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Match the inferences $X$, $Y$ and $Z$, about a system,to the corresponding properties of the elements of first column in Rouths' Table of the system characteristic equation.

$\begin{array}{ll}\text{X: The system is stable ... }&\text{P: ... when all elements are positive}\\\text{Y: The system is unstable ... }&\text{Q: ... when any one element is zero}\\\text{Z: The test breaks down ….}&\text{R: ... when there is a change in sign of coefficients} \end{array}$ 

  1. $X \to P, \: Y \to Q, \: Z \to R$
  2. $X \to Q, \: Y \to P, \: Z \to R$
  3. $X \to R, \: Y \to Q, \: Z \to P$
  4. $X \to P, \: Y \to R, \: Z \to Q$
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