Vector Calculus NAT Level - 1 - Physics MCQ

Vector Calculus NAT Level - 1 - Physics MCQ

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10 Questions MCQ Test Topic wise Tests for IIT JAM Physics - Vector Calculus NAT Level - 1

Vector Calculus NAT Level - 1 for Physics 2024 is part of Topic wise Tests for IIT JAM Physics preparation. The Vector Calculus NAT Level - 1 questions and answers have been prepared according to the Physics exam syllabus.The Vector Calculus NAT Level - 1 MCQs are made for Physics 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Vector Calculus NAT Level - 1 below.
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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 = t2, z = t3

Detailed Solution for Vector Calculus NAT Level - 1 - Question 1

x = t, y = t2, z = t3
dx = dt, dy = 2t dt, dz = 3t2dt

= 5

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Vector Calculus NAT Level - 1 - Question 2

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

Detailed Solution for Vector Calculus NAT Level - 1 - Question 2

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Vector Calculus NAT Level - 1 - Question 3

Detailed Solution for Vector Calculus NAT Level - 1 - Question 3

= –0.858

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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.

Detailed Solution for Vector Calculus NAT Level - 1 - Question 4

The conservative field vector

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Vector Calculus NAT Level - 1 - Question 5

If V = x2y2z the Laplacian of the field V at point  is :

Detailed Solution for Vector Calculus NAT Level - 1 - Question 5

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Vector Calculus NAT Level - 1 - Question 6

Div grad rm = m(m + 1)rm-α. Find the value of α.

Detailed Solution for Vector Calculus NAT Level - 1 - Question 6

= m(m + 1)rm-2
Hence value of  α = 2.

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Vector Calculus NAT Level - 1 - Question 7

are unit vectors satisfying  then

Detailed Solution for Vector Calculus NAT Level - 1 - Question 7

⇒ Angle between each pair is 120º

Now,

= 54 – 10 – 10 – 25 = 9

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Vector Calculus NAT Level - 1 - Question 8

S is the surface of sphere x2 + y2 + z2 = 9, the integral [(x + z) dydz + (y + z)dzdx + (x + y)dxdy] is equal to, (upto three decimal places)

Detailed Solution for Vector Calculus NAT Level - 1 - Question 8

By Gauss divergence theorem

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Vector Calculus NAT Level - 1 - Question 9

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

Detailed Solution for Vector Calculus NAT Level - 1 - Question 9

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Vector Calculus NAT Level - 1 - Question 10

If T(x, y, z) = x2 + y2 + 2z2 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)

Detailed Solution for Vector Calculus NAT Level - 1 - Question 10

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