Code:

<?php
if(isset($_POST['transport']))
{
 if($_POST['transport']=='airplanes')
 {
  echo '
  <form action="index.php" method="post">
  <select name="categories">
  <option value="fighter plane">Fighter plane</option>
  <option value="resuce plane">Resuce plane</option>
 </select><br /><br /><input type="submit" value="submit">';
 }
 elseif($_POST['transport']=='cars')
 {
   echo '
  <form action="index.php" method="post">
  <select name="categories">
  <option value="Van">Van</option>
  <option value="Truck">Truck</option>
 </select><br /><br /><input type="submit" value="submit">';
 }
}
else
{
 echo '<form action="index.php" method="post">
<input type="radio" name="transport" value="airplanes"> Airplanes<br />
<input type="radio" name="transport" value="cars"> Cars <br /><br />
<input type="submit" value="submit">
</form>';
}
?>

Code:

<script language="javascript">
var selectB='<select name="categories">';
var selectE='</select>';
function changeOptions()
{
 var setOption=document.transportForm.transport.value;
 var options='';
 if(setOption=='airplanes')
  options='<option value="fighter plane">Fighter plane</option><option value="resuce plane">Resuce plane</option>';
 else if(setOption=='cars')
  options='<option value="Van">Van</option><option value="Truck">Truck</option>';
 document.getElementById('selectsId').innerHTML=selectB+options+selectE;
}
</script>
<form action="index.php" method="post" name="transortForm">
<input type="radio" name="transport" value="airplanes" onclick="changeOptions()"> Airplanes<br />
<input type="radio" name="transport" value="cars" onclick="changeOptions()"> Cars <br />
<div id="selectsId"></div><br /><br />
<input type="submit" value="submit">
</form>