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Higher Study | Algorithms | Asymptotic Worst Case Time and Time Complexity

Which one of the following is the tightest upper bound that represents the time complexity of inserting an object into a binary search tree of n nodes?
Suppose we want to arrange the n numbers stored in any array such that all negative values occur before all positive ones. Minimum number of exchanges required in the worst case is
Let f(n) = n and g(n) = n(1 + sin n), where n is a positive integer. Which of the following statements is/are correct? I. f(n) = O(g(n)) II. f(n) = Ω(g(n))
Consider the following code snippet. It accepts a positive integer n as input. int i = 0. j = 0, val = 1; for (i = 1; i <= n; i++) {      j = n;      if (i% 2 == 0)    {        while (j > 1)      {         val = val * j;          j = j /2;      }    } } What is the worst-case time complexity of the algorithm?
Two alternative packages A and B are available for processing a database having 10k records. Package A requires 0.0001n2 time units and package B requires 10nlog10n time units to process n records. What is the smallest value of k for which package B will be preferred over A? 
What is the time complexity for the following C module? Assume that n > 0; int module(int n) { if(n == 1) return 1; else return (n + module(n-1)); }
In a balanced binary search tree with n elements, what is the worst case time complexity of reporting all elements in range [a, b]? Assume that the number of reported elements is k.
What is the complexity of the following code? sum=0;        for (i=1; I <= n; i*=2)                 for(j=1; j<=n;j++)                                 sum++;
Which one of the following statements is TRUE for all positive functions f(n) ?
Which of the following cases does NOT exist while calculating time complexity?
Which of the following decision procedure has atleast doubly exponential time complexity?
Let W(n) and A(n) denote respectively, the worst case and average case running time of an algorithm executed on an input of size n. Which of the following is ALWAYS TRUE? 
Which of the given options provides the increasing order of asymptotic complexity of functions f1, f2, f3 and f4? f1 (n) = 2n; f2 (n) = n3/2; f3 (n) = nlog2n; f4 (n) = nlog2n
What are the worst-case complexities of insertion and deletion of a key in a binary search tree?
Which of the given Options provides the increasing order of asymptotic complexity of functions f1, f2, f3, and f4? f1(n) = 2n f2(n) = n3/2 f3(n) = n log2 n f4(n) = nlog2n
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