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Vector Calculus MCQ Level - 2 - Question 1

The line integral taken along the closed path formed by y = x and x^{2} = y^{3} in the first quadrant will be valuated to :

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Vector Calculus MCQ Level - 2 - Question 2

where S : x^{2} + y^{2} + z^{2} = 1, z ≥ 0 and will have the value :

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Vector Calculus MCQ Level - 2 - Question 3

The line integral of the vector field along the helix defined by x = cos t, y = sin t, is equal to :

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Vector Calculus MCQ Level - 2 - Question 4

If u = x + y + z, v = x^{2} + y^{2} + z^{2} and w = yz = zx + xy then is equal to :

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Vector Calculus MCQ Level - 2 - Question 5

The potential function for the vector field will be :

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Vector Calculus MCQ Level - 2 - Question 6

The value of the surface integral where *S* is the closed surface of the solid bounded by the graphs of *x* = 4 and *z* = 9 – *y*^{2} and coordinate planes & will be given by :

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Vector Calculus MCQ Level - 2 - Question 7

The value of the integral where and where *S* is the entire surface of the paraboloid z = 1 - x^{2} - y^{2} with *z* = 0 together with the disk {(x, y) : x^{2} + y^{2} __<__ 1}

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Vector Calculus MCQ Level - 2 - Question 8

The value of where and *S* is the surface of the paraboloid z = 4 – (x^{2} + y^{2}) above the *xy*-plane will be :

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