List of top Signals and Systems Questions on Properties of Region of Convergence asked in GATE EE

Consider the infinite-length, discrete-time sequence \(x[n]=0.9^{|n|}\), where \(n\) is an integer. The region of convergence of its Z-transform \(X(z)\) is given by:
(Note: \(z\) is a complex variable)

The Z-transform of a discrete signal \(x[n]\) is \[ X(z) = \frac{4z}{\left(z-\tfrac{2}{3}\right)(z-3)}, \text{with ROC} = R. \] Which one of the following statements is true?