The value of integral ${\int }_{\mathrm{C}}\frac{\mathrm{dz}}{\left(\mathrm{z}-1\right)\left(\mathrm{z}-2\right)}$ , where $\mathrm{C}:\left|\mathrm{z}\right|=3$ , is _____ .

Which of the following is related to cauchy residue theorem?

Select the correct option for the following data.

(1) $\mathrm{f}\left(\mathrm{z}\right)=\frac{\mathrm{sinz}}{\mathrm{z}}$                              (a) z=0 is a removable singularity

(2) $\mathrm{f}\left(\mathrm{z}\right)={\mathrm{e}}^{\frac{1}{\mathrm{z}}}$                                (b) z=0 is a essential singularity

(3) $\mathrm{f}\left(\mathrm{z}\right)=\frac{1-{\mathrm{e}}^{\mathrm{z}}}{{\mathrm{z}}^3}$                             (c) z=0 is a pole