Vector Analysis -1


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


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This mock test of Vector Analysis -1 for Electrical Engineering (EE) helps you for every Electrical Engineering (EE) entrance exam. This contains 10 Multiple Choice Questions for Electrical Engineering (EE) Vector Analysis -1 (mcq) to study with solutions a complete question bank. The solved questions answers in this Vector Analysis -1 quiz give you a good mix of easy questions and tough questions. Electrical Engineering (EE) students definitely take this Vector Analysis -1 exercise for a better result in the exam. You can find other Vector Analysis -1 extra questions, long questions & short questions for Electrical Engineering (EE) on EduRev as well by searching above.
QUESTION: 1

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

Solution:

Here 

Also,

And, 

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

Solution:

Let the unit vector be given by 
Now,

∴ Unit vector,

QUESTION: 3

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

Solution:

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



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

Solution:
  •  is called “ product of four vectors ”.
  •  is called “vector triple product”.
  •  is called "vector product of four vectors ”.
QUESTION: 5

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

Solution:
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.

Solution:

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

QUESTION: 7

Which of the following identity is not true?

Solution:
  •  is called “vector triple product" which is a correct expression.





QUESTION: 8

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

Solution:

The vector   is given as

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.

Solution:

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

QUESTION: 10

The vector field given by 

Solution:


The vector field  will be irrotational,  
Now,


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

Hence,   is solenoidal.

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