Singularities, Poles, and Residues
Curriculum and historical examination lineage for Singularities, Poles, and Residues under Unit 5 (Complex Integration) of Advanced Calculus and Complex Analysis (21MAB102T) at SRMIST.
Historical appearance distribution across SRMIST Formative Tests (CT1, CT2) and University End Semester examinations.
Factual marks weightage of questions asked on this topic in historical examinations.
Question templates that recur across multiple examination cycles with similar conceptual stems.
“\text{If } f(z) = \frac{\sin z}{z} \text{ then} (A) z = 0 \text{ is a removable singularity} (B) z...”
“If \(f(z)\) is not analytic at \(z=z_0\) and there exists a neighborhood of \(z=z_0\) containing no...”
“f(z) = \frac{z+2}{(z-1)^2(z-2)} has (A) Only poles (B) A simple pole at \(z=1/2\) (C) Essential...”
“Find the residue of f(z) = \cot z is”
“What is the residue of \cot(z) at z = 0? A) 1 B) -1 C) 0 D) \pi”
Representative historical questions extracted directly from SRMIST examination papers.
If \(f(z)\) is not analytic at \(z=z_0\) and there exists a neighborhood of \(z=z_0\) containing no other singularity, then (A) \(z=z_0\) is isolated singularity of \(f(z)\) (B)...
If \(f(z) = \frac{\sin z}{z}\), then (A) \(z=0\) is a simple pole (B) \(z=0\) is a pole of order 2 (C) \(z=0\) is a removable singularity (D) \(z=0\) is a zero of \(f(z)\)
f(z) = \frac{z+2}{(z-1)^2(z-2)} has (A) Only poles (B) A simple pole at \(z=1/2\) (C) Essential singularity (D) No poles
If f(z) = \frac{\sin z - z}{z^3} then (A) z=0 is a simple pole (B) z=0 is a pole of order 2 (C) z=0 is a removable singularity (D) z=0 is a zero f f(z)
If \(f(z) = \frac{\sin z}{z}\), then (A) \(z = 0\) is a simple pole (B) \(z = 0\) is a pole of order 2 (C) \(z = 0\) is a removable singularity (D) \(z = 0\) is a zero of \(f(z)\)
Examinations where questions for Singularities, Poles, and Residues have appeared.
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