Indian Forest Service Mathematics Paper II 2025 Question Paper PDF
- Year 2025
- Conducted By UPSC
- Maximum Marks 200
- Duration Three Hours Maximum Marks: 200 Question Paper Specific Instructions Please Read Each Of The Following Instructions Carefully Before Attempting Questions 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. Assume Suitable Data, If Necessary, And Indicate The Same Clearly. Unless Otherwise Mentioned, Symbols And Notations Have Their Usual Standard Meanings. Answers Must Be Written In English Only. Djsm-b-math/55
- Languages English
Exam Details
| Detail | Information |
|---|---|
| Examination | Indian Forest Service (Main) Examination |
| Year | 2025 |
| Conducting Body | UPSC |
| Paper | Mathematics Paper - II |
| Subject | Mathematics |
| Duration | Three Hours Maximum Marks: 200 Question Paper Specific Instructions Please Read Each Of The Following Instructions Carefully Before Attempting Questions 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. Assume Suitable Data, If Necessary, And Indicate The Same Clearly. Unless Otherwise Mentioned, Symbols And Notations Have Their Usual Standard Meanings. Answers Must Be Written In English Only. Djsm-b-math/55 |
| Maximum Marks | 200 |
| Question Type | Descriptive / Subjective |
This document contains the Mathematics Paper II from the Indian Forest Service (Main) Examination conducted by UPSC in 2025. The paper is designed for candidates aspiring to join the Indian Forest Service. It consists of descriptive questions, with specific instructions on the number of questions to be attempted and compulsory questions. The paper aims to assess the candidates' in-depth knowledge and analytical skills in advanced mathematics relevant to forestry and environmental management. Aspirants can use this paper to understand the exam pattern, question types, and marking scheme, aiding in their preparation strategy.
Major Topics Covered
- Group Theory
- Real Analysis
- Series Convergence
- Bilinear Transformation
- Linear Programming
- Abstract Algebra
- Sequences and Series
- Complex Analysis
- Integral Calculus
- Differential Equations
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 2025 Mathematics Paper I
- Indian Forest Service (Main) Examination 2024 Mathematics Paper II
- UPSC Civil Services Main Examination Mathematics Optional Paper
- Indian Forest Service Mathematics Paper II 2025 Answer Key
- UPSC IFS Main 2025 Mathematics Solutions
- Indian Forest Service Main Syllabus
- UPSC Mathematics Optional Syllabus
- Indian Forest Service Main 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.
- Assume suitable data, if necessary, and indicate the same clearly.
- Unless otherwise mentioned, symbols and notations have their usual standard meanings.
- Answers must be written in ENGLISH only.
Questions (page 2)
Formatted from page 2 OCR. Download the PDF for the full paper.
Indian Forest Services (Main)
SECTION-A
If H and K are finite subgroups of a group and HK = \ hk | h ∈ H, k ∈ K \, prove:
1.
(a) Prove that |HK| = (|H||K|)/(|H ∩ K|). [8 Marks]
(b) Let S be a non-empty subset of R, bounded below, and T = \-x : x ∈ S\. Prove that the set T is bounded above and sup T = -\inf S. [8 Marks]
(c) Prove that the series 1 + 1/3 - 1/2 + 1/5 + 1/7 - 1/4 + ... converges to (3/2) log 2. [8 Marks]
(d) Find the image of |z| < 1 under the bilinear transformation mapping z = 1, i, −1 onto w = i, 0, −i respectively. [8 Marks]
(e) The Forest Department aims to afforest up to 100 hectares with teak and pine to maximize CO2 absorption, planting at least 10 hectares of each, and no more than 60 hectares of teak. The available resources are 3200 labour hours/week and 16000 litres of water/week. . Formulate this as a Linear Programming Problem. Also prove that if p is an odd prime, there is no group having exactly p elements of order p. [8 Marks]
2.
(a) Let fn(x) = nx(1-x)^n, x ∈ [0, 1], n ∈ \mathbbN. Show that (i) the sequence \fn\ converges to a function f on [0, 1] and (ii) f is integrable on [0, 1] and limn→∞ ∫01 fn = ∫01 f, but still the convergence of the sequence \fn\ is not uniform. [10 Marks]
(b) Evaluate the integral ∫0∞ sin(x2) dx using the method of contour integration. [15 Marks]
(c) ∬E (√(a^2b2 - b^2x2 - a^2y2))/(√(a^2b2 + b^2x2 + a^2y2)) dx dy the field of integration E being the positive quadrant of the ellipse (x2)/(a2) + (y2)/(b2) = 1. [10 Marks]
Paper Code: DJSM-B-MATH/55
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Frequently asked questions
What is the name of the exam?
The exam is the Indian Forest Service (Main) Examination.
Which paper is this question paper for?
This is for Mathematics Paper II.
What is the conducting body?
The Union Public Service Commission (UPSC) conducts this examination.
What is the year of this question paper?
The year is 2025.
What is the subject of this paper?
The subject is Mathematics.
What is the question type for this paper?
The question type is descriptive.