Q1 50M Compulsory state Index numbers, IRM, world class manufacturing, Chi-Square test, value analysis
(a) State the chief characteristics of Index Numbers. (10 marks)
(b) What do you mean by Information Resource Management ? State its features. (10 marks)
(c) State the attributes of world class manufacturing which are aimed to fulfil the customer demands. (10 marks)
(d) State the characteristics of Chi-Square Test. (10 marks)
(e) State the symptoms when the value analysis is to be initiated in a company. (10 marks)
हिंदी में पढ़ें
(a) सूचकांकों की प्रमुख विशेषताएँ बताइए । (10 अंक)
(b) सूचना संसाधन प्रबंध से आपका क्या अभिप्राय है ? इसकी विशेषताएँ बताइए । (10 अंक)
(c) विश्व स्तरीय विनिर्माण के गुण बताइए जिनका लक्ष्य ग्राहक की माँग को पूर्ण करना है । (10 अंक)
(d) काई-वर्ग (स्क्वायर) परीक्षण की विशेषताएँ बताइए । (10 अंक)
(e) एक कंपनी में मूल्य विश्लेषण आरंभ करने के लक्षण बताइए । (10 अंक)
Answer approach & key points
The directive 'state' demands precise, enumerated characteristics without elaborate explanation. Allocate approximately 2 minutes per mark, giving roughly 4 minutes per sub-part. Structure each part as numbered points: (a) 4-5 characteristics of index numbers; (b) definition plus 4-5 IRM features; (c) 4-5 WCM attributes for customer fulfillment; (d) 4-5 Chi-Square test characteristics; (e) 4-5 symptoms for value analysis initiation. No introduction or conclusion needed; begin directly with part (a).
- (a) Index Numbers: relative measurement, specific purpose, time series comparison, averaging of variables, percentage expression, and deflation capability
- (b) IRM: definition as strategic management of information assets; features include planning, organizing, controlling information resources, technology integration, and cost-benefit optimization
- (c) WCM attributes: customer focus, total quality management, continuous improvement, flexibility/responsiveness, and supply chain integration
- (d) Chi-Square Test: non-parametric nature, tests independence/goodness of fit, uses categorical data, compares observed vs expected frequencies, and degrees of freedom calculation
- (e) Value Analysis symptoms: rising costs without quality improvement, product obsolescence, customer complaints, competitive pressure, and declining profit margins
Q2 50M solve Chi-Square test, t-test, linear programming problem
(a) The following table gives the production in three shifts and the corresponding number of defective goods that turned out in three weeks. Test at 5% level of significance whether weeks and shifts are independent.
Table :
| Shift | 1st week | 2nd week | 3rd week | Total |
|-------|---------|---------|---------|-------|
| I | 20 | 20 | 20 | 60 |
| II | 5 | 10 | 15 | 30 |
| III | 15 | 20 | 25 | 60 |
| Total | 40 | 50 | 60 | 150 |
(15 marks)
(b) A random sample of 10 bags of urea are found to have the following weights (kg) : 40, 45, 49, 50, 55, 44, 52, 48, 50, 45
Test at 5% level of significance whether the average packing weight can be taken as 50 kg. (15 marks)
(c) A firm produces three products A, B and C which pass through three departments : Milling, Lathe and Grinder.
Each unit of Product A requires 8, 4 and 2 hours respectively in the three departments.
Each unit of Product B requires 2, 3 and 0 hours respectively in the three departments.
Each unit of Product C requires 3, 0 and 1 hours respectively in the three departments.
The available capacity on the machines which might limit output is given below.
Table : Capacity of the Machines for Production
| Machine Type | Available time (in machine hours per week) |
|---|---|
| Milling Machine | 250 |
| Lathe Machine | 150 |
| Grinder Machine | 50 |
The unit profit would be : ₹ 20, ₹ 6 and ₹ 8 for products A, B and C respectively.
(i) Formulate the problem in LPP.
