Correct Option: B

Here, the ROC	1	< |z| < 3 is a ring,
	2

which means that the signal x(n) is two sided. Therefore, one of terms corresponds to a causal signal and the other is anti-causal signal.

In the region	1	< |z| < 3
	2

i.e., |z| < 3 anti-causal and |z| >	1	causal,
	2

the pole p1 =	1	is interior and p2 = 3 is exterior and hence
	2

X(n) =	2	δ(n) +		1		n	u(n) –	1	(3)n u(– n – 1)
	3			2				3

Hence, alternative (B) is the correct answer.