Seems like last_accessed_on, is a date time, and you are converting '23-07-2014 09:37:00' to a varchar. This would not work, and give you conversion errors. Try
last_accessed_on= convert(datetime,'23-07-2014 09:37:00', 103)
I think you can avoid the cast though, and update with '23-07-2014 09:37:00'. It should work given that the format is correct.
Your query is not going to work because in last_accessed_on (which is DateTime2 type), you are trying to pass a Varchar value.
You query would be
UPDATE student_queues SET Deleted=0 , last_accessed_by='raja', last_accessed_on=convert(datetime,'23-07-2014 09:37:00', 103)
WHERE std_id IN ('2144-384-11564') AND reject_details='REJECT'