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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 Routh's Table of the system characteristic equation. X: The system is stable... Y: The system is unstable... Z: The test breaks down... P:... when all elements are positive Q:... when any one element is zero R:... when there is a change in sign of coefficients

1. X-P, Y-R, Z-Q
2. X-Q, Y-P, Z-R
3. X-P, Y-Q, Z-R
4. X-R, Y-Q, Z-P

Correct answer: X-P, Y-R, Z-Q

Solution

The correct option matches the stability of the system with the conditions of the Routh's Table: the system is stable when all elements are positive (X-P), unstable when there is a change in sign of coefficients (Y-R), and the test breaks down when any one element is zero (Z-Q).

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