The following postfix expression with single digit operands is evaluated using a stack: 8 2 3 ^ / 2 3 * + 5 1 * - Note that ^ is the exponentiation operator. The top two elements of the stack after the first * is evaluated are:

Consider the following C program:

#include 
#define EOF -1 
     void push (int); /* push the argument on the stack */ 
     int pop (void); /* pop the top of the stack */ 
     void flagError (); 
     int main () { 
       int c, m, n, r; 
       while ((c = getchar ()) != EOF) { 
         if (isdigit (c) ) 
           push (c); 
         else if ((c == '+') || (c == '*')) { 
           m = pop (); 
           n = pop (); 
           r = (c == '+') ? n + m : n*m; 
           push (r); 
         } else if (c != ' ') 
           flagError (); 
       } 
       printf("% c", pop ()); 
    } 

What is the output of the program for the following input ? 5 2 * 3 3 2 + * +

The following function computes the value of ^mC_n correctly for all legal values m and n (m≥1,n≥0 and m>n)

int func(int m, int n) 
{ 
     if (E) return 1; 
     else return(func(m -1, n) + func(m - 1, n - 1)); 
} 

In the above function, which of the following is the correct expression for E?

An implementation of a queue Q, using two stacks S1 and S2, is given below:

void insert(Q, X){
  push(S1, X);
}

void delete(Q){
 if(stack - empty(S1)) then {
   print("Q is empty");
   return;
 }else while (!(stack - empty(S1))){
   X = pop(S1);
   push(S2, X);
 }
 X = pop(S2);
}

Let n insert and $$m( \le n)$$ delete operations be performed in an arbitrary order on an empty queue Q. Let x and y be the number of push and pop operations performed respectively in the process. Which one of the following is true for all m and n?