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Vector Calculus MCQ Level - 2 - Physics MCQ


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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 Physics 2024 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 Physics exam syllabus.The Vector Calculus MCQ Level - 2 MCQs are made for Physics 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Vector Calculus MCQ Level - 2 below.
Solutions of Vector Calculus MCQ Level - 2 questions in English are available as part of our Topic wise Tests for IIT JAM Physics for Physics & Vector Calculus MCQ Level - 2 solutions in Hindi for Topic wise Tests for IIT JAM Physics course. Download more important topics, notes, lectures and mock test series for Physics Exam by signing up for free. Attempt Vector Calculus MCQ Level - 2 | 10 questions in 45 minutes | Mock test for Physics preparation | Free important questions MCQ to study Topic wise Tests for IIT JAM Physics for Physics Exam | Download free PDF with solutions
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

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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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