I got the solution for the problem. I am sharing the problem and its solution here.
When we are entering a date in dd/mm/yyyy format the compare validator couldn't able to get it and validation gets failed. This is because the validator implicitly gets the date format as mm/dd/yyyy format.
Changing the UICulture at page load we can able to pass the validation.
Thread.CurrentThread.CurrentCulture = CultureInfo.CreateSpecificCulture("en-GB");
The above code solved my problem.