Consider the following C functions.

int tob(int b, int* arr) {
     int i;
     for (i=0; b>0; i++) {
           if (b%2) arr[i] = 1;
           else arr[i]=0;
           b = b/2;
    }
    return (i);
}

____________________

int pp(int a, int b) {
     int arr[20];
     int i, tot = 1, ex, len;
     ex = a;
     len = tob (b, arr);
     for (i=0;  i < len; i++) {
           if (arr[i] ==1)
              tot = tot * ex;
           ex = ex * ex;
    }
    return (tot);
}

The value returned by pp (3, 4) is ________.

Consider the following C functions.

int fun1 (int n) {
     static int i = 0;
     if (n > 0) {
            ++i;
            fun1(n-1);
     }
     return (i);
}

___________________

int fun2 (int n) {
     static int i = 0;
     if (n > 0) {
            i = i + fun1 (n);
            fun2(n-1);
     }
     return (i);
}

The return value of fun2 (5) is _______.

Consider the following languages.

L₁ = {wxyx | w, x, y ∈ (0 + 1)⁺}

L₂ = {xy | x, y ∈ (a + b)*, |x| = |y|, x ≠ y}

Which one of the following is TRUE?

Which of the following languages are undecidable? Note that $$\langle M\rangle $$ indicates encoding of the Turing machine M.

L₁ = $$\left\{ {\langle M\rangle |L\left( M \right) = \phi } \right\}$$
L₂ = $$\{ \langle M,w,q\rangle |$$ M on input w reaches state q in exactly 100 steps }
L₃ = { $$\langle M\rangle |$$ L(M) is not recursive }
L₄ = { $$\langle M\rangle |$$ L(M) contains at least 21 members }