Indian Forest Service 2023 Mathematics Paper I Question Paper PDF

Central Government Jobs Other Jobs 2023

  • Year 2023
  • Conducted By UPSC
  • Questions 8
  • Maximum Marks 200
  • Duration Three Hours
  • Languages English

Exam Details

Detail Information
Examination Indian Forest Service (Main) Examination
Year 2023
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 conducted by UPSC in 2023. The paper consists of 8 questions, out of which 5 are to be attempted, with questions 1 and 5 being compulsory. Candidates must select at least one question from each of the two sections (A and B) from the remaining six questions. All questions carry equal marks, and answers must be written in English. This paper is crucial for aspirants preparing for the IFS Mains stage, offering insights into the expected difficulty and subject coverage.

Major Topics Covered

  • Mathematics
  • Calculus
  • Algebra
  • Differential Equations
  • Linear Algebra

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 2023 - General Studies Paper I
  • Indian Forest Service (Main) Examination 2023 - General Studies Paper II
  • Indian Forest Service (Main) Examination 2023 - Optional Subject Paper I
  • Indian Forest Service (Main) Examination 2023 - Optional Subject Paper II
  • IFS Main 2023 Mathematics Paper I Answer Key
  • IFS Mains Mathematics Syllabus
  • UPSC Mains Syllabus
  • IFS 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.
  • 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. Let V be a vector space of the dimension n over a field F. Then show that V is isomorphic to Fn. Let T: R3 -> R3 be a linear map defined by T(x, y, z) = (x, z, -2y - z) and let f(u) = -u3 + 2. Then find f(T). Test the convergence of improper integral If u = z sin (y/x); where x = 3r2 + 3s, y = 4r - 2s3, z = 2r2 - 3s2; then find (\partial u)/(\partial r) and (\partial u)/(\partial s). If the equation ax2 + 2hxy + by2 + 2gx + 2fy + c = 0, represents two intersecting straight lines, then show that the square of the distance of the point of intersection from the origin is (c(a + b)-(f2 + g2))/(ab-h2).

(integral) ∫ab (dx)/((x-a)^n)

Section A

Q2. If S1 = {(x, y, z)|x + 2y + z = 0} and S2 = {(x, y, z)|x + y - z = 0} are subspaces of R3, then Let the function f: R2 -> R be defined by

(i) find a basis of S1 ∩ S2.

(ii) determine dim (S1 + S2).

(iii) describe S1 ∩ S2 and S1 + S2 geometrically.

(function) f(x, y) = \begincases (xy2)/(x2 + y2), & \textif (x, y) ≠ (0, 0) \\ 0, & \textif (x, y) = (0, 0) \endcases

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Indian Forest Service (Main) Examination 2023 Mathematics Paper I question paper page 1 instructions scan PDF download UPSC
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Indian Forest Service (Main) Examination 2023 Mathematics Paper I question paper page 1 instructions scan PDF download UPSC

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Frequently asked questions

What is the name of the exam for which this paper was conducted?

This paper is from the Indian Forest Service (Main) Examination.

Which year is this question paper from?

This question paper is from the year 2023.

Who conducts the Indian Forest Service Examination?

The Indian Forest Service Examination is conducted by UPSC (Union Public Service Commission).

What is the subject of this paper?

The subject of this paper is Mathematics.

What is the paper code mentioned on the paper?

The paper code mentioned is BJKE-U-MTH.

How many questions are there in total in this paper?

There are a total of EIGHT questions in this paper.

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