Consider the following functions from positive integers to real numbers :

$10, \sqrt{n}, n, \log _2 n, \frac{100}{n}$.

The CORRECT arrangement of the above functions in increasing order of asymptotic complexity is :

Consider the following table :

Algorithms	Design Paradigms
(P) Kruskal	(ii) Greedy
(Q) Quicksort	(i) Divide and Conquer
(R) Floyd–Warshall	(iii) Dynamic Programming

Match the algorithms to the design paradigms they are based on.

A sender S sends a message m to receiver R, which is digitally signed by S with its private key. In this scenario, one or more of the following security violations can take place.

I. S can launch a birthday attack to replace m with a fraudulent message.
II. A third party attacker can launch a birthday attack to replace m with a fraudulent message.
III. R can launch a birthday attack to replace m with a fraudulent message.

Which of the following are possible security violations?

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.