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Vector Calculus NAT Level - 1 - Question 1

Evaluate the line integral from (0, 0, 0) to (1, 1, 1) along the curve x = t, y = t^{2}, z = t^{3}

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Vector Calculus NAT Level - 1 - Question 2

Compute the flux of across the cone (upto three decimal places)

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Vector Calculus NAT Level - 1 - Question 4

is a conservative field and potential any curve * C* in the path from (0, 0, 1) to evaluate upto three decimal places.

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Vector Calculus NAT Level - 1 - Question 5

If V = x^{2}y^{2}z^{2 } the Laplacian of the field V at point is :

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Vector Calculus NAT Level - 1 - Question 6

Div grad r^{m} = m(m + 1)r^{m-α}. Find the value of α.

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Vector Calculus NAT Level - 1 - Question 8

S is the surface of sphere x^{2} + y^{2} + z^{2} = 9**,** the integral [(x + z) dydz + (y + z)dzdx + (x + y)dxdy] is equal to, (upto three decimal places)

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Vector Calculus NAT Level - 1 - Question 9

Evaluate around any closed path C. (Ans. upto three decimal places)

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Vector Calculus NAT Level - 1 - Question 10

If T(x, y, z) = x^{2} + y^{2} + 2z^{2} defines the temperature at any location (x, y, z) then the magnitude of the temperature gradient point P(1, 1, 1), (upto three decimal places)

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