In planar graph, any face (except possibly the outer line) is bounded by atleast three edges and every edge touches atmost two faces.
Using Euler’s formula it states that,
if v ≥ 3 then e ≤ 3v-6
where e=edges
v=vertices
Go through the options
i) 9e and 5v ⇒ 9≤3(5)-6
⇒ 9≤15-6
⇒ 9≤9 (It’s satisfies planar graph)
ii) 9e and 6v ⇒ 9≤3(6)-6
⇒ 9≤12 (It’s planar graph)
iii) 10e and 5v ⇒ 10≤3(5)-6
⇒ 10≤9 (It’s not satisfies planar graph condition)
So, option C is non-planar graph.
iv) 10e and 6v ⇒ 10≤3(6)-6
⇒ 10≤12 (It’s planar graph)