The Mathematics Paper-II of the Civil Services (Main) Examination is known for its depth, logical structure and the way it tests an aspirant’s problem-solving ability. Many candidates look for the official question paper as soon as the exam finishes because it helps them understand the type of questions asked and the overall difficulty level of that year. In this post, I am sharing the details of the UPSC CSE 2025 Mathematics Paper-II along with the steps to download the official PDF.
I chose to write about this topic because Maths optional candidates depend heavily on past question papers to plan their preparation. Paper-II often carries more analytical and application-based problems compared to Paper-I, and knowing the exact style of questions helps aspirants judge how prepared they really are. Every year, I see students revising topics like Fluid Dynamics or Mechanics without understanding how much weightage these chapters actually get in the exam. Having the official question paper—cleanly accessible and easy to download—makes it simpler for future aspirants to analyse patterns, identify scoring areas and practise under a realistic exam environment. Since proper guidance is crucial, especially for technical optionals, providing reliable information becomes even more important.
About the Mathematics Paper-II
Mathematics Paper-II is a 250-mark paper that covers topics like Modern Algebra, Mechanics, Fluid Dynamics, Numerical Analysis, Linear Programming and Partial Differential Equations. This paper generally requires a mix of conceptual clarity and fast computation. Compared to Paper-I, Paper-II tends to have more applied mathematics questions, where understanding formulas alone is not enough; you must also know how to use them properly in complex scenarios.
Paper-II also follows the same structure as other optional papers: two sections with one compulsory question in each, and candidates must answer five questions in total.
Key Highlights of the 2025 Maths Paper-II Pattern
Based on UPSC’s standard pattern, here is what aspirants can expect:
- The paper is divided into Section A and Section B
- Each section consists of four questions
- Question 1 and Question 5 are compulsory
- Candidates need to attempt three additional questions
- The total duration is 3 hours
- Each question carries equal marks
This structure helps aspirants plan their attempts in advance, especially if they have stronger command over specific topics like Partial Differential Equations or Numerical Analysis.
Important Topics Usually Covered
Although the weightage may vary slightly each year, the following topics are regularly included:
- Modern Algebra
- Real Analysis
- Mechanics and Fluid Dynamics
- Numerical Methods
- Linear Programming and Game Theory
- Partial Differential Equations
- Complex Analysis
These areas form the core of the Paper-II syllabus, and past toppers often advise mastering these topics through repeated practice of previous year papers.
Question Paper Structure at a Glance
| Section | Focus Areas | Question Style |
|---|---|---|
| Section A | Modern Algebra, Real Analysis | Proof-based questions, conceptual problems |
| Section B | Mechanics, Fluid Dynamics, Linear Programming, PDEs | Application-based numerical problems |
| Total Marks | 250 | |
| Duration | 3 Hours |
Mathematics Paper-II 2025 PDF Download
You can download the official Maths Paper-II question paper directly from the UPSC website. Follow these steps:
- Open the official UPSC website
- Click on the “Examinations” tab
- Select “Previous Question Papers”
- Choose “Civil Services (Main) Examination 2025”
- Scroll to “Mathematics Optional Paper-II”
- Click the PDF link to download the question paper
N.B: If you want to download the question paper without any difficulty, you can easily download it by Click here.
If the PDF does not open immediately, refresh the page or try downloading it on a laptop for better access.
