GRE Subject 2026 Practice Test Maths Vector Calculus Free Quiz 2

11. What type of operator is ∇?

A. Scalar B. Vector C. Tensor D. Matrix

12. What direction does the gradient vector point?

A. Decrease B. Constant C. Greatest increase D. Random

13. What is the Laplacian in Cartesian coordinates?

A. ∂/∂x + ∂/∂y + ∂/∂z B. ∂²/∂x² + ∂²/∂y² C. ∂²/∂x² + ∂²/∂z² D. ∂²/∂x² + ∂²/∂y² + ∂²/∂z²

14. What is the surface integral of a vector field called?

A. Line integral B. Flux C. Volume integral D. Path integral

15. What matrix contains second-order partial derivatives?

A. Jacobian B. Gradient C. Hessian D. Laplacian

16. What is the path integral of a vector field?

A. Flux B. Surface C. Volume D. Line integral

17. Green's theorem is a special case of which theorem?

A. Divergence theorem B. Stokes' theorem C. Gradient theorem D. Laplacian

18. What is the fundamental theorem of line integrals?

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

19. What is the identity ∇·(fF) = f∇·F + F·∇f?

A. Chain rule B. Product rule C. Quotient rule D. Power rule

20. What is the identity ∇×(fF) = f∇×F + ∇f×F?

A. ∇×(fF) = f∇×F + ∇f×F B. ∇·(fF) = f∇·F + ∇f·F C. ∇(fF) = f∇F + ∇fF D. ∇²(fF) = f∇²F + 2∇f·∇F + F∇²f