ESE 2021 Technical Quiz || Z-Transform

Let X[z] is the z-transform of a summable signal, x[n] having pole at Z = 1/2, then

For the given ROC in z – plane which one of the following statement is correct?

The inverse Z-transform of the function  for

Consider a non-causal system whose Z-transform is given by

Find x(1) = ___________?

Find x(0) if the Z-transform of x(n) is X(z) which is equal to and the ROC pass the unit circle.