List of top Engineering Mathematics Questions on Complex numbers asked in GATE BM

Which of the following is/are CORRECT about the value of \( y = \log_e(-e^x) \), where \( x \) is a real number.
The function \( f(Z)=\dfrac{1}{Z-1} \) of a complex variable \(Z\) is integrated on a closed contour in an anti-clockwise direction. For which of the following contours, does this integral have a non-zero value?
In the complex z-domain, the value of the integral \[ \oint_{C} \frac{z^{3} - 9}{3z - i} \, dz \] is