Since mod 10 is used, the last digit matters. If you do cube all numbers from 0 to 9, you get following
Number Cube Last Digit in Cube
0 0 0
1 1 1
2 8 8
3 27 7
4 64 4
5 125 5
6 216 6
7 343 3
8 512 2
9 729 9
Therefore all numbers from 0 to 2020 are equally divided in 10 buckets. If we make a table for square, we don\'t get equal distribution. In the following table. 1, 4, 6 and 9 are repeated, so these buckets would have more entries and buckets 2, 3, 7 and 8 would be empty.
Number Square Last Digit in Square
0 0 0
1 1 1
2 4 4
3 9 9
4 16 6
5 25 5
6 36 6
7 49 9
8 64 4
9 81 1
Alternative approach -
Using the concept of power of cycle:
(a) (0,1,4,9,6,5,6,9,4,1,0) repeated
(b) (0,1,8,7,4,5,6,3,2,9) repeated
(c) (0,1,4,9,6,5,6,9,4,1,0) repeated
(d) (0,2,4,6,8) repeated
So, only h(i) =i3 mod 10 covers all the digits from 0 to 9.
Hence Option (C) is correct. answer