$\underline{\textbf{Answer:}\Rightarrow}\;\mathbf{c.}$
For a given $\mathrm{k-ary}$ tree with height $\mathrm N$
Total number of nodes $\mathrm{=\left ( \dfrac{K^{N+1-1}}{K-1} \right )}$
Total Nodes = Non-Leaf Nodes + Leaf Nodes.
Leaf Nodes = $\mathrm{\mathbf{N^{th}}}$ level nodes $\mathrm{=K^N}$
$\therefore $Non Leaf = Total Nodes– Leaf Nodes
$\mathrm{=\dfrac{K^{N+1}-1}{K-1}-K^N = \left ( \dfrac{K^N-1}{K-1}\right )}$
$\therefore \mathrm{\dfrac{Non Leaf}{Total}=\dfrac{\dfrac{K^N-1}{K-1}}{\dfrac{K^{N+1}}{K-1}}}=\dfrac{K^N-1}{K\left (K^N-\dfrac{1}{K}\right )}$
Now, if $\mathrm k\to \infty$, then $\mathrm{K^N-\dfrac{1}{K} = K^N = \dfrac{K^N-1}{K(K^N)} = \dfrac{1}{k}\bigg [1-\dfrac{1}{K^N}\bigg ]\approx \dfrac{1}{K}}$