Question 35

Given that height $h = 5$ is defined as the length of the longest root-to-leaf path (number of edges):

1. Minimum number of nodes:
   Occurs in a degenerate binary tree where every internal node has exactly one child. The number of nodes on a path with 5 edges is:

   $$N_{\min} = h + 1 = 5 + 1 = 6.$$

2. Maximum number of nodes:
   Occurs in a complete, full binary tree where every level $i$ (from $0$ to $5$) is completely filled:

   $$N_{\max} = \sum_{i=0}^{5} 2^i = 2^{5+1} - 1 = 2^6 - 1 = 64 - 1 = 63.$$

Therefore, the maximum and minimum numbers of nodes are $63$ and $6$, respectively (option A).