PooyanThe chairman being absent, the secretary chaired the meeting.

PooyanThe chairman's being absent, the secretary chaired the meeting.

The second is not correct. 'Being' is functioning as a participle, not as a gerund.

PooyanHer eyes's glistening with tears, she stood up and turned away from the p

well even i was having a doubt in this respect but after going through newspapers what i have found is that they both can be used.
The chairman being absent is used now quite a lot whereas other the chairman's being absent is not in vogue.
This is same as due to him being absent and due to his being absent.
let's see what others have to say

nagariyaThe chairman being absent is used now quite a lot whereas other the chairman's being absent is not in vogue.

It's not a question of it being not in vogue; it is incorrect in that sentence.

The chairman's being absent caused some problems is possible, though most of us would prefer the chairman's absence... .

I don't know whether it is right or wrong but i based my decision on this
"In a recent interview to The Hindu, Nayantara Sahgal pointed out that it was Indira Gandhi who created the “Nehru-Gandhi” dynasty, not her father. This is absolutely true. In a book published in 1960, the editor Frank Moraes (by that time a sharp critic of the Prime Minister) wrote that “there is no question o

nagariyaI don't know whether it is right or wrong

I do. It's wrong.

nagariya i based my decision on this"[...]Ithere is no question of Nehru’s attempting to create a dynasty of his own; it would be inconsistent with his character and career".

'Attempting' is used as a gerund in that sentence. That's fine.

You have out me in quandary.If this is the case then please tell us how do we decide what is gerund? and what is participle?
please use the above example and explain.
Thank you for your promptness in replying.Waiting for your answer eagerly.

A gerund is an -ing form used as a noun:

I enjoy smoking.
My wife doesn't like me/my smoking.
My smoking upsets her.

A participle is an -ing form used as an adjective.

Smoking a fat cigar, he delivered a lecture on healthy living.
We surveyed the smoking remains of the building.