Home › Previous year questions › GATE 2024 BM › Question 11GATE 2024 BM – Question 11 Engineering Mathematics · Complex Variables · 1 mark · Multiple choice
Evaluate counterclockwise $\oint_{|z|=3}\frac{8\,dz}{z(z-2)(z-4)}$.
+j2π −j2π −j10π +j10π Practise this question in The GATE Grind →
Show answer and explanation Correct answer: (B) −j2π
Explanation The contour encloses poles zero and two, but not four. Residues are 8/[(-2)(-4)]=1 at zero and 8/[2(−2)]=−2 at two. Their sum is −1. By the residue theorem the integral is 2πj×(−1)=−j2π, B.
More Complex Variables questions GATE 2024 BM Q44 – Using residues, evaluate -dx1+x4. GATE 2023 BM Q48 – For f(z)=1/(z−1), which counterclockwise circular contours yield contour integral 2πj? GATE 2023 BM Q58 – Expand sin z as a Taylor series about z=0. What is the reciprocal of the coefficient of… GATE 2022 BM Q36 – Evaluate Cz3-93z-i\,dz in the complex z plane. GATE 2020 BM Q26 – Evaluate 12 j Cz(z-1)(z-2)\,dz for positively oriented circle z =3/2. GATE 2020 BM Q61 – Find the de Broglie wavelength in nm of an electron accelerated through 1 V, to two… All Complex Variables questions →