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Question 3Asked in DSSSB TGT Computer Science (Technical), 1 Aug 2021, Shift 1

What is the value of ∮c e^(2z) / (z + 1)⁴ dz, where c is a circle with centre at origin, |z| = 3?

  1. A(4/3) πi e⁻²
  2. B2πi e⁻²
  3. C(8/3) πi e⁻²
  4. D3πi e⁻²
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Correct answer: (C) (8/3) πi e⁻²

Explanation

The only singularity, z = −1 (a pole of order 4), lies inside |z| = 3. By Cauchy's formula the integral is 2πi·f'''(−1)/3! with f = e^(2z), f''' = 8e^(2z), giving 2πi·8e⁻²/6 = (8/3)πi e⁻².

From DSSSB TGT Computer Science PYQ (Technical), 1 Aug 2021, Shift 1

This is question 3 of DSSSB TGT Computer Science PYQ (Technical), 1 Aug 2021, Shift 1. See all questions of this paper with answers, or attempt the paper as a timed online test to get your score and all-India rank.