Calculus-Functions of Two or Three Variables [IFS (Forest Services) Mathematics]: Questions 1 - 8 of 15

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Question 1

Appeared in Year: 2008 (IAS)

Describe in Detail Subjective▾

Determine the maximum and minimum distances of the origin from the curve given by the (Paper I)

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Explanation

  • Let be any point on the surface

    … eq. (1)

    Let

  • Where is the …

… (336 more equations) …

Question 2

Appeared in Year: 2007 (IAS)

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Find a rectangular parallelepiped of greatest volume for a given total surface areas, using Lagrange՚s method of multipliers. (Paper I)

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Explanation

  • Let v be the volume of the parallelepiped whose edges are
  • We have to find the maximum value of … eq. (1)

… (201 more equations) …

Question 3

Appeared in Year: 2011 (IAS)

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Find the shortest distance from the origin to the hyperbola . (Paper II)

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Explanation

  • Let be the distance of the origin from any point

    … eq. (1)

  • Where

… (331 more equations) …

Question 4

Appeared in Year: 2011 (IAS)

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Find the points on the sphere that are closest to and farthest from the point (Paper I)

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Explanation

  • Let be the distance of any point on the sphere

    … eq. (1)

  • From the point

… (392 more equations) …

Question 5

Appeared in Year: 2015 (IAS)

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Which point on the sphere is at the maximum distance from the point ? (Paper I)

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Explanation

  • Let be the distance of any point on the sphere

    … eq. (1)

  • From the point

… (507 more equations) …

Question 6

Appeared in Year: 2010 (IAS)

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If is a homogeneous function degree , and has continuous first and second order partial derivatives, then show that

(Paper II)

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Explanation

  • Since is a homogeneous function of of under n

    … eq. (1)

… (145 more equations) …

Question 7

Appeared in Year: 2021 (IAS)

Write in Short Short Answer▾

If where then find

(Paper -1)

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Question 8

Appeared in Year: 2019 (IAS)

Write in Short Short Answer▾

Let be a continuous function

Find the value of

(Paper -1)

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