You can use .is(':visible')
Selects all elements that are visible.
For example:
if($('#selectDiv').is(':visible')){
Also, you can get the div which is visible by:
$('div:visible').callYourFunction();
Live example:
console.log($('#selectDiv').is(':visible'));
console.log($('#visibleDiv').is(':visible'));
#selectDiv {
display: none;
}