Death certificate

Try to find out first whithin which municipality or hospital he died.If you find you can avail such certificate from such municipality records/burial ground records/hospital record. Otherwise you have to take recourse of civil court.

• No short-cuts please. Take some pain please, as pain is gain by making sincere discreet enquiries for the whereabouts of your  Dad,  as rightly said by Advocate Arvind, from the source she came to know that her hubby is dead .
• If all efforts fail after sincere search than an Affidavit signed by your mom and her offsprings with substantial proof that could be made available and witnessed by her family members, expressing the facts in a comprehensive manner and registering the declaration with the State Registration Office. Afterwhich, approach the District Collector who would decide the course of action, to certify whether he is declared dead or absconding, with the proof of evidence. These are different facets of life as individuals face varied problems. Thanks.   

i am appreciative of your sincere efforts with which you have provided all the available details to the experts. i am sure with their advice, you will definitely reach the destination. the first link in the string is the place and person from whom you got the news of demise of your father. you have to request , cajole,pursuade, negotiate,impress upon him the vitality of the information for you. after that, approach teh hospital /burial ground where he was treated/buried. then approach the municipality with these details to obtain the death certificate. it is going to be a time consuming and tedious task, but then there isn't a shortcut available.

Yes even if I find out where he was staying and where he died still it would be a problem for me because he always changed his name as per the caste womens that he married. That also would be a problem for my mom bcoz when he married my mom the name was different and when he got seperated from my mom, he married a rich parsi lady, after few years my mom said that he married some foreigner, then after that some other women and so on. So he always used to change his names and everything as per their religion and castes. So for the passport verification then that also would be a big problem for my mom. You know I feel so ashamed of him, but you know I am really proud of my mom that after taking so much pain she has given me birth and brought me up with lots and lots of love. She just stayed for me till date and I cant see a single tear in her eyes. So guys tell me still do I have to go and search for his whereabouts or do I have to follow Dr Chandran's way that he suggested.

If I submit an affidavit regarding death certificate of my dad for my mom's passport renewal then that would be fine, please let me know. If yes then can anyone let me know the format please.

My suggestion "If all efforts fail after sincere search than an Affidavit signed by your mom and her offsprings with substantial proof that could be made available and witnessed by her family members, expressing the facts in a comprehensive manner and registering the declaration with the State Registration Office. Afterwhich, approach the District Collector who would decide the course of action, to certify whether he is declared dead or absconding, with the proof of evidence. These are different facets of life as individuals face varied problems".                                                                                    

This was with due consideration of the most valuable and precious time of one's life span, as there has to be an alternative best solution to deal with keeping to the times, by the District Collector ( the Administrator of Public Services ) who would have the subject veified by the Police authorities with legal opinion suiting to the circumstances. 

1. File a "Declaration Suit" in jurisdiction Civil Court using father’s known (real) name under which they (your father and mother) were originally married some three decades back !
2. State in suit matter from more than last 7 (seven) many years Husband not heard of. Donot ever mention that father was known by hundred other names and was known (heard) of from last 31 years as they are not relevant to declaration suit for purpose matter and person stating that has to prove it!
3. Law of Evidence U/s 108 IEA applicable here. What S. 108 of the Act enables is the drawl of a presumption that if the person missing has not been heard of for a period of 7 years/calculated back from the date when the question is raised that such person is no more. Beyond that no other presumption can be drawn.  
4. Court may grant suit in your mother’s favour declaring from more than 7 years husband not heard of or is found to be missing.
5. Two imp. inter-dependent case laws on S. 107 / 108 IEA (from SC) are;

N. Jayalakshmi Animal and Ors. Vs. R. Gopal Pathar and Anr.  [indiankanoon.org/doc/1219951]
L.I.C. of India Vs. Anuradha  [indiankanoon.org/doc/458197] 

That is more than enough for passport renewal purposes and also applies more or less for Succession / Divorce (if any) purposes also.