Two alternate packages A and B are available for processing a database having 10^k records. Package A requires 0.0001n² time units and package B requires $$10n.\log _{10}^n$$ time units to process n records. What is the smallest value of k for which package B will be preferred over A?

Consider the following segment of C-code:

int j, n;
j=1;
while(j <= n)
 j = j * 2;

The number of comparisons made in the execution of the loop for any n > 0 is:

Consider the following C-program fragment in which i, j and n are integer variables.
for (i = n, j = 0; i > 0; i /= 2, j += i);
let val (j) denote the value stored in the variable j after termination of the for loop. Which one of the following is true?

The time complexity of computing the transitive closure of a binary relation on a set of elements is known to be: