Question

In which of the following ​tables $x$ and $y$ vary directly?​

$x$	$1^2$	$2^2$	$3^2$	$4^2$	$5^2$
$y$	$1^3$	$2^3$	$3^3$	$4^3$	$5^3$

Answer 1

Step: Check if $x$ and $y$ vary directly​

$x$	$1^2$	$2^2$	$3^2$	$4^2$	$5^2$
$y$	$1^3$	$2^3$	$3^3$	$4^3$	$5^3$

From the given table, we have

$\frac{1^2}{1^3}=1$

$\frac{2^2}{2^3}=\frac{4}{8}=\frac{1}{2}$

$\Rightarrow \frac{1^2}{1^3}\ne \frac{2^2}{2^3}$

It is evident that the ratio of the corresponding values of $x$ and $y$ is not constant.

Hence, $x$ and $y$ do not vary directly with each other.