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(C) The logic applied to the relation $x : y$ is $y = \frac{x^3}{2}$.For the given pair $8 : 256$:$8^3 = 512$$\frac{512}{2} = 256$Now,checking the opt

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$10 : 500$

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(C) The logic applied to the relation $x : y$ is $y = \frac{x^3}{2}$.For the given pair $8 : 256$:$8^3 = 512$$\frac{512}{2} = 256$Now,checking the options:$A) 2^3 / 2 = 8 / 2 = 4 
eq 343$$B) 9^3 / 2 = 729 / 2 = 364.5 
eq 243$$C) 10^3 / 2 = 1000 / 2 = 500$$D) 5^3 / 2 = 125 / 2 = 62.5 
eq 75$Therefore,the correct alternative is $10 : 500$.

Choose the correct alternative for the given relation.
$8 : 256$

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Choose the correct alternative for the given relation.$8 : 256$