Consider the following C program:

#include< stdio.h >
void fun1(char *s1, char *s2){
  char *tmp;
  tmp = s1;
  s1 = s2;
  s2 = tmp;
}
void fun2(char **s1, char **s2){
  char *tmp;
  tmp = *s1;
  *s1 = *s2;
  *s2 = tmp;
}
int main(){
  char *str1 = "Hi", *str2 = "Bye";
  fun1(str1, str2); printf("%s %s ", str1, str2);
  fun2(&str1, &str2); printf("%s %s", str1, str2);
  return 0;
}

The output of the program above is

Consider the following C code. Assume that unsigned long int type length is 64 bits.

unsigned long int fun(unsigned long int n){
     unsigned long int i, j = 0, sum = 0;
     for (i = n; i > 1; i = i/2) j++;
     for ( ; j > 1; j = j/2) sum++;
     return(sum);
}

The value returned when we call fun with the input $${2^{40}}$$ is

Consider the following languages:

$$\,\,\,\,\,\,\,\,{\rm I}.\,\,\,\,\,\,\,$$ $$\left\{ {{a^m}{b^n}{c^p}{d^q}} \right.|m + p = n + q,$$ where $$\left. {m,n,p,q \ge 0} \right\}$$
$$\,\,\,\,\,\,{\rm II}.\,\,\,\,\,\,\,$$ $$\left\{ {{a^m}{b^n}{c^p}{d^q}} \right.|m = n$$ and $$p=q,$$ where $$\left. {m,n,p,q \ge 0} \right\}$$
$$\,\,\,\,{\rm III}.\,\,\,\,\,\,\,$$ $$\left\{ {{a^m}{b^n}{c^p}{d^q}} \right.|m = n = p$$ and $$p \ne q,$$ where $$\left. {m,n,p,q \ge 0} \right\}$$
$$\,\,\,\,{\rm IV}.\,\,\,\,\,\,\,$$ $$\left\{ {{a^m}{b^n}{c^p}{d^q}} \right.|mn = p + q,$$ where $$\left. {m,n,p,q \ge 0} \right\}$$

Which of the languages above are context-free?

Consider the following problems. $$L(G)$$ denotes the language generated by a grammar $$G.$$ $$L(M)$$ denotes the language accepted by a machine $$M.$$

$$\,\,\,\,\,\,\,\,{\rm I}.\,\,\,\,\,\,\,$$ For an unrestricted grammar $$G$$ and a string $$W,$$ whether $$w \in L\left( G \right)$$
$$\,\,\,\,\,\,{\rm II}.\,\,\,\,\,\,\,$$ Given a Turing machine $$M,$$ whether $$L(M)$$ is regular
$$\,\,\,\,{\rm III}.\,\,\,\,\,\,\,$$ Given two grammars $${G_1}$$ and $${G_2}$$, whether $$L\left( {{G_1}} \right) = L\left( {{G_2}} \right)$$
$$\,\,\,\,{\rm IV}.\,\,\,\,\,\,\,$$ Given an $$NFA$$ $$N,$$ whether there is a deterministic $$PDA$$ $$P$$ such that $$N$$
$$\,\,\,\,\,\,\,\,\,\,\,\,\,$$ $$\,\,\,\,\,\,\,\\,\,\,$$and $$P$$ accept the same language.

Which one of the following statements is correct?