The distance from Patna to Ranchi is 260 km by air and 320 km by...

Displacement of the aeroplane is the straight line distance between Patna and Ranchi, which is $260 \text{ km}$.

Time taken by the aeroplane, $t = 30 \text{ minutes} = \dfrac{1}{2} \text{ h}$.

Average velocity is defined as the ratio of displacement to time taken.

Average velocity $= \dfrac{\text{Displacement}}{t} = \dfrac{260}{\dfrac{1}{2}} = 520 \text{ km/h}$.

The direction of average velocity is along the displacement, which is from Patna to Ranchi.