Solution

The correct answer is The cost of searching an AVL tree is θ (log n) but that of binary search is 0(n) 

EXPLANATION:

• AVL trees are a type of self-balancing binary search tree. The time complexity for search, insert, and delete operations in an AVL tree is O(log n), where "n" is number of nodes in the tree.
• This is because AVL trees ensure that the tree remains balanced, thus keeping the height at log n.
• On the other hand, a binary search tree (not necessarily balanced) could degenerate into something similar to a linked list in the worst-case scenario, leading to a time complexity of O(n) for aforementioned operations.
• The statement jumbles up terminologies a bit; binary search typically refers to an operation performed on sorted arrays rather than trees, and that indeed has a time complexity of O(log n). But if we understand that it's referring to a binary search tree, the statement is correct.

The other options incorrectly state the time complexities for AVL and binary trees.