Yes, it is possible to fly "under the radar".
The type of radio waves that are used by radar and similar equipment to track aircraft generally travel in straight lines. This means that, because of the curvature of the Earth, radars have blind spots at low altitudes when you are sufficiently far from the radar. See the top illustration (not to scale):
Because they don't want to be seen.
Are fighters allowed to just turn off their transponders in civilian airspace?
FR24 and ADS-B Ex are not based on normal transponders (that would require access to actual RADAR data) but rather ADS-B and mode-S transponders. The military can simply choose not to operate with this equipment. This does not make the ...
I asked Lucknow Airport via their official twitter. Their response was, erm, terse.
Q: Why does Indigo flight 6E8002 circle Lucknow Airport every single day for an hour?
@aailkoapt (LUCKNOW AIRPORT): Training Flight.
Per Twitter - Mar 16