Mathematics Paper II (Mains) 2025 Maharashtra OCR Repair
- Year 2025
- Conducted By Government of Maharashtra
- Maximum Marks 250
- Duration Three Hours
- Languages English
Exam Details
| Detail | Information |
|---|---|
| Examination | Maharashtra State Services Main Examination |
| Year | 2025 |
| Conducting Body | Government of Maharashtra |
| Paper | Mathematics Paper - II |
| Subject | Mathematics |
| Duration | Three Hours |
| Maximum Marks | 250 |
This JSON aggregates Mathematics Paper II (Paper - II) for the Maharashtra State Services Main Examination 2025. Page 1 provides the exam header, medium, time, and general instructions, while Page 2 delivers repaired and fully separated objective questions with clearly delimited stems and subparts. The content consolidates corrected questions across algebra, real/complex analysis, topology, and classical mathematics, along with section-wise guidance and meta-information to support SEO, FAQ, and structured data. The repair fixes word breaks, separates merged stems, and places each numbered item on its own line as a discrete object in the JSON. The result enables accurate indexing, search optimization, and accessible study references for aspirants.
Major Topics Covered
- Group theory
- Ring theory
- Commutative algebra
- Real analysis
- Complex analysis
- Riemann integration
- Continuity
- Uniform continuity
- Lipschitz
- Radius of convergence
- Power series
- Monotone functions
- Riemann integrable
- Analytic functions
- Morera's theorem
- Contour integrals
- Dihedral group
- Cyclic groups
- Modulo arithmetic
- GCD
Why This Paper is Important
- Useful for Maharashtra State Services Main Examinat 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
Instructions
- त्राव्यं लेतां (भूख्यं) परीक्षा- २०२५ - परीक्षा चिनांठ ०१ में, २०१६, 2025 T23(B) BOOKLET NO. 229080 Mathematics Paper - II
- There are EIGHT questions divided in two Sections, out of which FIVE are to be
- Question No. 1 and 5 are compulsory.
- Out of the remaining, THREE are to be attempted choosing at least ONE question from each Section.
- The number of marks carried by a question/sub-question is indicated against it.
- The medium of answer should be mentioned on the answer book as claimed in the application and
- printed on admission card.
- The answers written in medium other than the authorized medium will not be assessed and no marks will be assigned to them.
- Wherever option has been given, only the required number of responses in the serial order attempted
- Unless struck off, attempt of a question shall be counted even if attempted partly.
- Excess responses shall not be assessed and shall be ignored.
- Candidates are expected to answer all the sub-questions of a question together.
- question is attempted elsewhere (after leaving a few page or after attempting another question) the later sub-question shall be overlooked.
- Keep in mind the word limit indicated in the question if any.
- Any page or portion of the page left blank in the Answer Booklet must be clearly struck off.
- Unless otherwise mentioned, symbol and notation have their usual standard meanings. Assume suitable
- data, if necessary and indicate the same clearly. Neat sketches may be drawn, wherever required.
- Note: Candidates will be allowed to use Scientific (Non-programmable type) calculators. P.T.O.
Questions (page 2)
Q0. Is S a cyclic subgroup of ℤ? Justify.
Q0. Let R be a commutative ring with identity whose only ideals are {0} and R. Prove that R is a field. If x, y ∈ R with x > 0. Then prove that ∃ n ∈ ℕ such that nx > y.
Q0. Prove that a Riemann integrable function on an interval [a, b] ⊂ ℝ is bounded.
Q0. Prove that an analytic function with constant real part is constant.
Q0. Let m, n, a, b be integers and assume that gcd(m, n) = 1.
Q0. Prove that there is an integer x such that x ≡ a (mod m) and x ≡ b (mod n). Prove that a Lipschitz function f: A ⊂ ℝ → ℝ is uniformly continuous on A.
Q0. Find the radius of convergence of the power series ∑_{n=1}^{∞} (n! / nn) zn.
Q0. Let f: [a, b] → ℝ be monotone on [a, b]. Prove that f is Riemann integrable.
Q0. Prove that every group of order 6 is either isomorphic to the cyclic group of order 6 or to the dihedral group D3.
Q0. If f(z) is continuous in a domain D and for every closed contour C in D, ∮_C f(z) dz = 0, then f is analytic within D.
Q0. If ∮ f(z) dz = 0 for every closed contour in D, then f is analytic within D.
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Frequently asked questions
What is the full name of the exam and year?
Maharashtra State Services Main Examination, Mathematics Paper II, 2025.
How many questions must be attempted in Mathematics Paper II?
Five questions must be attempted out of eight.
Which questions are compulsory?
Question No. 1 and 5 are compulsory.
From how many sections are questions drawn?
There are two Sections. At least one question must be attempted from each Section.
What is the duration of the paper?
Three hours.
What is the maximum marks for this paper?
250 marks.