What will be the condition of Fourier transform existence & stability of the system especially with an inclusion of jw axis in the ROC of s-plane?

What will be the condition of Fourier transform existence & stability of the system especially with an inclusion of jw axis in the ROC of s-plane?

a. Fourier transform exists but system is unstable.
b. Fourier transform does not exists due to system instability
c. Fourier transform exists & system is stable.
d. Fourier transform does not exist with stable system

Correct Answer : c. Fourier transform exists & system is stable.

Explanation :

According to the property of ROC, system is assigned to be stable due to existence of Fourier transform.