(ii) How much of each product should the firm produce in order to maximize profit ? (8+12=20 marks)
हिंदी में पढ़ें
(a) निम्नलिखित तालिका तीन पालियों में उत्पादन और तीन सप्ताहों में निकले दोषपूर्ण माल की संबंधित संख्या देती है । 5% सार्थकता स्तर पर परीक्षण कीजिए कि क्या सप्ताह और पाली स्वतंत्र हैं ।
तालिका :
| पाली | प्रथम सप्ताह | द्वितीय सप्ताह | तृतीय सप्ताह | योग |
|------|-----------|------------|-----------|-----|
| प्रथम | 20 | 20 | 20 | 60 |
| द्वितीय | 5 | 10 | 15 | 30 |
| तृतीय | 15 | 20 | 25 | 60 |
| योग | 40 | 50 | 60 | 150 |
(15 अंक)
(b) 10 बैग यूरिया का एक यादृच्छिक नमूना निम्न भार (किलोग्राम) के अनुसार है : 40, 45, 49, 50, 55, 44, 52, 48, 50, 45
5% सार्थकता स्तर पर परीक्षण कीजिए कि क्या औसत पैकिंग भार 50 किलोग्राम लिया जा सकता है । (15 अंक)
(c) एक फर्म तीन उत्पादों अ, ब एवं स का उत्पादन करती है, जो कि तीन विभागों : मिलिंग, लेथ एवं ग्राइंडर से होकर गुजरते हैं ।
उत्पाद अ की प्रत्येक इकाई को क्रमशः: 8, 4 एवं 2 घंटों की तीन विभागों में आवश्यकता है ।
उत्पाद ब की प्रत्येक इकाई को क्रमशः: 2, 3 एवं 0 घंटों की तीन विभागों में आवश्यकता है ।
उत्पाद स की प्रत्येक इकाई को क्रमशः: 3, 0 एवं 1 घंटों की तीन विभागों में आवश्यकता है ।
मशीनों पर उपलब्ध क्षमता, जो कि आउटपुट को सीमित करती है, निम्नवत् है ।
तालिका : उत्पादन हेतु मशीन की क्षमता
| मशीन का प्रकार | उपलब्ध समय (मशीन घंटे प्रति सप्ताह) |
|---|---|
| मिलिंग मशीन | 250 |
| लेथ मशीन | 150 |
| ग्राइंडर मशीन | 50 |
उत्पाद अ, ब एवं स के लिए प्रति इकाई लाभ क्रमशः: ₹ 20, ₹ 6 तथा ₹ 8 होगा ।
(i) प्रश्न को एल.पी.पी. में सूत्रबद्ध (सुविन्यस्त) कीजिए ।
(ii) अधिकतम लाभ प्राप्त करने के लिए, फर्म को प्रत्येक उत्पाद का कितना उत्पादन करना चाहिए ? (8+12=20 अंक)
Answer approach & key points
The directive 'solve' demands precise numerical working with clear methodological steps. Allocate approximately 30% time to part (a) Chi-Square test (15 marks), 30% to part (b) t-test (15 marks), and 40% to part (c) LPP formulation and solution (20 marks). Structure each part with: null/alternative hypotheses or objective function, step-by-step calculations with formulae, critical value comparison, and final decision. No traditional introduction or conclusion needed; begin directly with part (a) and end with final LPP solution.
- Part (a): Calculate expected frequencies for all 9 cells using (Row Total × Column Total)/Grand Total; compute Chi-Square statistic Σ(O-E)²/E; compare with χ² critical value at df=4, α=0.05 (9.488); conclude independence or dependence
- Part (b): Calculate sample mean (47.8 kg) and sample standard deviation; compute t-statistic using formula (x̄-μ)/(s/√n); compare with t-critical at df=9, α=0.05 (two-tailed ±2.262); conclude whether population mean can be 50 kg
- Part (c)(i): Formulate correct LPP with decision variables X₁, X₂, X₃ for products A, B, C; objective function Max Z = 20X₁ + 6X₂ + 8X₃; constraints: 8X₁+2X₂+3X₃ ≤ 250, 4X₁+3X₂ ≤ 150, 2X₁+X₃ ≤ 50; non-negativity conditions
- Part (c)(ii): Solve using Simplex method or graphical/simplex approach; identify optimal solution with values of X₁, X₂, X₃ and maximum profit; verify slack variables and binding constraints
- Correct application of statistical tables and critical values; proper degrees of freedom calculation for each test
- Clear presentation of calculations with proper units and interpretation of results in management context
Q3 50M state Operations management and decision making
(a) State the different forms of waste management. 15 marks
(b) State the various factors affecting plant location. 15 marks
(c) An automobile company has additional capacity that can be used to manufacture brakes that the company is presently buying for ₹ 500 each. If the company makes the brakes, it will incur materials cost of ₹ 100 per unit, labour cost of ₹ 130 per unit and variable overhead cost of ₹ 30 per unit.
The annual fixed cost associated with the unused capacity is ₹ 2,50,000. Demand over the next year is estimated to be 5000 units of brakes.
(i) Would it be profitable for the company to manufacture the brakes ?
(ii) Suppose the capacity could be used by another department for production of some agricultural equipment that would cover its fixed and variable cost and contribute ₹ 1,00,000 to profit. Which would be more advantageous, brakes production or agricultural equipment production ? 12+8=20 marks
हिंदी में पढ़ें
(a) अपशिष्ट (वेस्ट) प्रबंधन के विभिन्न स्वरूप बताइए । 15
(b) संयंत्र स्थान को प्रभावित करने वाले विभिन्न घटक बताइए । 15
(c) एक ऑटोमोबाइल कंपनी अपनी अतिरिक्त क्षमता का उपयोग ब्रेक्स निर्माण में कर सकती है, जो कि अभी कंपनी ₹ 500 प्रति में क्रय कर रही है । यदि कंपनी ब्रेक्स बनाती है, तो उस पर सामग्री लागत ₹ 100 प्रति इकाई, मजदूरी लागत ₹ 130 प्रति इकाई एवं परिवर्तनीय उपरिव्यय लागत ₹ 30 प्रति इकाई आती है ।
वार्षिक स्थायी लागत जो अप्रयुक्त क्षमता से संबंधित है ₹ 2,50,000 है । आगामी वर्ष की ब्रेक्स की अनुमानित मांग 5000 इकाई है ।
(i) क्या ब्रेक्स का निर्माण करना कंपनी के लिए लाभप्रद होगा ?
