Vector Analysis-Gradient, Divergence and Curl in Cartesian and Cylindrical Coordinates [IFS (Forest Services) Mathematics]: Questions 1 - 8 of 14

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Question 1

Appeared in Year: 2011 (IAS)

Describe in Detail Subjective▾

If be the potion vector of a point find the values of for which the vector is –

Irrotational

Solenoidal (15 marks)

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Explanation

  • Let, given position vector is,

… (266 more equations) …

Question 2

Appeared in Year: 2015 (IAS)

Describe in Detail Subjective▾

A vector field is given by

Verify that the field is irrotational or not. Find the Scalar potential. (CS Paper 1)

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Explanation

We have

… (136 more equations) …

Question 3

Appeared in Year: 2011 (IAS)

Describe in Detail Subjective▾

Examine whether the vectors are coplanar, where are the scalar functions defined by:

And (Paper I)

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Explanation

  • Given

… (100 more equations) …

Question 4

Appeared in Year: 2010 (IAS)

Write in Short Short Answer▾

Prove that

Where f is a scalar function. (Paper I)

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Question 5

Appeared in Year: 2009 (IAS)

Describe in Detail Subjective▾

Find the directional derivative of –

(i)

(ii) in the direction of (Paper 1)

Edit

Explanation

(i) Here

… (537 more equations) …

Question 6

Appeared in Year: 2007 (IAS)

Describe in Detail Subjective▾

If , find the value of n in order that may be (i) solenoidal, (ii) irrational (Paper 1)

Edit

Explanation

Here

(i)

… (310 more equations) …

Question 7

Appeared in Year: 2009 (IAS)

Describe in Detail Subjective▾

Show that where (Paper 1)

Edit

Explanation

Grad

… (321 more equations) …

Question 8

Appeared in Year: 2020 (IAS)

Describe in Detail Subjective▾

For what value of is the vector field

irrational? Hence express as the gradient of a scalar function

(Paper 1)

Edit

Explanation

The vector is irrational if

We have

… (205 more equations) …