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Question:

State true or false.(i) Cube of any odd number is even.(ii) A perfect cube does not end with two zeros.(iii) If square of a number ends with 5, then its cube ends with 25.(iv) There is no perfect cube which ends with 8.(v) The cube of a two digit number may be a three digit number.(vi) The cube of a two digit number may have seven or more digits.(vii) The cube of a single digit number may be a single digit number.

Solution:

(i) Cube of any odd number is even. FALSE: Odd multiplied by odd is always odd
(ii) A perfect cube does not end with two zeros. TRUE: A perfect cube will end with an odd number of zeroes
(iii) If square of a number ends with 5, then its cube ends with 25. TRUE: 5 multiplied by 5 any number of times always gives 5 at units place
(iv) There is no perfect cube which ends with 8. False: 2³=8
(v) The cube of a two digit number may be a three digit number. FALSE: The smallest two digit number is 10 and 10³=1000 is a three digit number
(vi) The cube of a two digit number may have seven or more digits. FALSE: 99 is the largest 2 digit number; 99³=970299 is a 6 digit number
(vii) The cube of a single digit number may be a single digit number. TRUE: 2³=8 is a single digit number.