(ii) मान लीजिए क्षमता अन्य विभाग द्वारा कृषि उपकरणों के उत्पादन पर प्रयोग होगी जो कि स्थायी एवं परिवर्तनीय लागत को कवर (सम्मिलित) कर लेगी तथा ₹ 1,00,000 लाभ में योगदान करेगी । ब्रेक्स के निर्माण अथवा कृषि उपकरणों के निर्माण में कौन-सा निर्माण अधिक लाभदायक होगा ? 12+8=20
Answer approach & key points
The directive 'state' demands clear, systematic presentation of facts and calculations. Allocate approximately 30% time to part (a) on waste management forms, 30% to part (b) on plant location factors, and 40% to part (c) numerical analysis. Structure: brief introduction, then systematic coverage of (a) and (b) with definitions and classifications, followed by detailed cost-benefit calculations for (c)(i) and opportunity cost analysis for (c)(ii), ending with a synthesized conclusion on operational decision-making.
- Part (a): Classification of waste management forms — industrial (hazardous, non-hazardous), municipal (solid, liquid), biomedical, e-waste; treatment methods (landfilling, incineration, recycling, composting, waste-to-energy)
- Part (b): Plant location factors — proximity to raw materials and markets, labour availability and costs, transportation infrastructure, power and water supply, government policies and incentives, environmental regulations, agglomeration economies
- Part (c)(i): Make-or-buy cost calculation: variable cost per unit = ₹260; total manufacturing cost = ₹26,00,000 + ₹2,50,000 = ₹28,50,000; buying cost = ₹25,00,000; manufacturing is NOT profitable
- Part (c)(ii): Opportunity cost analysis: compare net loss from brakes (₹3,50,000) versus ₹1,00,000 contribution from agricultural equipment; latter is advantageous
- Integrated insight: Demonstrate understanding of relevant costs, sunk costs, and capacity utilization decisions in operations management
Q4 50M discuss Information systems and e-Governance
(a) (i) Define e-Governance.
(ii) State the advantages of e-Governance.
(iii) State the e-Governance initiatives. 5+5+5=15 marks
(b) (i) Define DSS.
(ii) State the main characteristics of DSS.
(iii) State the components of DSS. 5+5+5=15 marks
(c) (i) Define ERP.
(ii) Discuss the various types of Information Systems.
(iii) Define Expert System. State its common characteristics. 6+7+7=20 marks
हिंदी में पढ़ें
(a) (i) ई-गवर्नेंस को परिभाषित कीजिए ।
(ii) ई-गवर्नेंस के लाभ बताइए ।
(iii) ई-गवर्नेंस पहलों (इनिशिएटिव्स) के बारे में बताइए । 5+5+5=15
(b) (i) डी.एस.एस. को परिभाषित कीजिए ।
(ii) डी.एस.एस. की प्रमुख विशेषताएँ बताइए ।
(iii) डी.एस.एस. के अवयव बताइए । 5+5+5=15
(c) (i) ई.आर.पी. को परिभाषित कीजिए ।
(ii) विभिन्न प्रकार की सूचना प्रणालियों की चर्चा कीजिए ।
(iii) विशेषज्ञ प्रणाली को परिभाषित कीजिए तथा उसकी सामान्य विशेषताएँ बताइए । 6+7+7=20
Answer approach & key points
The question demands defining and elaborating on five distinct sub-parts across e-Governance, DSS, and information systems. Allocate approximately 30% time/words to part (a) e-Governance (15 marks), 30% to part (b) DSS (15 marks), and 40% to part (c) ERP and Information Systems (20 marks). Structure with brief definitions first, followed by characteristics/components, and conclude each part with Indian illustrations. Use diagrams for DSS components and ERP architecture where possible.
- For (a)(i-iii): Define e-Governance as ICT-enabled governance transformation; list advantages (transparency, citizen empowerment, cost reduction); cite initiatives like Digital India, UMANG, e-Office, and state-level examples
- For (b)(i-iii): Define DSS as computer-based system supporting decision-making; characteristics include semi-structured problems, user-interaction, model-driven; components—data management, model management, user interface, knowledge base
- For (c)(i): Define ERP as integrated enterprise-wide information system automating core business processes; mention SAP, Oracle as examples
- For (c)(ii): Discuss types—TPS, MIS, DSS, EIS/ESS, ES, SCM, CRM—explaining their hierarchical levels and functional domains
- For (c)(iii): Define Expert System as AI-based system emulating human expertise; characteristics—knowledge base, inference engine, explanation facility, knowledge acquisition; cite MYCIN, DENDRAL or Indian healthcare/agriculture applications
- Integrative element: Show progression from transaction processing to strategic decision support across the three parts
- Indian relevance: Link to NIC, NeGP 2.0, AI-driven governance in parts (a) and (c)