The pole-zero pattern of the z-transform X(z) for a system is as shown:

The ROC of the system for which the Fourier transform exists, and the ROC for which the system is causal are respectively:

1
1/2 < |z| < 2, |z|> 5
2
|z|< ½, |z| > 5
3
|z|< ½, |z|< 5
4
None of these

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