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Vector Calculus MCQ Level - 2


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

Vector Calculus MCQ Level - 2 for IIT JAM 2023 is part of Topic wise Tests for IIT JAM Physics preparation. The Vector Calculus MCQ Level - 2 questions and answers have been prepared according to the IIT JAM exam syllabus.The Vector Calculus MCQ Level - 2 MCQs are made for IIT JAM 2023 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Vector Calculus MCQ Level - 2 below.
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Vector Calculus MCQ Level - 2 - Question 1

The line integral  taken along the closed path formed by y = x and x2 = y3 in the first quadrant will be valuated to :

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

By Green's theorem, we have,

 

The correct answer is: 1/198

Vector Calculus MCQ Level - 2 - Question 2

 where S : x2 + y2 + z2 = 1, z ≥ 0 and  will have the value :

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

By Stoke’s Theorem,

where C : x2 + y2 = 1, z = 0




The correct answer is: -π

Vector Calculus MCQ Level - 2 - Question 3

The line integral of the vector field  along the helix defined by x = cos t, y = sin t,   is equal to :

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

We have,

Hence, the line integral of the given vector field will be,


The correct answer is: 1/3

Vector Calculus MCQ Level - 2 - Question 4

If  u = x + y + z, v = x2 + y2 + z2  and w = yz = zx + xy then  is equal to :

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

u = x + y + z



= 0
The correct answer is: 0

Vector Calculus MCQ Level - 2 - Question 5

The potential function for the vector field  will be :

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

Compare the given vector field with the gradient of some function, say φ, i.e.,




⇒ The potential function for the given vector field would be x2y3z4.

The correct answer is: x2y3z4

Vector Calculus MCQ Level - 2 - Question 6

The value of the surface integral  where S is the closed surface of the solid bounded by the graphs of x = 4 and z = 9 – y2 and coordinate planes &  will be given by :

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

The given surface is z + y2 = 9






The correct answer is:  

Vector Calculus MCQ Level - 2 - Question 7

The value of the integral   where  and where S is the entire surface of the  paraboloid z = 1 - x2 - y2 with z = 0 together with the disk {(x, y) : x2 + y2 < 1}

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

By Gauss Divergence Theorem,





The correct answer is: 2π

Vector Calculus MCQ Level - 2 - Question 8

The value of    where  and S is the surface of the paraboloid z = 4 – (x2 + y2) above the xy-plane will be :

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

By Stokes theorem,


Here, the boundary curve C of the surface will be given by x2 + y2 = 4, z = 0, or 


The correct answer is: -4π

Vector Calculus MCQ Level - 2 - Question 9

 is equal to :

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

Consider, 



The correct answer is: 

Vector Calculus MCQ Level - 2 - Question 10

  is equivalent to :

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

The correct answer is:  

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