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Vector Calculus NAT Level - 1 - IIT JAM MCQ

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10 Questions MCQ Test - Vector Calculus NAT Level - 1

Vector Calculus NAT Level - 1 for IIT JAM 2024 is part of IIT JAM preparation. The Vector Calculus NAT Level - 1 questions and answers have been prepared according to the IIT JAM exam syllabus.The Vector Calculus NAT Level - 1 MCQs are made for IIT JAM 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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*Answer can only contain numeric values

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
The correct answer is: 5

*Answer can only contain numeric values

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

The correct answer is: 4.187

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*Answer can only contain numeric values

Vector Calculus NAT Level - 1 - Question 3

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

= –0.858
The correct answer is: -0.858

*Answer can only contain numeric values

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

The correct answer is: 4.141

*Answer can only contain numeric values

Vector Calculus NAT Level - 1 - Question 5

If V = x²y²z² the Laplacian of the field V at point is :

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

The correct answer is: 24

*Answer can only contain numeric values

Vector Calculus NAT Level - 1 - Question 6

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

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

= m(m + 1)r^m-2
Hence value of α = 2.

The correct answer is: 2

*Answer can only contain numeric values

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

The correct answer is: 3

*Answer can only contain numeric values

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

The correct answer is: 226.194

*Answer can only contain numeric values

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

The correct answer is: 6.282

*Answer can only contain numeric values

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

Magnitude of temperature gradient

The correct answer is: 4.898

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