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Vector Calculus NAT Level - 2 - Physics MCQ


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10 Questions MCQ Test Topic wise Tests for IIT JAM Physics - Vector Calculus NAT Level - 2

Vector Calculus NAT Level - 2 for Physics 2024 is part of Topic wise Tests for IIT JAM Physics preparation. The Vector Calculus NAT Level - 2 questions and answers have been prepared according to the Physics exam syllabus.The Vector Calculus NAT Level - 2 MCQs are made for Physics 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Vector Calculus NAT Level - 2 below.
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*Answer can only contain numeric values
Vector Calculus NAT Level - 2 - Question 1

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

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

*Answer can only contain numeric values
Vector Calculus NAT Level - 2 - Question 3

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

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

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
x
2 + y2 = 1



= –0.416
The correct answer is: -0.416

*Answer can only contain numeric values
Vector Calculus NAT Level - 2 - Question 6

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

*Answer can only contain numeric values
Vector Calculus NAT Level - 2 - Question 7

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

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

  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 + xdz
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

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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