(a) Draw a precedence graph for the following sequential code. The statements are numbered from S₁ to S₆

 S1       read n
 S2       i:=1
 S3       if i>n goto next
 S4       a(i):=i+1
 S5       i:=i+1
 S6       next : Write a(i) 

(b) Can this graph be converted to a concurrent program using parbegin-parend construct only?

What function of x, n is computed by this program?

 Function what (x, n:integer): integer:
 Var
     value : integer;
     begin
     value:=1
     if n>0 then
 begin
     if n mod 2 = 1 then
     value:=value*x;
     value:=value*what(x*x, n div 2);
     end;
     what:value
     end; 

On the set N of non-negative integers, the binary operation __________ is associative and non-commutative.

Consider the following C functions.

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

The return value of fun2 (5) is _______.

How many onto (or surjective) functions are there from an n-element (n ≥ 2) set to a 2-element set?

Let A be a set of n(>0) elements. Let N_r be the number of binary relations on A and let N_f be the number of functions from A to A.

(a) Give the expression for N_r in terms of n.
(b) Give the expression for N_f in terms of n.
(c) Which is larger for all possible n, N_r or N_f?

Let A and B be sets with cardinalities m and n respectively. The number of one-one mappings (injections) from A to B, when m < n, is:

The Laplace transform of the periodic function f(t) described by the curve below, i.e.,

is _________

The function f(x,y) = x²y - 3xy + 2y + x has

Consider the following C function.

               void convert (int n) {
                       if (n < 0)
                          printf ("%d", n);
                       else {
                          convert (n/2);
                          printf ("%d", n%2);
                       }
               }

Which one of the following will happen when the function convert is called with any positive integer n as argument?

Consider the following C program:

         #include <stdio.h>
         int jumble (int x, int y)  {
               x = 2 * x + y ;
               return x ;
         }
         int main ( )  {
               int x=2, y=5 ;
               y = jumble (y, x) ;
               x = jumble (y, x) ;
               printf ("%d \n", x) ;
               return 0 ;
         }

The value printed by the program is ______.

The time complexity of the following C function is (assume n>0)

int recursive (int n)
{
  if (n==1) return(1);
  else return(recursive (n-1) + recursive(n-1));
}

int function (int x, int y)
{
 if(y<=0) return x;
 return function (y, x%y);
} 

The above recursive function computes ______