# If the slopes of the line of regression of $y$ on $x$ and of $x$ on $y$ are $30^{\circ}$ and $60^{\circ}$ respectively. Then $r(x,y)$ is

$\begin {array} {1 1} (A)\;-1 & \quad (B)\;1 \\ (C)\;\large\frac{1}{\sqrt 3} & \quad (D)\;\sqrt 3 \end {array}$

We have
$b_{yx}= \tan 30^{\circ}$
$\large\frac{1}{\sqrt 3}$
$\large\frac{1}{b_{xy}}$ $= \tan 60^{\circ} = \sqrt 3$
$\therefore b_{yx}.b_{xy} = \large\frac{1}{3}$
$\Rightarrow r^2=\large\frac{1}{3} \: or \: r=+\large\frac{1}{\sqrt 3}$
$b_{yx} \: and \: b_{xy}$ are positive
Hence Ans (C)