Q1 50M Compulsory solve Probability, sampling, quality control, maintenance decision, e-governance
(a) A train is scheduled to arrive at a station at a random time between 09:00 AM and 09:30 AM. The actual arrival time is equally likely to be any moment within this interval.
(i) Define a suitable probability density function (PDF).
(ii) What is the probability that the train will arrive before 09:13 AM ?
(iii) Find the expected arrival time and the variance of the arrival time.
(iv) Given that the train has not arrived by 09:11 AM, what is the expected arrival time ?
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(b) Determine the required sample size for estimating the true weight cereal container from a population of N = 5000.
Based on the past records variance of weight is 121 grams and this estimate should be within 2·5 grams of the true average weight with 99% confidence.
Will there be a change in the size of the sample if we assume population to be infinite ? If so, explain by how much ? (Table enclosed)
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(c) A manufacturing facility specializing in Sheet Metal Production has implemented a Statistical Quality Control Program to monitor and improve process performance. As a part of this initiative, an Engineer has recorded the number of visible surface defects identified on 20 sequential metal sheets, each representing one production unit. The data collected during this inspection phase are given below :
[Table with Sheet No. 1-20 and Defect Counts: 5, 6, 4, 4, 6, 7, 0, 6, 5, 3, 1, 4, 5, 3, 6, 4, 3, 1, 3, 4]
Using the above information :
(i) Determine the Center line (CL), Upper control limit (UCL) and Lower control limit (LCL).
(ii) Plot the appropriate Control Chart and interpret the result.
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(d) A Tech Solutions is a mid-sized IT consulting company specializing in automated HR and payroll systems for small business. The company has successfully digitized most of its operations, relying heavily on its internal computer systems for payroll processing and report generations. However, despite its automation efforts, the computer system has experienced periodic failures. Over the past 20 months, the computer system has broken down as indicated in the table below :
Each breakdown results in an average loss of ₹4500/- due to time delay and technical service expenses. As a preventive measure, company is considering a monthly service contract for preventive maintenance. If they sign up for the contract, the average number of breakdowns is expected to decrease to 1 per month, and the contract would cost ₹3300/- per month.
Based on the given information, advise that the company should go for contract for preventive maintenance or not ?
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(e) Critically analyse the advantages of E Governance for Government, Public and Business giving suitable examples.
10
Answer approach & key points
Solve all five numerical and analytical parts systematically, allocating approximately 20% time to each sub-part given equal 10-mark weighting. Begin with precise mathematical derivations for (a) continuous uniform distribution and conditional expectation, (b) finite population correction for sample size, (c) c-chart construction with control limit calculations, (d) expected cost comparison for maintenance decisions, and conclude with (e) critical analysis of e-governance stakeholders. Present calculations step-wise with proper formulae, units, and interpretations.
- (a) Define PDF f(t) = 1/30 for t ∈ [0,30] minutes; calculate P(T<13) = 13/30; derive E(T)=15 min, Var(T)=75; apply memoryless property for conditional expectation E(T|T>11) = 11 + 15 = 26 min or 09:26 AM
- (b) Apply sample size formula n₀ = Z²σ²/E² with Z=2.576, σ²=121, E=2.5; compute n₀ ≈ 139; apply finite population correction n = n₀/(1+n₀/N) ≈ 135; show infinite population increases sample size by ~4 units
- (c) Calculate c̄ = Σcᵢ/k = 80/20 = 4; determine CL=4, UCL=4+3√4=10, LCL=max(0,4-3√4)=0; construct c-chart and interpret no points outside limits, process in statistical control
- (d) Compute expected breakdown cost without contract: compare historical rate (20 breakdowns/20 months = 1/month) vs stated data; calculate expected monthly cost = ₹4500 vs contract cost ₹3300 + ₹4500×1 = ₹7800; recommend against contract if current rate ≤ 1, or detailed cost-benefit if data shows higher breakdowns
- (e) Critically analyse e-governance advantages: Government (efficiency, transparency—MCA21, GSTN), Public (accessibility, grievance redressal—UMANG, Digital India), Business (ease of doing business, reduced corruption—e-way bills, GeM); include challenges like digital divide, cybersecurity
Q2 50M solve Trend analysis, hypothesis testing, linear programming
(a) The electrical power demand of TATA Power Corporation from 2018 to 2024, measured in megawatts, is provided below. Using the data, forecast the demand for the year 2025 by fitting and plotting the linear trend line.
Year | Electrical Power Demand (Megawatts)
2018 | 94
2019 | 99
2020 | 100
2021 | 110
2022 | 125
2023 | 162
2024 | 142
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(b) In a study to evaluate the effectiveness of two different animal feeds, researchers recorded the weight gains (in kilograms) of animals after fed each type of feed.
Feed A | 45 | 48 | 47 | 50 | 46 | 49 | 47 | 48
Feed B | 51 | 53 | 52 | 55 | 50 | 52 | 54 | 33
(i) If the two samples are considered independent, can we conclude that Feed B is more effective than Feed A at the 0·025 level of significance ?
