How can we check that which chat room is famous among the users and is there any ranking process for them on the basis of number of users or activity per days like that.
Can I find that ranking of my room in India or in world?
No. You cannot. Like others have pointed out, you can sort the rooms by various criteria, but none of them include a popularity ranking. How would you measure that anyway?
The most frequented and active rooms are usually the four listed on the screenshot below:
Picking one of the Sort options, sorts the chat rooms by their current number of people or activity. Each chat room also lists their total number of messages and people in the info box for the chat room. You cannot sort by the latter, but it's usually the same rooms that are also active atm.
Number of messages doesn't necessarily imply popularity though. The Lounge contains about 22k+ messages containing the F word. A lot of noise. Also, the Lounge is infamous for being only popular among it's regular users and being unfriendly and hostile to anyone else. Oh well. And look at their room description. 'Nuff said?
The People count alone doesn't necessarily imply popularity either, since a lot of users just come to the rooms to ask for help and then never come back again (which might tentatively be an indicator for the popularity of a language, but not of a room).
We could probably count the favorites. That might be an indicator for popularity. But we don't.
TL;DR: There is no popularity metric. Chat is not a popularity contest. Just stay in the rooms you like and that feel useful to you.
Currently there is no ranking system for chat room. However when you visit the htp://chat.stackoverflow.com it displays the chat room based on the current active.