SZABMU AHS 2026 Vector and Scalar Free Quiz 7

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SZABMU AHS 2026 Vector and Scalar Free Quiz 7

SZABMU AHS Quiz

10:00

Answered: 0 / 10

Remaining: 10

Navigator 10 Q

General

General 10 MCQs

61. What is the vector triple product expansion?

A. B(A·C) - C(A·B) B. C(A·B) - B(A·C) C. A(B·C) - B(A·C) D. A(B·C) - C(A·B)

62. What matrix contains all partial derivatives of a vector function?

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

63. What does the Jacobian determinant represent?

A. Jacobian determinant B. Trace C. Rank D. Nullity

64. How do differential operators change in curvilinear coordinates?

A. Same as Cartesian B. Modified expressions C. Not defined D. Simpler

65. What theorem relates surface integral to volume integral of divergence?

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

66. What theorem relates line integral of curl to surface integral?

A. Divergence theorem B. Stokes theorem C. Green's theorem D. Fundamental theorem

67. Which theorem is Stokes' theorem for a plane?

A. Divergence theorem B. Stokes theorem C. Green's theorem D. Gauss law

68. What term describes a zero‑curl vector field?

A. Irrotational B. Solenoidal C. Harmonic D. Conservative

69. What characterizes a harmonic vector field?

A. Divergence and curl zero B. Divergence zero only C. Curl zero only D. None

70. How does gradient differ in spherical coordinates?

A. Same as Cartesian B. Involves 1/r, 1/(r sinθ) C. Involves 1/r only D. Involves r only

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