The average number of key comparisons done on a successful sequential search in list of length n is

Quicksort is run on two inputs shown below to sort in ascending order taking first element as pivot
i) 1, 2, 3,......., n
ii) n, n-1, n-2,......, 2, 1
Let C₁ and C₂ be the number of comparisons made for the inputs (i) and (ii) respectively. Then,

The recurrence relation
T(1) = 2
T(n) = 3T(n/4) + n
has the solution, T(n) equals to

A binary search tree is generated by inserting in order the following integers:

50, 15, 62, 5, 20, 58, 91, 3, 8, 37, 60, 24

The number of nodes in the left subtree and right subtree of the root respectively is