Indian Forest Service 2019 Mathematics Paper II Question Paper PDF

Central Government Jobs Other Jobs 2019

  • Year 2019
  • Conducted By UPSC
  • Questions 8
  • Maximum Marks 200
  • Duration Three Hours
  • Languages English

Exam Details

Detail Information
Examination Indian Forest Service (Main) Examination
Year 2019
Conducting Body UPSC
Paper Mathematics Paper - II
Subject Mathematics
Duration Three Hours
Maximum Marks 200
Number of Questions 8
Question Type Mixed

This is the Mathematics Paper II from the Indian Forest Service (Main) Examination held in 2019 by UPSC. The paper carries a maximum of 200 marks and candidates are allowed three hours to complete it. It consists of eight questions, of which five are to be attempted, with questions 1 and 5 being compulsory. Aspirants must select at least one question from each of the two sections (A and B) from the remaining six questions. This paper is crucial for candidates preparing for the IFS Main examination, offering insights into the types of mathematical problems and the depth of knowledge required.

Major Topics Covered

  • Integral Domain
  • Characteristic of Ring
  • Continuity
  • Boundedness
  • Uniform Continuity
  • Riemann Integrability
  • Cauchy's Integral Formula
  • Linear Programming
  • Graphical Method
  • Ideals in a Ring
  • Quotient Ring
  • Isomorphism
  • Improper Integrals
  • Analytic Functions
  • Complex Integration

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 2019 Mathematics Paper I
  • Indian Forest Service (Main) Examination 2019 General Studies Paper I
  • Indian Forest Service (Main) Examination 2019 General Studies Paper II
  • Indian Forest Service (Main) Examination 2019 Mathematics Paper II 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.
  • 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) Let R be an integral domain. Then prove that ch R (characteristic of R) is 0 or a prime.

(b) Show that the function f(x) = sin(1)/(x)) is continuous and bounded in (0, 2π), but it is not uniformly continuous in (0, 2π).

(c) Test the Riemann integrability of the function f defined by
f(x) = \begincases 0 & \textwhen x \text is rational \\ 1 & \textwhen x \text is irrational \endcases
on the interval [0, 1].

(d) Using Cauchy's Integral formula, evaluate the integral ∮ (dz)/((z2 + 4)2) where c: |z - i| = 2.

(e) A firm manufactures two products A and B on which the profits earned per unit are ₹ 3 and ₹ 4 respectively. Each product is processed on two machines M1 and M2. Product A requires one minute of processing time on M1 and two minutes on M2, while B requires one minute on M1 and one minute on M2. Machine M1 is available for not more than 7 hours 30 minutes, while machine M2 is available for 10 hours during any working day. Find the number of units of products A and B to be manufactured to get maximum profit, using graphical method.

Section A

Q2.

(a) Let I and J be ideals in a ring R. Then prove that the quotient ring (I + J)/J is isomorphic to the quotient ring I/(I ∩ J).

(b) Show that the integral ∫0π/2 log sin x , dx is convergent and hence evaluate it.

(c) If f(z) is analytic in a domain D and |f(z)| is a non-zero constant in D, then show that f(z) is constant in D.

Question paper preview

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Indian Forest Service Main 2019 Mathematics Paper II question paper page 1 instructions scan PDF download UPSC
Page 2
Indian Forest Service Main 2019 Mathematics Paper II question paper page 1 instructions 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 year is this question paper from?

This question paper is from the year 2019.

Who conducts the Indian Forest Service Examination?

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

What is the subject of this paper?

This paper is Mathematics Paper - II.

What is the maximum marks for this paper?

The maximum marks for this paper are 200.

What is the time allowed to complete the paper?

The time allowed to complete the paper is Three Hours.

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