When searching for the key value 60 in a binary search tree, nodes containing the key values 10, 20, 40, 50, 70 80, 90 are traversed, not necessarily in the order given. How many different orders are possible in which these key values can occur on the search path from the root to the node containing the value 60?

A complete n-ary tree is a tree in which each node has n children or no children. Let I be the number of internal nodes and L be the number of leaves in a complete n-ary tree. If L = 41, and I = 10, what is the value of n?

What is the largest integer m such that every simple connected graph with n vertices and n edges contains at least m different spanning trees?

Consider the following two statements:
i. A hash function (these are often used for computing digital signatures) is an injective function.
ii. encryption technique such as DES performs a permutation on the elements of its input alphabet.
Which one of the following options is valid for the above two statements?