Vector Analysis-Gauss and Stokes' Theorems, Green's Identities [IAS (Admin.) Mains Mathematics]: Questions 1 - 8 of 19
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Question 1
Appeared in Year: 2015
Describe in Detail Subjective▾
Evaluate , where is the reactangle with vertices [CS (Main) Paper 1]
EditExplanation
- By Green՚s Theorem in plane,
- Here
… (101 more equations, 3 figures) …
Question 2
Appeared in Year: 2012
Describe in Detail Subjective▾
If evaluate
Where S is the surface of the sphere above the plane. (Paper I)
EditExplanation
- The boundary c of the surface s is the circle
- The parametric equation of c are
… (27 more equations) …
Question 3
Appeared in Year: 2011
Describe in Detail Subjective▾
If , calculate the double integral over the hemisphere given by (Paper I)
EditExplanation
- Here is the surface of the sphere lying above the plane. Let c be one foundry ABED of the surface S. Then the curve C is a circle in the plane and equation of C are
… (97 more equations, 3 figures) …
Question 4
Appeared in Year: 2012
Describe in Detail Subjective▾
Verify Green՚s theorem in the plane for
Where c is the closed curve of the region bounded by (Paper I)
EditExplanation
By Green՚s theorem in a plane
… (117 more equations, 8 figures) …
Question 5
Appeared in Year: 2009
Describe in Detail Subjective▾
Using divergence Theorem, evaluate
Where and is the surface of the sphere (Paper I)
EditExplanation
- Let be denotes the entire surface of the sphere and let be the volume enclosed by
i.e..
… (108 more equations) …
Question 6
Appeared in Year: 2010
Describe in Detail Subjective▾
Verify Green՚s Theorem for the path of integration being the boundary of the square whose vertices are (Paper I)
EditExplanation
By green՚s Theorem in plane,
- We have to verify this result
- No…
… (82 more equations, 4 figures) …
Question 7
Appeared in Year: 2007
Describe in Detail Subjective▾
Determine by using stoke՚s theorem, where c is the curve defined by
That starts from the point and goes at first below the z-plane (Paper I)
EditExplanation
- The curve c is given by
… (177 more equations, 6 figures) …
Question 8
Appeared in Year: 2014
Describe in Detail Subjective▾
Verify Gauss divergence theorem for the vector
Taken over the cube (Paper I)
EditExplanation
- Let be the surface of the cube bounded by the planes
- Let v be the volume enclosed by s then we have to prove
… (127 more equations, 3 figures) …