panels do not show in applet viewer, yet there are no errors

Question

There were several issues in your code, and there probably are several more, but here (for now) a "runnable" version:

import java.awt.*;

import java.awt.event.*;

import javax.swing.*;


public class ApplicationCentre extends JApplet implements ActionListener {


JButton b1, b2, b3, b4, b5, b6;
JRadioButton rb1 ;
JLabel l1, l2, l3, l4, l5, l6, l7, l8, l9, l10, l11;
JTextField t1,t2,t3,t4,t5,t6;
JTextArea ta1, ta2;
JList j1;
JComboBox studentList;
JRadioButton accept[], reject[];
ButtonGroup radioGroup[];  
JPanel deck;
CardLayout cardManager = new CardLayout();
Student s[];
String uniList [] = {"Toronto", "York", "Western", "Brock", "Guelph", "Waterloo",       "McGill", "Concordia", "Laval", "Macmaster"};

public void init(){
s= new Student [100];

Container container = getContentPane();


deck = new JPanel();
cardManager = new CardLayout(); 
deck.setLayout( cardManager ); 

//add panels to deck

deck.add( inputPanel(), "input" );
deck.add( admitPanel(), "admit" );
deck.add( allPanel(), "displayAll" );
deck.add( onePanel(), "displayOne" );

//Left-side Buttons

JPanel P1 = new JPanel();
P1.setLayout (new GridLayout(4, 1));

b1 = new JButton("INPUT");
b1.addActionListener(this);
P1.add(b1);
b2 = new JButton("ADMIT");
b2.addActionListener(this);
P1.add(b2);
b3 = new JButton("DISPLAY ALL");
b3.addActionListener(this);
P1.add(b3);
b4 = new JButton("DISPLAY ONE");
b4.addActionListener(this);    
P1.add(b4);

container.add(P1, BorderLayout.WEST);

// add deck to container


container.add(deck, BorderLayout.CENTER); 


 }

// Input panel

public JPanel inputPanel (){
JPanel P2 = new JPanel();
P2.setLayout (new GridLayout(6,2));

l1 = new JLabel ("Name");    
P2.add(l1);    
t1 = new JTextField (15);

P2.add(t1);    
l2 = new JLabel ("Name of Program");
P2.add(l2);    
t2 = new JTextField ();
P2.add(t2);
l3 = new JLabel ("Average Mark");
P2.add(l3);    
t3 = new JTextField ();
P2.add(t3);
l4 = new JLabel ("Type of postgrad degree");
P2.add(l4);
t4 = new JTextField ();
P2.add(t4);    
l5 = new JLabel ("Universities (select 3)");
P2.add(l5);

j1 = new JList (uniList);
j1.setVisibleRowCount(3);
j1.setSelectionMode(ListSelectionModel.MULTIPLE_INTERVAL_SELECTION);
P2.add(j1);

b5 = new JButton ("Submit");
P2.add(b5);
l7 = new JLabel ();
P2.add(l7);

return P2;
}

// Admit panel

public JPanel admitPanel(){
JPanel P3 = new JPanel();
P3.setLayout (new BorderLayout());


studentList = new JComboBox(s);
studentList.setMaximumRowCount(8);


P3.add(studentList, BorderLayout.NORTH);


JPanel P3a = new JPanel();
P3a.setLayout (new GridLayout (3,3));
radioGroup = new ButtonGroup[3];
accept = new JRadioButton[3];
reject = new JRadioButton[3];
  for (int j=0; j<3; j++) {
    radioGroup[j] = new ButtonGroup();
    accept[j] = new JRadioButton("Accept", false);
    reject[j] = new JRadioButton("Reject", true);
    radioGroup[j].add(accept[j]);
    radioGroup[j].add(reject[j]);
  }

 l8 = new JLabel ();
 P3a.add(l8);
 P3a.add(accept[0]);
 P3a.add(reject[0]);

 l9 = new JLabel ();
 P3a.add(l9);     
 P3a.add(accept[1]);
 P3a.add(reject[1]);

 l10 = new JLabel ();
 P3a.add(l10);     
 P3a.add(accept[2]);
 P3a.add(reject[2]);

 P3.add(P3a, BorderLayout.CENTER);

 b6 = new JButton ("Submit");
 P3.add(b6, BorderLayout.SOUTH);

 return P3;
}

// DisplayAll panel

public JPanel allPanel(){
 JPanel P4 = new JPanel();

 ta1 = new JTextArea ();
 ta1.setFont(new Font("Serif", Font.ITALIC, 12));
 ta1.setEditable(false);

 P4.add(ta1);

 return P4;
}

//DisplayOne Panel

public JPanel onePanel(){
 JPanel P5 = new JPanel();
 P5.setLayout (new BorderLayout());

 JPanel P5a = new JPanel();
 l11 = new JLabel ("Enter Student's name");
 P5a.add(l11);
 t6 = new JTextField ();
 P5a.add(t6);

 P5.add(P5a, BorderLayout.NORTH);

 ta2 = new JTextArea();
 ta2.setFont(new Font("Arial", Font.PLAIN, 14));
 ta2.setEditable(false);

 P5.add(ta2, BorderLayout.CENTER);


 return P5;
}







public void actionPerformed(ActionEvent e) {

 if ( e.getSource() == b1 )    
     cardManager.show( deck,"input" );
 else if ( e.getSource() == b2 )    
     cardManager.show( deck,"admit" );
 else if ( e.getSource() == b3 )    
     cardManager.show( deck,"displayAll" ); 
 else if ( e.getSource() == b4 )    
     cardManager.show( deck,"displayOne" ); 

}
}

// student class and extensions

abstract class Student {
  private String name, programName, uni1, uni2, uni3;
  public boolean u1a=false;
  public boolean u2a=false;
  public boolean u3a=false;

  public Student (String n, String p, String u1, String u2, String u3){
    setName(n);
    setProgramName(p);
    setUni1(u1);
    setUni2(u2);
    setUni3(u3);
  }

public String getProgramName() {
    return programName;
}

public void setProgramName(String programName) {
    this.programName = programName;
}

public String getUni3() {
    return uni3;
}

public void setUni3(String uni3) {
    this.uni3 = uni3;
}

public String getUni2() {
    return uni2;
}

public void setUni2(String uni2) {
    this.uni2 = uni2;
}

public String getUni1() {
    return uni1;
}

public void setUni1(String uni1) {
    this.uni1 = uni1;
}

public String getName() {
    return name;
}

public void setName(String name) {
    this.name = name;
}
}


class Postgrad extends Student{

  private double avgMark;
  private String degree;

  public Postgrad (String n, String p, String u1, String u2, String u3, double avg,    String d){
    super(n, p, u1, u2, u3);
    setAvgMark(avg);
    setDegree(d);
  }

public double getAvgMark() {
    return avgMark;
}

public void setAvgMark(double avgMark) {
    this.avgMark = avgMark;
}

public String getDegree() {
    return degree;
}

public void setDegree(String degree) {
    this.degree = degree;
}

}


class Undergrad extends Student {

  private double avgMark;

  public Undergrad (String n, String p, String u1, String u2, String u3, double   avg){
    super( n, p, u1, u2, u3);
    setAvgMark(avg);
  }

public double getAvgMark() {
    return avgMark;
}

public void setAvgMark(double avgMark) {
    this.avgMark = avgMark;
}
}

Most important issues: You forgot to initialize your arrays radioGroup, accept and reject, and you tried to access the first three elements on the indices 1, 2, 3, but Java (as most languages) starts to count with 0, so you have to access via the indices 0, 1, 2 to get the first three elements.