As per the sec. 256 of companies act if the copmany has not filled up the vacancy at the AGM then meeting should resolved expressively that vacancy shold not be filled up.Otherwise meeting will be adjourned to the same day next week at the same time and place and if that day is public holiday till the next succeeding day which is not a public holiday at the same time and place. Such adjournment is for filling up the vacancy.
If in the adjouned meeting also vacancy is not filled or the meeting does not resolves expressively not to fill up the vacancy then the retiring director will be deemed to have been reappointed at the adjourned meeting.
However the retiring director will not be deemed to have been reappointed if:
1)either at the orignal meeting or at the adjourned meeting a resoulution for reappointment of such director has been put and lost.
2)director expressed his unwillingness in writting to be reappointed.
3)he is not disqulified as per provisions of the act ie under sec. 274
4) a resolution whether ordinery or special is required for his reappointment by any provision of the comapnies act.
Now examine the given case in thelight of above provisions you will get your answer that is in which case he is not to be reappointed automaticly.
and one more thing please consider the answer of miss arpita because in case of alternate director the orignal director will be able to be reappointed and in case of casual director and addional directors the position will be different plz refer sec 260,262 and 313 for that purpose.