Mathematics Paper I (Maharashtra 2025) - Main Exam
- Year 2025
- Conducted By Maharashtra State Government
- Maximum Marks 250
- Duration Three Hours
- Languages English
Exam Details
| Detail | Information |
|---|---|
| Examination | Mathematics Paper-I |
| Year | 2025 |
| Conducting Body | Maharashtra State Government |
| Paper | Mathematics Paper-I |
| Subject | Mathematics |
| Duration | Three Hours |
| Maximum Marks | 250 |
This JSON aggregates the Mathematics Paper I (Maharashtra State Services Main Examination 2025). Page 1 provides overall exam metadata: time, marks, language, and paper format. Page 2 contains the repaired OCR for objective-style questions (Q1 parts a–e and Q2(a)) with full descriptive prompts and required marks. The questions cover linear algebra (vector spaces, linear dependence, systems), calculus concepts (Mean Value Theorem, limits), analytic geometry (coplanar lines and planes), as well as linear operators and eigen-spaces. The SEO-friendly content includes metadata, FAQ-ready topics, and image optimization data suitable for multi-page exposure.
Major Topics Covered
- Maharashtra
- Mathematics
- Paper I
- Main Examination
- Question Paper
- Linear Algebra
- Vector Spaces
- Eigenvalues
- Eigenvectors
- Matrix
- Systems of Linear Equations
- Mean Value Theorem
- Limits
- Exponential Function
- Coplanar Lines
- Planes
- 3D Geometry
- Linear Operator
- Dimension
- Algebraic Multiplicity
Why This Paper is Important
- Useful for Mathematics Paper-I 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
- ज्ञान्च खेता (प्रुम्ना)परीसा- २०२५ वरीक्षा जिनोक ०२ मे, २०२६ 2025 T22 BOOKLET NO. 156116 Mathematics Paper-I Time Allowed: Three Hours Maximum Marks: 250 Medium : English Type of Paper: Conventional / Descriptive
- There are EIGHT questions divided in two Sections, out of which FIVE are to be attempted.
- 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. З.
- 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 shall be assessed.
- 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.
- of a 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.
Questions (page 2)
Q2. Q1. (b) Solve the following system of linear equations : 3x1 + 2x2 + 3x3 - 2x4 = 1; x1 + x2 + x3 = 3; x1 + 2x2 + x3 - x4 = 2.
Q3.
Q1.
(c) Using Mean Value theorem, prove the following : 1 + x < ex < 1 + xex, for every x > 0.
Q4. Q1. (d) Evaluate lim_{x→0} (tan x / x)^{1/x^2}.
Q5. Q1. (e) Show that the lines (x+3)/2 = (y+5)/3 = (z-7)/3, (x+1)/4 = (y+1)/5 = (z+1)/-1 are coplanar and find the equation of the plane containing them. Also find the equations of the line that intersects the lines 2x + y - 4 = 0 = y + 2z, x + 3z = 4, 2x + 5z = 8 and passes through the point (2, -1, 1).
Q6. Q2. (a) Let λ be an eigen-value of T having algebraic multiplicity m. Let E_{λ} denotes an eigen space of T corresponding to an eigen value λ, then show that 1 ≤ dim(E_{λ}) ≤ m. Further, let T be the linear operator on R3 defined by T([a1, a2, a3]^T) = [4a1 + a3, 2a1 + 3a2 + 2a3, a1 + 4a3]^T. Then determine the eigen space of T corresponding to each eigen-value.
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Frequently asked questions
How many questions are in the paper and how are they divided?
There are eight questions divided into two sections.
Which questions are compulsory?
Questions 1 and 5 are compulsory.
How many questions must a candidate attempt?
Candidates must attempt five questions, choosing at least one from each section.
What is the medium of answer?
The medium of answer should be English as per the paper; mention it in the answer booklet per application form.
Are calculators allowed?
Yes, scientific (non-programmable) calculators are allowed.
What is the paper code?
The paper code indicated is T22.