PYQs Based Test - 25 : Residue Theorem and Solution Integral

The integral $\oint f\left(z\right)dz$ evaluated around the unit circle on the complex plane for $f\left(z\right)=\frac{\cos z}{z}$ is

For $\mathrm{f}\left(\mathrm{z}\right)=\frac{\sin \left(\mathrm{z}\right)}{{\mathrm{z}}^2}$ the residue of the pole at z = 0 is __________

Let z = x + iy be a complex variable. Consider that contour integration is performed along the unit circle in anticlockwise direction. Which one of the following statements is Not True?

The value of $\oint \frac{1}{z^2}dz,$ where the contour is the unit circle traversed clockwise, is

The contour C given below is on the complex plane z = x + jy, where $\mathrm{j}=\sqrt{-1}$



The value of the integral $\frac{1}{\pi \mathrm{j}}\underset{\mathrm{c}}{\oint }\frac{\mathrm{dz}}{{\mathrm{z}}^2-1}$ is _______