How to make specific options to appear in select menu?
You can do it with using onChange method and with querySelectorAll.
display or visibility attributes doesn't work for cross browsers. So you should recreate options.
var noc=document.getElementById("noc");
var po=document.getElementById("po");
var options=po.querySelectorAll("option");
function nochange(){
po.innerHTML="";
[...options].filter(x=>parseInt(x.value)<=parseInt(noc.value)).forEach(x=>{po.append(x)})
po.value=noc.value;
}<select id="noc"onChange="nochange()">
<option value="1">1</option>
<option value="2">2</option>
<option value="3">3</option>
<option value="4">4</option>
<option value="5">5</option>
<option value="6">6</option>
<option value="7">7</option>
<option value="8">8</option>
<option value="9">9</option>
<option value="10">10</option>
</select><br/>
<!--Some text---->
<select id="po">
<option value="1">1</option>
<option value="2">2</option>
<option value="3">3</option>
<option value="4">4</option>
<option value="5">5</option>
<option value="6">6</option>
<option value="7">7</option>
<option value="8">8</option>
<option value="9">9</option>
<option value="10">10</option>
</select>