Question Bank • QB_SUB_EM_0112 MCQ • 1 Mark

Section 1: Engineering Mathematics

Vector Calculus

Subtopic: Physical interpretations – line, surface and volume integrals

Question Statement:

Gauss' Divergence theorem transforms:

Options:

  • (A) A surface integral over a closed surface into a volume integral over the enclosed region
  • (B) A line integral around a closed curve into a surface integral
  • (C) A volume integral into a line integral
  • (D) A scalar product into a vector cross product

Answer Key:

A

Step-by-Step Solution & Explanation

Divergence theorem: $\iint_S \vec{F} \cdot \hat{n}\, dS = \iiint_V (\nabla \cdot \vec{F})\, dV$.
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