GRE Subject 2026 Practice Test Maths Vector Calculus Free Quiz 1

1. What is the gradient of a scalar field?

A. Divergence B. Curl C. Gradient D. Laplacian

2. What does divergence measure?

A. Gradient B. Curl C. Laplacian D. Divergence

3. What is the Laplacian?

A. ∇·∇ B. ∇(∇·) C. ∇×∇× D. ∇·(∇×)

4. What theorem relates a line integral to a double integral?

A. Stokes B. Divergence C. Green's D. Gradient

5. What theorem relates a surface integral to a line integral?

A. Green B. Divergence C. Gradient D. Stokes'

6. What theorem relates a volume integral to a surface integral?

A. Green B. Divergence theorem C. Stokes D. Gradient

7. What is the relationship between a conservative field and a scalar potential?

A. F = ∇×φ B. F = ∇·φ C. F = ∇²φ D. F = -∇φ

8. What is the curl of a gradient?

A. Gradient of divergence B. Curl of gradient C. Divergence of curl D. Laplacian

9. What is the divergence of a curl?

A. Divergence of curl B. Curl of divergence C. Gradient of curl D. Laplacian

10. What does it mean for a vector field to be irrotational?

A. Divergence zero B. Gradient zero C. Curl zero D. Laplacian zero