Consider a weighted undirected graph with positive edge weights and let $$uv$$ be an edge in the graph. It is known that the shortest path from the source vertex $$s$$ to $$u$$ has weight 53 and the shortest path from $$s$$ to $$v$$ has weighted 65. Which one of the following statements is always true?

The height of a binary tree is the maximum number of edges in any root to leaf path. The maximum number of nodes in a binary tree of height $$h$$ is:

The maximum number of binary trees that can be formed with three unlabeled nodes is:

If all the edge weights of an undirected graph are positive, then any subject of edges that connects all the vertices and has minimum total weight is a