What is the question type for Mathematics Paper II?

Mathematics Paper II is a mixed paper, including compulsory and optional questions.

Are the answers to be written in English or Hindi?

Answers must be written in English only.

How many questions are to be attempted?

Out of eight questions, five are to be attempted. Question Nos. 1 and 5 are compulsory. Three more questions must be selected from the remaining six, with at least one from each of the two sections (A and B).

Do all questions carry equal marks?

Yes, all questions carry equal marks, and the marks for each question/part are indicated against it.

Can I download the Indian Forest Service (Main) 2017 Mathematics Paper II?

Yes, you can typically find and download previous year question papers like this one for exam preparation.

Indian Forest Service (Main) 2017 Mathematics Paper II PDF

Name: Indian Forest Service (Main) 2017 Mathematics Paper II PDF
Creator: UPSC
Keywords: Indian Forest Service Main 2017 Mathematics Paper II, IFS Main 2017 Mathematics Paper II PDF, UPSC IFS 2017 Mathematics Paper II, Mathematics Paper II IFS Main Exam, 2017 IFS Mathematics Paper II Question Paper, Indian Forest Service Mathematics, UPSC Main Exam Papers, IFS Previous Year Papers, Mathematics for IFS, Forest Service Exam, UPSC Exam, Competitive Exam, Government Jobs, Civil Services Exam, Indian Exam

Central Government Jobs Other Jobs 2017

Year 2017
Conducted By UPSC
Maximum Marks 200
Duration Three Hours
Languages English

Exam Details

Detail	Information
Examination	Indian Forest Service (Main) Examination
Year	2017
Conducting Body	UPSC
Paper	Mathematics Paper II
Subject	Mathematics
Duration	Three Hours
Maximum Marks	200
Question Type	Mixed

This is the Mathematics Paper II from the Indian Forest Service (Main) Examination held in 2017, conducted by UPSC. The paper carries a maximum of 200 marks and candidates are allowed three hours to complete it. It consists of a mix of compulsory and optional questions, designed to test advanced mathematical concepts. Aspirants preparing for the IFS exam can use this paper to understand the difficulty level, question types, and marking scheme, aiding in their focused preparation.

Major Topics Covered

Group Theory
Real Analysis
Complex Analysis
Linear Programming
Ring Theory
Euclidean Domains
Calculus
Multivariable Calculus
Integral Calculus
Contour Integration
Residues

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 2016 Mathematics Paper II
UPSC Civil Services Exam 2017 Mathematics Optional Paper
Indian Forest Service (Main) Examination 2017 Mathematics Paper II Answer Key
Indian Forest Service (Main) Examination Mathematics Syllabus
UPSC Mathematics Optional 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.
Question Nos. 1 and 5 are compulsory.
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.
All questions carry equal marks.
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)

Q1. (c) u + 2v = x³ - 2y³ + 3xy(2x - y) then find f(z) in terms of z 8 (d) Solve by simplex method the following LPP: Minimize Z = x₁ - 3x₂ + 2x₃ subject to the constraints 3x₁ - x₂ + 2x₃ ≤ 7 -2x₁ + 4x₂ ≤ 12 -4x₁ + 3x₂ + 8x₃ ≤ 0 and x₁, x₂, x₃ ≥ 0 14 Let G be the set of all real numbers except -1 and define a*b = a + b + ab

Q2. (a) $\forall$ a, b ∈ G. Examine if G is an Abelian group under *. 10 Let H and K are two finite normal subgroups of co-prime order of a group G. Prove (b) that $hk = kh \vee h \in H$ and k ∈ K. 10 Let A be an ideal of a commutative ring R and (c) $B = \{x \in R : x^n \in A \text{ for some positive integer } n\}.$ Is B an ideal of R ? Justify your answer. 10 (d) Prove that the ring $\mathbb{Z}[i] = \{a + ib : a, b \in \mathbb{Z}, i = \sqrt{-1}\}\$ of Gaussian integers is a Euclidean domain. 10 Evaluate f_xy(0, 0) and f_yx(0, 0) given that

Q3. (a) $f(x, y) = \begin{cases} x^2 \tan^{-1} \frac{y}{x} - y^2 \tan^{-1} \frac{x}{y} & \text{if } xy \neq 0 \\ 0 & \text{otherwise} \end{cases}$ 10 Find the maximum and minimum values of x² + y² + z² subject to the condition 3. (b) (x²)/(4) + (y²)/(5) + (z²)/(35) = 1. 10 Prove that ∫_-∞^∞ (sin x)/(x) dx is convergent but not absolutely convergent. (c) 12 Find the volume of the region common to the cylinders x² + y² = a² and x² + z² = a². 3. (d) 8 Prove by the method of contour integration that ∫₀^π (1 + 2cosθ)/(5 + 4cosθ) dθ = 0.

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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 2017.

Who conducts the Indian Forest Service Examination?

The Indian Forest Service Examination is conducted by UPSC.

What is the subject of this paper?

This paper is for Mathematics Paper II.

What is the maximum marks for this paper?

The maximum marks for Mathematics Paper II is 200.

How much time is allowed for this paper?

Candidates are allowed three hours to complete this paper.

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