To perform a work, when one is involved to do so in working day,i.e. in school or out of school,then the question arises about ON DUTY.
But in case of 31/03/2013 (Sunday), will not be on duty. Because (i)the day is Sunday and (ii)the staffs who will deliver their duty for smooth sailing/performing or conducting the examination (TET),they will get the remuneration for this purpose.
There is no question of ON DUTY.