List of top Algorithms Questions on Asymptotic worst case time and space complexity

Which one of the following statements is TRUE for all positive functions \( f(n) \)?

Let \(P\) be an array containing \(n\) integers. Let \(t\) be the lowest upper bound on the number of comparisons of the array elements, required to find the minimum and maximum values in an arbitrary array of \(n\) elements. Which one of the following choices is correct?

Consider the following three functions:
\[ f_1 = 10^n, f_2 = n^{\log n}, f_3 = n^{\sqrt{n}} \] Which one of the following options arranges the functions in the increasing order of asymptotic growth rate?

Consider the following recurrence relation.
\[ T(n) = \begin{cases} T(n/2) + T(2n/5) + 7n, & \text{if } n > 0 \\ 1, & \text{if } n = 0 \end{cases} \] Which one of the following options is correct?