As we know that sum of degree of vertex $= 2\times edges.$
let there is $u$ vertex with odd degrees and $v$ vertex with even degrees.
Then $\sum\left(u\right) + \sum\left(v\right) = 2e.$
now $2e = \text{even}.$
$\sum\left(v\right) =$ sum of even number will be even.
$\sum\left(u\right) =$ if you consider odd number of vertices of odd degree then sum will be odd and this will violate $2e$
so there will be always the even number of vertices with odd degree
Hence, Ans is (c)There are the even number of vertices of odd degree.