The least number should be multiplied to 2560 to get a perfect cube number is ……………….. 

Correct option is (A) 1/6 Possible outcomes are S = {1, 2, 3, 4, 5, 6} \(\therefore\) n(S) = 6 Number which is a perfect square and a perfect cube is 1.    \((\because1^3=1\;\&\;1^2=1)\) Hence, favourable outcome...

Correct option is  B) 64

Correct option is (D) 15 6000 \(=100\times4\times3\times5=10^2\times2^2\times3\times5.\) Since, factors 10 & 2 are in square but 3 & 5 are in not square. \(\therefore\) We have to multiply 6000 by 15 to get a perfect...

Correct option is (C) 5 720 \(=9\times16\times5=3^2\times4^2\times5.\) Since, factors 3 & 4 are in square but 5 is not in square. \(\therefore\) We have to multiply 720 by 5 to get a perfect square number.

Correct option is (D) 64 \(64=8^2\) and \(64=4^3\) Thus, 64 is a perfect square and perfect cube number.

Correct option is  A) 512

(i) false (ii) true (iii) true

Let the number is = a  Cube of number will be = a3  Now, the number is trebled = 3 × a = 3a  Cube of new number = (3a)3 = 27a3  Hence, new...