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Test: Vector Analysis- 2

20 Questions MCQ Test Topicwise Question Bank for Electrical Engineering | Test: Vector Analysis- 2

Description

Attempt Test: Vector Analysis- 2 | 20 questions in 60 minutes | Mock test for Electrical Engineering (EE) preparation | Free important questions MCQ to study Topicwise Question Bank for Electrical Engineering for Electrical Engineering (EE) Exam | Download free PDF with solutions

QUESTION: 1

If then the value of at (2, 2, 0) will be

A.
-0.0884
B.
0.0264
C.
-0.0356
D.
0.0542

Solution:

Given,

QUESTION: 2

If then the value of is

Solution:

Thus,

QUESTION: 3

What is the value of constant b so that the vector
is solenoidal?

A.
2
B.
-1
C.
3
D.
-2

Solution:

Since vector is solenoidal, therefore
= 0

or, [1 + 1 + b] = 0 or b = -2

QUESTION: 4

Match List-I with List-ll and select the correct answer using the codes given below the lists:
List-I
A. Gauss’s divergence theorem
B. Stroke’s theorem
C. The divergence
D. The curl
List-ll

A.
a
B.
b
C.
c
D.
d

Solution:

QUESTION: 5

Assertion (A): Vector differential operator is a vector quantity and it signifies that certain operations of a differentiation are to be carried out on the scalar function following it.
Reason (R): Vector differential operator posses properties similar to ordinary vectors

A.
Both A and R are true and R is a correct explanation of A
B.
Both A and R are true but R is not a correct explanation of A
C.
A is true but R is false
D.
A is false but R is true

Solution:

Vector differential operator (‘∇’) is not a vector quantity. Hence, assertion is a false statement.

QUESTION: 6

Consider the following statements:
1. Divergence of a vector function at each point gives the rate per unit volume at which the physical entity is issuing from that point.
2. If a vector function ϕ represents temperature, then grad ϕ or ∇ϕ will represents rate of change of temperature with distance.
3. The curl of a vector function A gives the measure of the angular velocity at every point of the vector field.

A.
2 and 3 only
B.
1, 2 and 3
C.
1 and 3 only
D.
2 only

Solution:

All the given statements are correct.

QUESTION: 7

Assertion (A): The Gauss’s divergence theorem permits us to express certain integrals by means of surface integrals.
Reason (R): Gauss’s divergence theorem states that “the surface integral of the curl of a vector field taken over any surface s is equal to the line integral of the vector field around the closed periphery (contour) of the surface.

A.
Both A and R are true and R is a correct explanation of A
B.
Both A and R are true but R is not a correct explanation of A
C.
A is true but R is false
D.
A is false but R is true

Solution:

Reason is a statement of stroke’s theorem not that of Gauss's divergence theorem.

QUESTION: 8

If is any vector field in cartesian co-ordinates system, then

A.
B.
Div. curl
C.
D.
Div. curl

Solution:

Let, be any vector field in cartesian co-ordinate system then, we can prove that

Also, Div. Curl

QUESTION: 9

If and , then

A.
and
B.
Only
C.
Only
D.

Solution:

Given,

∴
Also,

QUESTION: 10

If S is any closed surface enclosing a volume V and then the value of (is a unit vector) will be equal to

A.
B.
(a - b - c) V
C.
D.
(a + b + c) V

Solution:

QUESTION: 11

Assertion (A): The laplacian operator of a scalar function ϕ can be defined as “Gradient of the divergence of the scalar ϕ”
Reason (R): Laplacian operator may be a “scalar laplacian" or a “vector laplacian'’ depending upon whether it is operated with a scalar function or a vector, respectively.

A.
Both A and R are true and R is a correct explanation of A.
B.
Both A and R are true but R is not a correct explanation of A.
C.
A is true but R is false.
D.
A is false but R is true..

Solution:

Assertion is not true because the laplacian operator (∇²)of a scalar function ϕ can be defined as “Divergence of the gradient of the scalar ϕ”. i.e. ∇.∇ϕ

QUESTION: 12

Match List-I (Terms) with List-II (Type) and select the correct answer using the codes given below the lists:
List-I
A. Curl= 0
B. Div = 0
C. Div grad (ϕ) = 0
D. Div div (ϕ) = 0
List-ll
1. Laplace equation
2. Irrotational
3. Solenoidal
4. Not defined
Codes:
A B C D
(a) 2 3 1 4
(b) 4 1 3 2
(c) 2 1 3 4
(d) 4 3 1 2

A.
(a)
B.
(b)
C.
(c)
D.
(d)

Solution:

QUESTION: 13

Which of the following relations are not correct?

A.
[B x C, C x A, A x B] = [ABC]²
B.
A x [B x (C x D)] = B.D (A x C) - B.C(A x D)
C.
(B x C)·(A x D) + (C x A)·(B x D) + (A x B)·(C x D) = 0
D.
(A x B)² = A²B²- (A.B)²

Solution:

(A x B)² = A²B² - (A·B)²

QUESTION: 14

If uF = ∇_v, where u and v are scalar fields and F is a vector field, then F. curl F is equal to

A.
zero
B.
C.
D.
not defined

Solution:

Given,

∴
or,

Hence,

QUESTION: 15

A vector field which has a vanishing divergence is called as ____________

A.
Rotational field
B.
Hemispheroidal field
C.
Solenoidal field
D.
Irrotational field

Solution:

By the definition: A vector field whose divergence comes out to be zero or Vanishes is called as a Solenoidal Vector Field.

i.e.

is a Solenoidal Vector field.

QUESTION: 16

Which of the following statements is not true of a phasor?

A.
It may be a scalar or a vector.
B.
It is a time dependent quantity.
C.
It is a complex quantity.
D.
All are true

Solution:

A phasor is always a vector quantity.

QUESTION: 17

Match List-I (Physical quantities) with List-ll (Dimensions) and select the correct answer using the codes given below the lists:
List-I
A. Electric potential
B. Magnetic flux
C. Magnetic field intensity
D. Magnetic flux density
List-ll
1. MT^-2I^-1
2. ML²T^-3I^-1
3. IL^-1
4. ML²T^-2I^-1
Codes:
A B C D
(a) 2 4 3 1
(b) 4 2 3 1
(c) 1 2 1 3
(d) 4 2 1 3

A.
(a)
B.
(b)
C.
(c)
D.
(d)

Solution:

Emf induced, V = dφ/dt
or, ϕ = v.t = Magnetic flux
∴ [ϕ] = [ML²T^-3I^-1[T]
= [ML²T^-2I^-1]
Magnetic field intensity,
H = NI/I

Magnetic flux density B = ϕ/A

QUESTION: 18

Which of the following statements is not true regarding vector algebra?

A.
Dot product of iike unit vector is unity
B.
Dot product of unlike unit vector is zero
C.
Cross product of two like unit vectors is a third unit vector having positive sign for normal rotation and negative for reverse rotation.
D.
All the above statements are true

Solution:

Option (c) is not correct because cross product of two unlike vectors is a third unit vector having positive sign for normal rotation and negative for reverse rotation while cross product of two like unit vectors is zero.

QUESTION: 19

A rigid body is rotating with an angular velocity of ω where, and v is the line velocity. If is the position vector given by then the value of curl will be equal to