Which one of the following statements is false?

Following algorithm(s) can be used to sort n integers in the range [1....... n³] in O(n) time

Minimum number of comparisons required to sort 5 elements

Match the pairs in the following:

List - I

(a) Heap construction
(b) Constructing hash table witn linear probing
(c) AVL Tree construction
(d) Digital tree construction

List - II

(p) $$\Omega \left( {n\log _{10}^n} \right)$$
(q) O(n)
(r) O(n²)
(s) $$\Omega \left( {n\log _2^n} \right)$$