In a Binary Tree, can two nodes have the same value?
If you say "binary tree", my answer is " yes", since binary tree to me only says: A tree of nodes that only have at most 3 edges, of which two (binary) are pointing in the same direction (to tree leafs).

If you mean a "binary search tree", my answer is "no", since a search tree does not have any advantage in allowing duplicates, since SEARCHING for ONE value in a BST can only result in ONE value, not in two or more. Since BST search is a deterministic algorithm, one of the two mentioned duplicates will never be found and hence is totally useless. Inserting a duplicate in a BST must be skipped since its position in tree is already occupied.