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# If two random variables $x$ and $y$ are connected by the relation $2x+y=3$ then $r_{xy} =$

$\begin {array} {1 1} (A)\;1 & \quad (B)\;-1 \\ (C)\;-2 & \quad (D)\;3 \end {array}$

$2x+y=3$
$\Rightarrow 2\overline x+\overline y=3$
$2(x-\overline x)+(y-\overline y)=0$
$y-\overline y=-2(x-\overline x)$
$\Rightarrow b_{xy} = -\large\frac{1}{2}$
$\Rightarrow \therefore r=-\sqrt{ b_{yx} \times b_{xy}}$
$= - \sqrt{(-2)(-\large\frac{1}{2})}$
$= -1$
Ans : (B)