$$${\rm I}$$$${\rm I}$$ only
C
$${\rm I}$$$${\rm I}$$$${\rm I}$$ and $${\rm IV}$$ only
D
$${\rm II}$$ and $${\rm IV}$$ only
4
GATE CSE 2016 Set 1
+1
-0.3
Which one of the following regular expressions represents the language: the set of all binary strings having two consecutive $$0s$$ and two consecutive $$1s?$$
A
$$\left( {0 + 1} \right){}^ * 0011\left( {0 + 1} \right){}^ * + \left( {0 + 1} \right){}^ * 1100\left( {0 + 1} \right){}^ *$$
B
$$\left( {0 + 1} \right){}^ * \left( {00\left( {0 + 1} \right){}^ * 11 + 11\left( {0 + 1} \right){}^ * \left. {00} \right)} \right.\left( {0 + 1} \right){}^ *$$
C
$$\left( {0 + 1} \right){}^ * 00\left( {0 + 1} \right){}^ * + \left( {0 + 1} \right){}^ * 11\left( {0 + 1} \right){}^ *$$
D
$$00\left( {0 + 1} \right){}^ * 11 + 11\left( {0 + 1} \right){}^ * 00$$
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