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Theorems Related to Vector Calculus

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Question 1

Stokes theorem connects

  • a line integral and a surface integral

  • a surface integral and a volume integral

  • a line integral and a volume integral

  • gradient of a function and its surface integral.

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Question 2

Value of the integral [Tex]\,\,\oint {xydy - {y^2}dx,\,\,} [/Tex] where, [Tex]c[/Tex] is the square cut from the first quadrant by the line [Tex]x=1[/Tex] and [Tex]y=1[/Tex] will be (Use Green's theorem to change the line integral into double integral)

  • [Tex]1/2[/Tex]

  • [Tex]1[/Tex]

  • [Tex]3/2[/Tex]

  • [Tex]5/3[/Tex]

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Question 3

The Divergence Theorem connects which two types of integrals?


  • Line integral and surface integral

  • Surface integral and volume integral

  • Volume integral and line integral

  • Scalar integral and vector integral

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Question 4

Green’s Theorem is applicable to which type of regions?


  • Open surfaces in 3D

  • Closed surfaces in 3D

  • Simple, closed, and positively oriented plane curves

  • Any curve in 3D space

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Question 5

Which theorem can be considered the three-dimensional generalization of Green’s Theorem?

  • Divergence Theorem

  • Stokes’ Theorem

  • Both A and B

  • None

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Question 6

In Green’s Theorem, the positive direction of curve C corresponds to which orientation of the area D?

  • Clockwise

  • Anticlockwise

  • Vertical

  • Any arbitrary direction

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There are 6 questions to complete.

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