I got the solution by assigning it to a string value and checking in if condition as string.
$(document).ready(function () {
var prm = Sys.WebForms.PageRequestManager.getInstance();
prm.add_initializeRequest(InitializeRequest);
prm.add_endRequest(EndRequest);
Search("Other");
});
function InitializeRequest(sender, args) {
}
function EndRequest(sender, args) {
var str1 = new String(sender._postBackSettings.sourceElement.id);
if (str1 == "ContentPlaceHolder1_btnNew") {
alert("You have clicked new")
}
else {
alert("You have clicked others")
}
}