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Vector Calculus MSQ - Question 1

Evaluate where *S* is the cylinder *x*^{2} + *y*^{2} = 1 bounded by the planes z = 0 and z = 1 and r is the distance between a point on the surface and the origin.

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Vector Calculus MSQ - Question 2

Evaluate the line integral where and C is the curve in xy–plane consisting curve C_{1}: straight lines from (0, 0) to (1, 0) and curve C_{2}: straight line from (1, 0) to (3, 4)

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Vector Calculus MSQ - Question 5

Evaluate where where *C* is the boundary of the triangle with vertices at (0, 0, 0), (1, 0, 0), (1, 1, 0) oriented counter clockwise.

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Vector Calculus MSQ - Question 7

If C is a smooth curve in R^{3} from path joining (–1, 0, 1) to (1, 1, –1), then the value of (3x^{2}y + z)dx + (x^{3} + 4y^{3}z)dy + (x + y^{4})dz is :

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Vector Calculus MSQ - Question 8

What is the divergence of the vector fieldat the point (1, 2, 3).

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Vector Calculus MSQ - Question 9

Which of the following statement(s) is(are) true about function

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Vector Calculus MSQ - Question 10

Evaluate over the entire surface of the region above *xy–*plane bounded by the cone ** z^{2} = x^{2} + y^{2}** and the plane

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