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# GATE EC 2021: Engineering Mathematics Quiz 12 (App update required to attempt this test)

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Question 1

If C is the rectangle curve that shown below, so the value of (y4 – 2y) dx – (6x – 4xy3) dy is __ Question 2

Consider the time-varying vector  in Cartesian coordinates,
Where is a constant. When the vector magnitude |I| is at its minimum value, the angle 0 that I make with the x axis (in degrees, such that ) is

Question 3

Let If is a unit vector such that then is equal to

Question 4

A vector field D = exists inside a cylindrical region enclosed by the surfaces r = 1, z = 0 and z = 5. Let S be the surface bounding this cylindrical region. The surface integral of this field on S is _____.

Question 5

The directional derivative of f (x, y, z) =x2 - y2 +2zat P (1, 2, 3) in the direction of line PQ, where Q = (5, 0, 4), is ________.

Question 6

If and the angle between is then is equal to ________.
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