Why am i getting an ip address from lucknow even though i live in ranchi

In short: Limited IPv4, large user base. Not enough IPs. At least you are still getting public ipv4.
Enjoy it while it lasts.
because no Airtel Broadband Gateway in Ranchi. You are getting services from Lucknow. Similar as few other locations
That’s very common, you can read my post about it.
Due to some reason few of the Delhi subscribers are served from Noida. I also used to get Noida IP earlier but post I purchased static IP, Now my location shows as Delhi

someone in this forum called it Geo tagging or something. It does not change anything
I fail to see why this is an issue. Sometimes my IP shows Airtel Pune and sometimes Airtel Mumbai. Makes no difference. IP geo identification isn't perfectly accurate and is only a guide.
Look for the "PPPoE Concentrator" in the "Wan Status" page of the Nokia Router. It will be something like "brasnoi2" etc which means it is Noida BRAS (a.k.a BNG)
If in bridge mode and running PPPoE from Pfsense, then it will show up in the "Point to Point" Log file as PPPoE: rec'd ACNAME "xxxxxxx"
i have a connection of Airtel Fiber in Patna Bihar. checked in the wan status page of router it has the ipv4 address of Lucknow and gateway of Mumbai 🙁 sadge life, the pings are fucked 100+ even for mumbai server