Test: Vector Analysis - 1


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10 Questions MCQ Test Topicwise Question Bank for Electrical Engineering | Test: Vector Analysis - 1

Test: Vector Analysis - 1 for Electrical Engineering (EE) 2023 is part of Topicwise Question Bank for Electrical Engineering preparation. The Test: Vector Analysis - 1 questions and answers have been prepared according to the Electrical Engineering (EE) exam syllabus.The Test: Vector Analysis - 1 MCQs are made for Electrical Engineering (EE) 2023 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Vector Analysis - 1 below.
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Test: Vector Analysis - 1 - Question 1

If φ = xy2z3 then match List-I with List-II and select the correct answer using the codes given below the lists: 

Detailed Solution for Test: Vector Analysis - 1 - Question 1

Here 

Also,

And, 

Test: Vector Analysis - 1 - Question 2

The unit vector which points from z = h on the z-axis towards (r, φ, 0) in cylindrical co-ordinates as shown below is given by

Detailed Solution for Test: Vector Analysis - 1 - Question 2

Let the unit vector be given by 
Now,

∴ Unit vector,

Test: Vector Analysis - 1 - Question 3

If the vector V given below is irrotational, then the values of a, b and c will be respectively

Detailed Solution for Test: Vector Analysis - 1 - Question 3

Since the given vector is irrotational, therefore curl V = 0 or,



Since,  therefore, a = 4, b = 2, and c = -1

Test: Vector Analysis - 1 - Question 4

Match List-I (Vector Identities) with List-ll. (Equivalent expression) and select the correct answer using the codes given below the lists:

Detailed Solution for Test: Vector Analysis - 1 - Question 4
  •  is called “ product of four vectors ”.
  •  is called “vector triple product”.
  •  is called "vector product of four vectors ”.
Test: Vector Analysis - 1 - Question 5

The vector differential operator, in spherical co-ordinate system is given by

Test: Vector Analysis - 1 - Question 6

Assertion (A): Divergence of a vector function at each point gives the rate per unit volume at which the physical entity is issuing from that point.

Reason (R): If some physical entity is generated or absorbed within a certain region of the field, then that region is known as source or sink respectively and if there are no sources or sinks in the field, the net outflow of the incompressible physical entity over any part of the region is zero. However, the net outflow is said to be positive, if the total strength of the sources are greater than the total strength of sink and vice-versa.

Detailed Solution for Test: Vector Analysis - 1 - Question 6

Both assertion and reason are true and reason is the correct explanation of assertion. Reason is the physical interpretation of divergence.

Test: Vector Analysis - 1 - Question 7

Which of the following identity is not true?

Detailed Solution for Test: Vector Analysis - 1 - Question 7
  •  is called “vector triple product" which is a correct expression.





Test: Vector Analysis - 1 - Question 8

The vector directed from (2, - 4,1) to (0, -2,0) in Cartesian coordinates is given by

Detailed Solution for Test: Vector Analysis - 1 - Question 8

The vector   is given as

Test: Vector Analysis - 1 - Question 9

What is the value of  where  
Here, s is the surface bounded by x = 0, x = 1, y = o, y = 1, z = 0, z =1 and are unit vectors along x, yand z axes respectively.

Detailed Solution for Test: Vector Analysis - 1 - Question 9

By divergence theorem,



Since, the surface s is bounded by x = 0, 1; y = 0, 1 and z = 0, 1 so, putting the limits, we have

Test: Vector Analysis - 1 - Question 10

The vector field given by 

Detailed Solution for Test: Vector Analysis - 1 - Question 10


The vector field  will be irrotational,  
Now,


Hence,   is irrotationai.
The vector field  will be solenoidal, 
Here, 

Hence,   is solenoidal.

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