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

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

Test: Vector Analysis- 2 - Question 3

What is the value of constant b so that the vector

is solenoidal?

Detailed Solution for Test: Vector Analysis- 2 - Question 3

Test: Vector Analysis- 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
**

Test: Vector Analysis- 2 - 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

Detailed Solution for Test: Vector Analysis- 2 - Question 5

Test: Vector Analysis- 2 - 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.

Detailed Solution for Test: Vector Analysis- 2 - Question 6

Test: Vector Analysis- 2 - 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.

Detailed Solution for Test: Vector Analysis- 2 - Question 7

Test: Vector Analysis- 2 - Question 8

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

Detailed Solution for Test: Vector Analysis- 2 - Question 8

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Test: Vector Analysis- 2 - 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

Detailed Solution for Test: Vector Analysis- 2 - Question 10

Test: Vector Analysis- 2 - 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.

Detailed Solution for Test: Vector Analysis- 2 - Question 11

Test: Vector Analysis- 2 - 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

Detailed Solution for Test: Vector Analysis- 2 - Question 13

Test: Vector Analysis- 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

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Test: Vector Analysis- 2 - Question 15

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

Detailed Solution for Test: Vector Analysis- 2 - Question 15

Test: Vector Analysis- 2 - Question 16

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

Detailed Solution for Test: Vector Analysis- 2 - Question 16

Test: Vector Analysis- 2 - 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^{-2}I^{-1}

2. ML^{2}T^{-3}I^{-1 }

3. IL^{-1}

4. ML^{2}T^{-2}I^{-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

Detailed Solution for Test: Vector Analysis- 2 - Question 17

Test: Vector Analysis- 2 - Question 18

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

Detailed Solution for Test: Vector Analysis- 2 - Question 18

Test: Vector Analysis- 2 - 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

Detailed Solution for Test: Vector Analysis- 2 - Question 19

Detailed Solution for Test: Vector Analysis- 2 - Question 20

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