Indian Forest Service 2022 Mathematics Paper I Question Paper PDF

Central Government Jobs Other Jobs 2022

  • Year 2022
  • Conducted By UPSC
  • Questions 8
  • Maximum Marks 200
  • Duration Three Hours
  • Languages English

Exam Details

Detail Information
Examination Indian Forest Service (Main) Examination
Year 2022
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 official question paper for the Indian Forest Service (Main) Examination 2022, Mathematics Paper I. Conducted by UPSC, this paper carries a maximum of 200 marks and is allocated a time of three hours. It is designed to assess the mathematical aptitude and knowledge of candidates aspiring to join the Indian Forest Service. The paper consists of eight questions, of which five are to be attempted, with compulsory questions 1 and 5. Aspirants can gain valuable insights into the exam's difficulty level, question types, and marking scheme by studying this paper, which is crucial for effective preparation.

Major Topics Covered

  • Vector Spaces
  • Linear Transformations
  • Limits
  • Calculus
  • Jacobians
  • Coordinate Geometry
  • Matrices
  • Ellipsoids
  • Shortest Distance between Lines

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 2021 Mathematics Paper I
  • Indian Forest Service (Main) Examination 2022 General Studies Paper I
  • UPSC Engineering Services Examination Mathematics Paper
  • Indian Forest Service (Main) Examination 2022 Mathematics Paper I Answer Key
  • Indian Forest Service (Main) Examination Mathematics Syllabus
  • UPSC Main Exam Syllabus
  • Indian Forest Service (Main) Examination Pattern
  • UPSC 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.
  • Unless otherwise mentioned, symbols and notations have their usual standard meanings.
  • Assume suitable data, if necessary, and indicate the same clearly.
  • Answers must be written in ENGLISH only.

Questions (page 2)

Section A

Q1.

(a) Let U and W be subspaces of a vector space V and x, y in V. Then prove that x+U subseteq y+W iff U subseteq W and x-y in W.

(b) Let v1 = (1, 1, -1), v2 = (4, 1, 1), v3 = (1, -1, 2) be a basis of \mathbbR3 and let T : \mathbbR3 → \mathbbR2 be the linear transformation such that Tv1 = (1, 0), Tv2 = (0, 1), Tv3 = (1, 1). Describe the linear transformation T.

(c) Evaluate limx→ 0 (1)/(x2) - \cot2 x).

(d) If x + y + z = u, y + z = uv, z = uvw, then determine (\partial(x, y, z))/(\partial(u, v, w)).

(e) A variable plane is at a constant distance of 6 units from the origin and meets the axes in A : (a, 0, 0), B : (0, b, 0) and C : (0, 0, c). Find the locus of the centroid of the triangle ABC.

Section A

Q2.

(a) Are the matrices A = \beginbmatrix 2 & 4 \\ 0 & 4 \endbmatrix and B = \beginbmatrix 3 & 1 \\ 1 & 3 \endbmatrix similar ? Justify your answer.

(b) Using Lagrange's undetermined multipliers method, find the volume of the greatest rectangular parallelepiped that can be inscribed in the ellipsoid (x2)/(a2) + (y2)/(b2) + (z2)/(c2) = 1.

(c) Obtain the coordinates of the points where the shortest distance line between the straight lines (x-3)/(-1) = (y-2)/(2) = (z-2)/(-1); (x-2)/(2) = (y + 3)/(3) = (z + 2)/(2) meets them. Also find the magnitude of the shortest distance and the equation of the shortest distance line between the straight lines mentioned above.

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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 2022.

Who conducts the Indian Forest Service Examination?

The examination is conducted by UPSC (Union Public Service Commission).

What is the subject of this paper?

The subject is Mathematics, Paper I.

What is the maximum marks for Mathematics Paper I?

The maximum marks for Mathematics Paper I is 200.

What is the time allowed for this paper?

The time allowed for Mathematics Paper I is Three Hours.

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