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GATE 2019: Engineering Mathematics Test 8

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Question 1

Consider a function f (x, y, z) given by


The partial derivative of this function with respect to x at the point, x = 2, y = 1 and z = 3 is ________

Question 2

The expression for the volume of a cone is equal to

Question 3

X is a uniformly distributed random variable that takes values between 0 and 1. The value of E {X3} will be

Question 4

F(x, y) = (x2 + xy). It’s line integral over the straight line from (x, y) = (0, 2) to (x, y) = (2, 0) evaluates to

Question 5

f(x, y) is a continuous function defined over (x, y) ï[0, 1] × [0, 1]. Given the two constraints, x > y2 and y > x2, the volume under f(x, y) is

Question 6

The volume enclosed by the surface f(x, y) = ex over the triangle bounded by the lines x = y; x = 0; y = 1 in the xy plane is ________.
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Aug 21ESE & GATE EE