Allied & ICAR Exam Bank • ALLIED_0064 MCQ • 1 Mark

Section 1: Engineering Mathematics

Vector Calculus

Subtopic: Stokes, Gauss and Green's theorems

Question Statement:

Stokes' theorem equates a line integral around a boundary curve $C$ to:

Options:

  • (A) The surface integral of the curl of the vector field over the bounded surface $S$
  • (B) The volume integral of divergence
  • (C) The surface integral of gradient
  • (D) The arc length of $C$

Answer Key:

A

Step-by-Step Solution & Explanation

Stokes' theorem: $\oint_C \vec{F} \cdot d\vec{r} = \iint_S (\nabla \times \vec{F}) \cdot \hat{n} dS$.
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