OnCheckedChanged event of checkbox within a gridview

Modern jQuery

Use .prop():

$('.myCheckbox').prop('checked', true);
$('.myCheckbox').prop('checked', false);

DOM API

If you're working with just one element, you can always just access the underlying HTMLInputElement and modify its .checked property:

$('.myCheckbox')[0].checked = true;
$('.myCheckbox')[0].checked = false;

The benefit to using the .prop() and .attr() methods instead of this is that they will operate on all matched elements.

jQuery 1.5.x and below

The .prop() method is not available, so you need to use .attr().

$('.myCheckbox').attr('checked', true);
$('.myCheckbox').attr('checked', false);

Note that this is the approach used by jQuery's unit tests prior to version 1.6 and is preferable to using $('.myCheckbox').removeAttr('checked'); since the latter will, if the box was initially checked, change the behaviour of a call to .reset() on any form that contains it – a subtle but probably unwelcome behaviour change.

For more context, some incomplete discussion of the changes to the handling of the checked attribute/property in the transition from 1.5.x to 1.6 can be found in the version 1.6 release notes and the Attributes vs. Properties section of the .prop() documentation.

How do I successfully query the checked property?

The checked property of a checkbox DOM element will give you the checked state of the element.

Given your existing code, you could therefore do this:

if(document.getElementById('isAgeSelected').checked) {
    $("#txtAge").show();
} else {
    $("#txtAge").hide();
}

However, there's a much prettier way to do this, using toggle:

$('#isAgeSelected').click(function() {
    $("#txtAge").toggle(this.checked);
});

<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<input type="checkbox" id="isAgeSelected"/>
<div id="txtAge" style="display:none">Age is something</div>