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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

*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 = x2y2z 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 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.

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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