After that try again to see if the Exist method return true.
If it is still returning true, in IE, use Internet Explorer Toolbar (open it) and check how many textboxes with the id "Vijay" exists in the page. If it is just only one, and the Smart Matching Algorithm is disable, than there is a problem (until
now, I didn't meet such issues with the Smart Algorithm Disabled). In this case, just post the page source and the object definition (like in your previous example).