Question

Match List-I with List-II.

List-I (Complex integrate)	List-II (Value)
A. \( \displaystyle \int_{0}^{2\pi} \cos^2 x \, dx \) B. \( \displaystyle \int_{0}^{\pi} \cos x \, dx \) C. \( \displaystyle \oint_C dz \), where \(C\) is a simple closed curve D. \( \displaystyle \oint_C \frac{dz}{z^2-1} \), around circle \(|z-1|=1\)	I. \(4\pi i\) II. \(0\) III. \(\frac{\pi}{4}\) IV. \( \frac{1}{4}\cosh 2 - \frac{1}{2}\sinh 2 + \frac{1}{2}\pi i \sinh 2 \)

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

Hint:

Closed contour of analytic function → zero; residues give non-zero integrals.

Answer 1

The Correct Option is B