Home › MCQs › CSS Pure Mathematics › Question #1271
Back to Questions
CSS Pure Mathematics QUESTION #1271
Question 1
Using the Cauchy Residue Theorem, \(\oint_{|Z|=2}\dfrac{5Z-2}{Z(Z-1)}\,dZ\) equals:
  • \(2\pi i\)
  • \(4\pi i\)
  • \(6\pi i\)
  • \(10\pi i\)✔️
Correct Answer Explanation
Partial fractions: \(\dfrac{5Z-2}{Z(Z-1)}=\dfrac{2}{Z}+\dfrac{3}{Z-1}\). Both poles \(Z=0\) and \(Z=1\) lie inside \(|Z|=2\). By residue theorem: \(2\pi i(\text{Res at }0+\text{Res at }1)=2\pi i(2+3)=10\pi i\).