Question

Match List-I with List-II.

List-I (Cauchy Integral)	List-II (Value)
A. \( \displaystyle \oint_C \frac{\sin z + \cos \pi z}{(z-1)(z-2)} dz \) B. \( \displaystyle \oint_C \frac{dz}{(z+1)^4} \) C. \( \displaystyle \oint_C \frac{e^z}{(z+2)^2} dz \) D. \( \displaystyle \oint_C \frac{\sin z}{z^2} dz \)	I. \( \frac{8\pi i e^{-2}}{3} \) II. \(4\pi i\) III. \( \frac{\pi i}{32} \) IV. \( \frac{i}{\pi} \)

• A. A-I, B-I, C-IV, D-III
• B. A-I, B-II, C-IV, D-III
• C. A-II, B-I, C-III, D-IV
• D. A-I, B-II, C-III, D-IV

Hint:

Higher-order poles → use derivative form of Cauchy integral formula.

Answer 1

The Correct Option is D