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IIT JAM Exam  >  IIT JAM Tests  >  Vector Calculus NAT Level - 2 - IIT JAM MCQ

Vector Calculus NAT Level - 2 - IIT JAM MCQ


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10 Questions MCQ Test - Vector Calculus NAT Level - 2

Vector Calculus NAT Level - 2 for IIT JAM 2024 is part of IIT JAM preparation. The Vector Calculus NAT Level - 2 questions and answers have been prepared according to the IIT JAM exam syllabus.The Vector Calculus NAT Level - 2 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 - 2 below.
Solutions of Vector Calculus NAT Level - 2 questions in English are available as part of our course for IIT JAM & Vector Calculus NAT Level - 2 solutions in Hindi for IIT JAM course. Download more important topics, notes, lectures and mock test series for IIT JAM Exam by signing up for free. Attempt Vector Calculus NAT Level - 2 | 10 questions in 45 minutes | Mock test for IIT JAM preparation | Free important questions MCQ to study for IIT JAM Exam | Download free PDF with solutions
*Answer can only contain numeric values
Vector Calculus NAT Level - 2 - Question 1
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Evaluate  where   and S is the part of the plane 2x + 3y + 6z = 12 which is located in the first octant.


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




= 24
The correct answer is: 24

*Answer can only contain numeric values
Vector Calculus NAT Level - 2 - Question 2
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Find the value of constant (a + b + c) so that the directional derivative of the function f = axy2 + byz + cz2x3 at the point (1, 2, –1) has maximum magnitude 64 in the direction  parallel to y axis :


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


  lies along y axis
So, 4a + 3c = 0
2b – 2c = 0

The correct answer is: -20

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*Answer can only contain numeric values
Vector Calculus NAT Level - 2 - Question 3
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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 z2 = x2 + y2 and z = y + 1.


Detailed Solution for Vector Calculus NAT Level - 2 - Question 3

  can be expressed as gradient of scalar function 

written the common term once

The line integral  along the portion (1, 0, 1) to (3, 4, 5)

= (375 + 108 – 20) – (1)
= 463 – 1
= 462

The correct answer is: 462

*Answer can only contain numeric values
Vector Calculus NAT Level - 2 - Question 4
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The work done by the force   in moving a particle over circular path x2 + y2 = 1, z = 0 from (1, 0, 0) to (0, 1, 0) is :

Detailed Solution for Vector Calculus NAT Level - 2 - Question 4

on the curve 

The correct answer is: -4.142

*Answer can only contain numeric values
Vector Calculus NAT Level - 2 - Question 5
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Evaluate  where C is the path shown in figure.

Detailed Solution for Vector Calculus NAT Level - 2 - Question 5

Path AO
y = 1
dy = 0

Path OB
x2 + y2 = 1



= –0.416
The correct answer is: -0.416

*Answer can only contain numeric values
Vector Calculus NAT Level - 2 - Question 6
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Let C be any curve x2 + y2 + z2 = 4, z > 0 and the vector field 

find out 

(Ans. upto three decimal places)

Detailed Solution for Vector Calculus NAT Level - 2 - Question 6

Consider a closed surface  consisting of S and S' i.e 


The correct answer is: 25.132

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Vector Calculus NAT Level - 2 - Question 7
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The value of the  and C is the curve y2 = x joining (0, 0) to (1, 1) is (correct upto three decimal places)

Detailed Solution for Vector Calculus NAT Level - 2 - Question 7

The correct answer is: 0.583

*Answer can only contain numeric values
Vector Calculus NAT Level - 2 - Question 8
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Find the value of 

Detailed Solution for Vector Calculus NAT Level - 2 - Question 8

Let 

The correct answer is: 0

*Answer can only contain numeric values
Vector Calculus NAT Level - 2 - Question 9
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  along the curve x = sin θ cos θ, y sin2 θ, z = cos θ with θ  increasing from 0 to π/2. Find the value of α + β.

Detailed Solution for Vector Calculus NAT Level - 2 - Question 9


= xz dx + y dy + x2 dz
Along the given curve, we have

Putting values

The correct answer is: 43

*Answer can only contain numeric values
Vector Calculus NAT Level - 2 - Question 10
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If f(x, y, z) = x2y + y2z + z2x for all (x, y, x) ∈ R3 and   then the value of  at (2, 2, 2) is :

Detailed Solution for Vector Calculus NAT Level - 2 - Question 10


Hence, 

The correct answer is: 12

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