Indian Forest Service Mathematics Paper I 2018 Question Paper PDF

Central Government Jobs Other Jobs 2018

  • Year 2018
  • Conducted By UPSC
  • Questions 8
  • Maximum Marks 200
  • Duration Three Hours
  • Languages English

Exam Details

Detail Information
Examination Indian Forest Service (Main) Examination
Year 2018
Conducting Body UPSC
Paper Mathematics Paper - I
Subject Mathematics
Duration Three Hours
Maximum Marks 200
Number of Questions 8
Question Type Mixed

This is the Mathematics Paper I from the Indian Forest Service (Main) Examination held in 2018, conducted by UPSC. The paper is designed to test candidates' in-depth knowledge of mathematics, with a total of 8 questions, of which 5 are to be attempted. Questions 1 and 5 are compulsory, and candidates must select at least one from each of the two sections (A and B) from the remaining six questions. The paper allows three hours for completion and carries a maximum of 200 marks. This question paper is a crucial resource for aspirants preparing for the IFS (Main) examination, providing valuable insights into the exam's structure, difficulty, and subject matter.

Major Topics Covered

  • Linear Algebra
  • Calculus
  • Differential Equations
  • Geometry
  • Hermitian Matrices
  • Eigenvalues

Why This Paper is Important

  • Useful for Indian Forest Service (Main) Examination preparation
  • Helps understand the latest exam pattern
  • Useful for practice and self-assessment
  • Covers frequently asked General Studies topics
  • Helpful for analysing question trends

Related Resources

  • Indian Forest Service (Main) Examination 2017 Mathematics Paper - I
  • Indian Forest Service (Main) Examination 2019 Mathematics Paper - I
  • Indian Forest Service (Main) Examination 2018 General Studies Paper - I
  • Indian Forest Service (Main) Examination 2018 Mathematics Paper - I Answer Key
  • Indian Forest Service (Main) Examination Mathematics Syllabus
  • UPSC Mains Mathematics Syllabus
  • Indian Forest Service (Main) Examination Pattern
  • UPSC Mains Exam Pattern

Instructions

  • There are EIGHT questions in all, out of which FIVE are to be attempted.
  • Out of the remaining SIX questions, THREE are to be attempted selecting at least ONE question from each of the two Sections A and B.
  • Attempts of questions shall be counted in sequential order.
  • Unless struck off, attempt of a question shall be counted even if attempted partly.
  • Any page or portion of the page left blank in the Question-cum-Answer Booklet must be clearly struck off.
  • The number of marks carried by a question/part is indicated against it.
  • Answers must be written in ENGLISH only.
  • Unless otherwise mentioned, symbols and notations have their usual standard meanings.
  • Assume suitable data, if necessary, and indicate the same clearly.

Questions (page 2)

Section A

Q1.

(a) Show that the maximum rectangle inscribed in a circle is a square.

(b) Given that Adj A = $
\beginvmatrix
2 & 2 & 0 \\
2 & 5 & 1 \\
0 & 1 & 1
\endvmatrix
$ and det A = 2. Find the matrix A.

(c) If f : [a, b] u2192 R be continuous in [a, b] and derivable in (a, b), where 0 < a < b, show that for c in (a, b) f(b) - f(a) = cf'(c) log(b/a).

(d) Find the equations of the tangent planes to the ellipsoid 2x2 + 6y2 + 3z2 = 27 which pass through the line x - y - z = 0 = x - y + 2z - 9.

(e) Prove that the eigenvalues of a Hermitian matrix are all real.

Section A

Q2.

(a) Find the equation of the cylinder whose generators are parallel to the line (x)/(1) = (y)/(-2) = (z)/(3) and whose guiding curve is x2 + y2 = 4, z = 2.

(b) Show that the matrices A = \beginbmatrix 1 & 1 & -1 \\ 1 & 2 & 1 \\ -1 & 1 & 3 \endbmatrix and B = \beginbmatrix 1 & 0 & 3 \\ 0 & 2 & 2 \\ 3 & 2 & 0 \endbmatrix are congruent.

(c) If \phi and \psi be two functions derivable in [a, b] and \phi(x) \psi'(x) - \psi(x) \phi'(x) > 0 for any x in this interval, then show that between two consecutive roots of \phi(x) = 0 in [a, b], there lies exactly one root of \psi(x) = 0.

(d) Show that the vectors α_1 = (1, 0, -1), α_2 = (1, 2, 1), α_3 = (0, -3, 2) form a basis for R3. Express each of the standard basis vectors as a linear combination of α_1, α_2, α_3.

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Indian Forest Service Main 2018 Mathematics Paper I question paper page 1 instructions and header scan PDF download UPSC
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Frequently asked questions

What is the name of the exam?

The exam is the Indian Forest Service (Main) Examination.

What is the year of this question paper?

This question paper is from the year 2018.

Which paper is this?

This is Mathematics Paper - I.

Who conducts the Indian Forest Service Examination?

The Union Public Service Commission (UPSC) conducts the Indian Forest Service Examination.

What is the maximum marks for Mathematics Paper - I?

The maximum marks for Mathematics Paper - I is 200.

What is the time duration allowed for this paper?

The time allowed for Mathematics Paper - I is Three Hours.

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