Allied & ICAR Exam Bank • ALLIED_1034 MCQ • 1 Mark

Section 1: Engineering Mathematics

Vector Calculus

Subtopic: Solenoidal vector fields

Question Statement:

The vector field $\vec{F} = (x + 3y)\hat{i} + (y - 2z)\hat{j} + (x + c z)\hat{k}$ is solenoidal if the constant $c$ is:

Options:

  • (A) -2
  • (B) 0
  • (C) 2
  • (D) -1

Answer Key:

A

Step-by-Step Solution & Explanation

A vector field is solenoidal if $\nabla \cdot \vec{F} = 0$. $\nabla \cdot \vec{F} = \frac{\partial}{\partial x}(x + 3y) + \frac{\partial}{\partial y}(y - 2z) + \frac{\partial}{\partial z}(x + cz) = 1 + 1 + c = 2 + c = 0 \implies c = -2$.
← Previous (ALLIED_1033) Next (ALLIED_1035) →

Practice In Authentic CBT Exam Interface

Test your skills under authentic timed conditions with live scoring and AIR percentile ranking.

Launch CBT Mock Test