Question : Find the mean proportion of $x^3y$ and $xy^3$.
Option 1: $x^2y^2$
Option 2: $x^3y^3$
Option 3: $xy$
Option 4: $x^4 y^4$
Correct Answer: $x^2y^2$
Solution : Let the mean proportion be $a$ Given numbers, $x^3y$ and $xy^3$ ⇒ $a^2=x^3y\times xy^3$ ⇒ $a^2=x^4y^4$ ⇒ $a=x^2y^2$ Hence, the correct answer is $x^2y^2$.
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