Hi Ravik,
Ajax is a technology targeted to make it possible to perform a partial web page update without the necessity to reload the whole page and thus it does not define the used control.
Regardless of the technology used by the given (calendar) control, I know only two possible options to set its value:
1) Investigate the control in the Object Browser and find a property or method (ther may be more than one such property/method available, for example text and value properties) that can be used to assign a value to the control. After you assigned the value to the control check if the assigned value can be correctly accessed by the tested web application;
2) If you cannot locate the property/method mentioned in the paragraph 1) or if the tested application behaves incorrectly after the value is assigned to the control from the test code, you will need to open the calendar drop-down and select/confirm the value from there. If you are lucky, then the calendar drop-down will have the entered date highlighted when opened so you will have just to confirm it. It the tested control is implemented in a way that it does not highlight the date according to the entered value, then you will have to create a test code to deal with the drop-down control;
3) One more possible approach is to use TestComplete's functionality to call JavaScript functions from web page. So, if the tested web page provides a JavaScript function that sets the value of the calendar control you may call it from your test code. See
http://support.smartbear.com/viewarticle/55290/ for more details. To use this approach you may need to consult with your web developers.