Allied & ICAR Exam Bank • ALLIED_2682 MSQ • 2 Marks

Section 1: Engineering Mathematics

Vector Calculus

Subtopic: Divergence and curl

Question Statement:

Which of the following vector fields are SOLENOIDAL (i.e. $\nabla \cdot \vec{F} = 0$)?

Options:

  • (A) $\vec{F}_1 = y \hat{i} + z \hat{j} + x \hat{k}$
  • (B) $\vec{F}_2 = x \hat{i} - y \hat{j} + 2z \hat{k}$
  • (C) $\vec{F}_3 = -y \hat{i} + x \hat{j}$
  • (D) $\vec{F}_4 = x^2 \hat{i} + y^2 \hat{j} + z^2 \hat{k}$

Answer Key:

A, C

Step-by-Step Solution & Explanation

For (A): $\nabla \cdot \vec{F}_1 = 0 + 0 + 0 = 0$. For (B): $\nabla \cdot \vec{F}_2 = 1 - 1 + 2 = 2 \neq 0$. For (C): $\nabla \cdot \vec{F}_3 = 0 + 0 = 0$. For (D): $\nabla \cdot \vec{F}_4 = 2x + 2y + 2z \neq 0$.
← Previous (ALLIED_2681) Next (ALLIED_2683) →

Practice In Authentic CBT Exam Interface

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

Launch CBT Mock Test