Consider the following algorithm for searching for a given number x in an unsorted array A[1..n] having n distinct values:
1. Choose an i uniformly at random fro 1..n;
2. If A[i]=x then stop else Goto 1;
Assuming that x is present A, what is the expected number of comparisons made by the algorithm before it terminates?

Consider the following functions
$$f(n) = 3{n^{\sqrt n }}$$
$$g(n) = {2^{\sqrt n {{\log }_2}n}}$$
$$h(n) = n!$$
Which of the following is true?

Conside the following two functions:
$${g_1}(n) = \left\{ {\matrix{ {{n^3}\,for\,0 \le n < 10,000} \cr {{n^2}\,for\,n \ge 10,000} \cr } } \right.$$
$${g_2}(n) = \left\{ {\matrix{ {n\,for\,0 \le n \le 100} \cr {{n^3}\,for\,n > 100} \cr } } \right.$$ Which of the following is true:

$$\sum\limits_{1 \le k \le n} {O(n)} $$ where O(n) stands for order n is: