The number of odd numbers lying between 40000 and 70000 that can be made from the digits 0, 1, 2, 4, 5, 7 if digits can be repeated any number of times is

Required numbers must be between 40000 and 70000.  So, the fast digit must be chosen as 4 or 5

As the required numbers are odd, the last digit must be 1, 5, 7

Repetition of digits is allowed as the numbers are between 40000 and 70000

$\therefore$  Required number of ways $=2\times 6^3\times 3$

$=1296$