Maharashtra Stats Paper II 2025 Section A Questions
- Year 2025
- Conducted By Not specified in OCR
- Questions 8
- Maximum Marks 250
- Duration Three Hours
- Languages English & Hindi
Exam Details
| Detail | Information |
|---|---|
| Examination | Maharashtra State Services Main Examination |
| Year | 2025 |
| Conducting Body | Not specified in OCR |
| Paper | Optional Subject - Statistics - Paper II |
| Subject | Statistics |
| Duration | Three Hours |
| Maximum Marks | 250 |
| Number of Questions | 8 |
| Question Type | Section-a |
This JSON aggregates OCR-repaired content for Maharashtra State Services Main Examination Statistics Paper II (2025). Page 1 provides the exam branding, duration (three hours), maximum marks (250), and English medium. Page 2 (SECTION-A) presents Q1 with five sub-parts (a)–(e) covering quality-control topics such as X-bar and R charts, double sampling plans, linear programming, duals, and Monte Carlo estimation of pi. Q2 introduces a descriptive item about shaft diameter as a critical quality characteristic, with an observation dataset snippet. The JSON combines these into a structured SEO-ready format including metadata, an objective_questions_preview with each sub-question split into separate items, FAQ, topics, keywords, and image metadata to optimize search visibility. The repair preserves mathematical notation using the given <math>...</math> tags and maintains bilingual support in parts where OCR shows mixed language content.
Major Topics Covered
- Quality Control
- Statistical Process Control
- X-bar Chart
- R Chart
- Control Charts
- Process Capability
- Acceptance Sampling
- Double Sampling Plans
- ASN
- Linear Programming
- Graphical Method
- LP Duals
- Monte Carlo Methods
- Pi Estimation
- Normal Distribution
- Quality Characteristics
- Shaft Diameter
- Observational Data
- Observation Data
- Statistical Inference
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
- 2ाय खेता (मुख्या) परीक्षा - 2024 परीक्षा 'डिमोक ०२ में 2026 2025 C24(B) BOOKLET NO. 247011 Statistics Paper-II Time Allowed : Three Hours Maximum Marks: 250 Type of Paper: Conventional / Descriptive Medium : English
- 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. \bf *SE 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. \mathbb I
Questions (page 2)
Q2.
114) 10 Q1. (b) Consider a double sampling plan (n1, c1, r1, n2, c2). Derive analytical expression for the probability of acceptance and Average Sample Number (ASN) function. 10 Q1. Solve the following Linear Programming Problem (LPP) using graphical method.
(c) Max. Z = 4x1 + 3x2 Subject to 3x1 + 5x2 ≤ 5 x1 - x2 ≤ 0 x1, x2 ≥ 0 10 (d) Write duals of the following problems. Q1. i) Min Z = 15x1 + 12x2 Subject to x1 + 2x2 ≥ 3 2x1 - 4x2 ≤ 5 x1, x2 ≥ 0 ii) Min Z = 5x1 + 6x2 Subject to x1 + 2x2 = 5 -x1 + 5x2 ≥ 3 x1 unrestricted x2 ≤ 0. 10 (e) How Monte-Carlo method can be used to estimate the value of π(Pi)? Derive Q1. the estimator. Verify its unbiasedness. 10 Q2. A precision engineering company manufactures steel shafts for automobile (a) gear assemblies. The diameter of each shaft is a critical quality characteristic. Historical data shows that, when the process is operating normally, the shaft diameter is normally distributed with mean μ_0 = 50 mm and standard deviation σ = 1 mm. Individual diameters are measured sequentially and the following observations are recorded. Observation No.: \overlinec 3 4 5 6 -1 7 8 49 50 51 53 52 Diameter (mm) : 51 52 54
Q3. Q1. (c) Solve the following Linear Programming Problem (LPP) using graphical method. (c) Max. Z = 4x1 + 3x2 Subject to 3x1 + 5x2 5 x1 - x2 0 x1, x2 0
Q4. Q1. (d) Write duals of the following problems. Q1. i) Min Z = 15x1 + 12x2 Subject to x1 + 2x2 3 2x1 - 4x2 5 x1, x2 0 ii) Min Z = 5x1 + 6x2 Subject to x1 + 2x2 = 5 -x1 + 5x2 3 x1 unrestricted x2 0.
Q5. Q1. (e) How Monte-Carlo method can be used to estimate the value of Pi (Pi)? Derive the estimator. Verify its unbiasedness.
Q6. Q2. A precision engineering company manufactures steel shafts for automobile (a) gear assemblies. The diameter of each shaft is a critical quality characteristic. Historical data shows that, when the process is operating normally, the shaft diameter is normally distributed with mean mu0 = 50 mm and standard deviation sigma = 1 mm. Individual diameters are measured sequentially and the following observations are recorded. Observation No.: c 3 4 5 6 -1 7 8 49 50 51 53 52 Diameter (mm) : 51 52 54
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Frequently asked questions
What is the duration of Statistics Paper II?
Three hours.
How many questions are there and how many must be attempted?
There are eight questions; five are to be attempted. Question 1 and Question 5 are compulsory; others can be chosen with at least one from each section.
What is the medium of the paper?
English.
What is the maximum marks for Statistics Paper II?
250.
What topics are covered in Section A (Q1)?
Quality control (X-bar and R charts), double sampling plans, linear programming, duals, Monte Carlo estimation of pi.
Is a scientific calculator allowed?
Yes, a scientific (non-programmable) calculator is allowed.