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Test: Partial Derivatives, Gradient- 2 - Question 1

f(x, y) = x^{2} + xyz + z Find f_{x} at (1,1,1)

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Test: Partial Derivatives, Gradient- 2 - Question 2

Eight people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by:

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Test: Partial Derivatives, Gradient- 2 - Question 3

The minimum point of the function f(x) = (x^{2/3}) – x is at

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Test: Partial Derivatives, Gradient- 2 - Question 4

If x=a(θ+ sin θ) and y=a(1-cosθ), then dy/dx will be equal

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Test: Partial Derivatives, Gradient- 2 - Question 5

The minimum value of function y = x^{2} in the interval [1, 5] is

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Test: Partial Derivatives, Gradient- 2 - Question 6

The function f(x) = 2x^{3} – 3x^{2} – 36x + 2 has its maxima at

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Test: Partial Derivatives, Gradient- 2 - Question 7

What should be the value of λ such that the function defined below is continuous at x = π/22?

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Test: Partial Derivatives, Gradient- 2 - Question 8

Consider function f(x) =(x^{2}-4)^{2} where x is a real number. Then the function has

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Test: Partial Derivatives, Gradient- 2 - Question 9

If f where ai (i = 0 to n) are constants, then

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Test: Partial Derivatives, Gradient- 2 - Question 11

A point on a curve is said to be an extremum if it is a local minimum or a local maximum. The number of distinct exterma for the curve 3x^{4} – 16x^{3} – 24x^{2} + 37 is

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Test: Partial Derivatives, Gradient- 2 - Question 12

∇ × ∇ × P, where P is a vector, is equal to

Test: Partial Derivatives, Gradient- 2 - Question 13

The value of the integral of the function g(x, y) = 4x^{3} + 10y^{4} along the straight line segment from the point (0, 0) to the point (1, 2) in the x-y plane is

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Test: Partial Derivatives, Gradient- 2 - Question 14

If is a differentiable vector function and f is a sufficient differentiable scalar function, then curl

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Test: Partial Derivatives, Gradient- 2 - Question 15

The temperature field in a body varies according to the equation T(x,y) = x^{3}+4xy. The direction of fastest variation in temperature at the point (1,0) is given by

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Test: Partial Derivatives, Gradient- 2 - Question 18

Among the following, the pair of vectors orthogonal to each other is

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Test: Partial Derivatives, Gradient- 2 - Question 19

The directional derivative of the scalar function f(x, y, z) = x^{2} + 2y^{2} + z at the point P = (1,1, 2) in the direction of the vector

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Test: Partial Derivatives, Gradient- 2 - Question 20

The Gauss divergence theorem relates certain

Test: Partial Derivatives, Gradient- 2 - Question 21

If P, Q and R are three points having coordinates (3, –2, –1), (1, 3, 4), (2, 1, –2) in XYZ space, then the distance from point P to plane OQR (O being the origin of the coordinate system) is given by

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Test: Partial Derivatives, Gradient- 2 - Question 22

Let x and y be two vectors in a 3 dimensional space and <x, y> denote their dot product.

Then the determinant det

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Test: Partial Derivatives, Gradient- 2 - Question 23

If a - b = 3 and a^{2} + b^{2} = 29, find the value of ab.

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Test: Partial Derivatives, Gradient- 2 - Question 24

If a vector R(t) ^{→} has a constant magnitude, then

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Test: Partial Derivatives, Gradient- 2 - Question 25

For the scalar field magnitude of the gradient at the point(1,3) is

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