Let $T$ be a binary search tree with 15 nodes. The minimum and maximum possible heights of $T$ are :

Note : The height of a tree with a single node is 0.

Consider a binary tree $$T$$ that has $$200$$ leaf nodes. Then, the number of nodes in $$T$$ that have exactly two children are ________.

While inserting the elements $$71, 65, 84, 69, 67, 83$$ in an empty binary search tree $$(BST)$$ in the sequence shown, the element in the lowest level is

Consider a complete binary tree where the left and the right sub-trees of the root are max-heaps. The lower bound for the number of operations to convert the tree to a heap is