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*Answer can only contain numeric values

Vector Calculus NAT Level - 2 - Question 1

Evaluate where and S is the part of the plane 2x + 3y + 6z = 12 which is located in the first octant.

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Vector Calculus NAT Level - 2 - Question 2

Find the value of constant (a + b + c) so that the directional derivative of the function f = axy^{2} + byz + cz^{2}x^{3} at the point (1, 2, –1) has maximum magnitude 64 in the direction parallel to y axis :

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Vector Calculus NAT Level - 2 - Question 3

Evaluate the along the portion from path (1, 0, 1) to (3, 4, 5) of the curve C**,** which is the intersection of the surface z^{2} = x^{2} + y^{2} and z = y + 1.

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Vector Calculus NAT Level - 2 - Question 4

The work done by the force in moving a particle over circular path x^{2} + y^{2} = 1, z = 0 from (1, 0, 0) to (0, 1, 0) is :

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Vector Calculus NAT Level - 2 - Question 6

Let *C* be any curve x^{2} + y^{2} + z^{2} = 4, z __>__ 0 and the vector field

find out

(Ans. upto three decimal places)

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Vector Calculus NAT Level - 2 - Question 7

The value of the and C is the curve y^{2} = x joining (0, 0) to (1, 1) is (correct upto three decimal places)

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Vector Calculus NAT Level - 2 - Question 9

along the curve x = sin θ cos θ, y sin^{2} θ, z = cos θ with θ increasing from 0 to π/2. Find the value of α + β.

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Vector Calculus NAT Level - 2 - Question 10

If f(x, y, z) = x^{2}y + y^{2}z + z^{2}x for all (x, y, x) ∈ R^{3} and then the value of at (2, 2, 2) is :

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