Try this.
simple and short and usable in the whole project:
jQuery.fn.exists=function(){return !!this[0];}; //jQuery Plugin
Usage:
console.log($("element-selector").exists());
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OR EVEN SHORTER: (for when you don't want to define a jQuery plugin):
if(!!$("elem-selector")[0]) ...;
or even
if($("elem-selector")[0]) ...;