1. {7,5}. For a general array 'process' will swap the first two elements
   in the array

2. 
import java.util.*;

public class Question2 {
  public static boolean isPalindrome(char[] a) {
    for (int i = 0; i < a.length/2; i++) {
      if (a[i] != a[a.length-i-1])
        return false;
    }
    return true;
  }

  public static void main(String[] args) {
    Scanner scanner = new Scanner(System.in);
    String s = scanner.nextLine();
    System.out.println(isPalindrome(s.toCharArray()));
  }
}

3. 

public static List nub(List list)
{
	List copy = new ArrayList();
	for (int i = 0; i < list.size(); i++) {
	  Object elem = list.get(i);
	  boolean found = false;
	  for (int j = 0; j < copy.size(); j++) {
	    if (elem.equals(copy.get(j))) { // Here you can choose to use ==.
	                                    // The question is not explicit.
          found = true;
          break;
	    }
	  }
	  
	  if (!found)
	    copy.add(elem);
	}
	return copy;
}

4.

public class Game {
  private boolean[] state;
  
  public Game(int n) {
    state = new boolean[n];
    for (int i = 0; i < n; i++) {
      state[i] = (Math.random() > 0.5);
    }
  }
  
  public void step() {
    boolean[] new_state = new boolean[state.length];
    for (int i = 1; i < state.length-1; i++) {
      if (state[i-1] == state[i] && state[i] == state[i+1]) {
        new_state[i] = !state[i];
      } else {
        new_state[i] = state[i];
      }
    }
    state = new_state;
  }
  
  public void print() {
    for (int i = 0; i < state.length; i++) {
      if (state[i])
        System.out.print('*');
      else
        System.out.print(' ');
    }
    System.out.println();
  }
}