gate 2017 EE(Set-B) q47-solution

z = 2 is the singularity lies inside $$C:|z|=3$$
therefore $$\oint _c\frac{Z^3-2z+3}{z-2}dz=2\pi i (z^3-2z+3)_{z=2}=14\pi i$$
(Using Cauchys Integral formula)