(ii) Also examine the case if the same set of eight animals received both feeds, and test at the 0·01 level of significance. (Table enclosed)
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(c) Techline Pvt. Ltd. is a consumer electrics manufacturing concern producing three models of Smart Devices : X, Y and Z. The company operates under the constraints of two key resources, viz. raw materials and labor hours. Each week, the availability of raw materials is restricted to 800 kg, while labor availability is limited to 600 hours. To maximize profit, the company needs to decide, how many units of each product to manufacture weekly without exceeding the available resources. The relevant details for each product are provided below :
| Product | Raw Material per unit (Kg) | Labor Hours per unit (Hours) | Profit contribution per unit (₹) |
|---------|---------------------------|------------------------------|----------------------------------|
| X | 6 | 5 | 80 |
| Y | 4 | 4 | 60 |
| Z | 2 | 3 | 40 |
(i) Formulate this scenario as a Linear Programming Problem (LPP), and solve it for optimal product mix.
(ii) Based on the optimal solution, analyze the situation if the company wants to introduce a New product W, requiring 2 kg of raw materials and 2 hours of labor hours per unit. Its estimated profit contribution is ₹35/- per unit.
Should the company include this new product in its production mix ?
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Answer approach & key points
Solve this multi-part numerical question by allocating approximately 30% time to part (a) trend analysis with linear regression, 30% to part (b) hypothesis testing for both independent and paired samples, and 40% to part (c) linear programming formulation and sensitivity analysis. Begin with clear problem identification, show all computational steps with formulas, present results in structured tables, and conclude with managerial interpretations for each sub-part.
- Part (a): Calculate linear trend line using least squares method (Y = a + bX), compute 2025 forecast, and describe plotting procedure with proper axes labeling
- Part (b)(i): Conduct independent samples t-test with pooled variance, calculate t-statistic, compare with critical t-value at α=0.025 (one-tailed), and state conclusion about Feed B effectiveness
- Part (b)(ii): Perform paired t-test for same animals, compute mean difference and standard error, compare with critical t-value at α=0.01, and interpret results
- Part (c)(i): Formulate LPP with objective function (Max Z = 80X + 60Y + 40Z) and constraints (6X+4Y+2Z ≤ 800, 5X+4Y+3Z ≤ 600, X,Y,Z ≥ 0), solve using graphical or simplex method, identify optimal product mix and maximum profit
- Part (c)(ii): Calculate opportunity cost/range of feasibility for new product W, determine shadow prices, assess whether ₹35 profit covers resource opportunity cost, and give definitive recommendation
- For all parts: Show complete working with formulas, degrees of freedom, and critical values from enclosed table; interpret results in business context
Q3 50M calculate Operations management and PERT/CPM
3.(a) A company has an annual demand of 1600 units for an item, whose unit cost is ₹70/-. The annual holding cost comprises 18% for interest charges, 1% for insurance, 1·5% allowances for obsolescence of unit cost and ₹2·50 for building overheads, ₹3·40 for damage loss, and ₹7·0 miscellaneous costs. Placing each order costs the company ₹100/-.
(i) Calculate Economic Order Quantity (EOQ) and the total costs of stocking the units.
(ii) If the supplier of the items will only deliver batches of 250 units, how is the total variable cost influenced ?
(iii) If the supplier relaxes their order size requirements, as the company has limited storage space it can stock a maximum of 100 units at any time. What would be the optimal ordering policy and associated costs ? 15
(b) Consider the following aggregate planning problem for four months :
| | Regular time | Overtime | Subcontracting |
|---|---|---|---|
| Production capacity/month | 900 units | 300 units | 200 units |
| Production cost/unit | ₹6/- | ₹8/- | ₹9/- |
The forecasted demand for the next four months is 1300, 1400, 1225 and 1475 units respectively. Shortages are not permitted. The initial inventory is 50 units, and the carrying cost is ₹1·60 per unit per month.
Provide the aggregate plan for this problem. 15
(c) The warehouse owner of Quick Industries is considering a new computer system for accounting and inventory control. A computer vendor sent the following information about the system installation :
| Activity Identification | Activity description | Immediate Predecessor | Time (Days) Most optimistic | Time (Days) Most likely | Time (Days) Most pessimistic |
|---|---|---|---|---|---|
| A | Selection of Computer Model | – | 5 | 7 | 9 |
| B | Input/output System Design | A | 6 | 8 | 16 |
| C | Monitoring System Design | A | 5 | 9 | 13 |
| D | Computer Hardware Assembly | B | 16 | 21 | 26 |
| E | Development of main Programs | B | 11 | 19 | 27 |
| F | Input/output routines development | C | 9 | 10 | 17 |
| G | Database Creation | E | 5 | 9 | 13 |
| H | Installation of the system | D, F | 2 | 3 | 4 |
| I | Testing and Implementation | G, H | 7 | 8 | 9 |
(i) Draw the network diagram for this information. Identify the Critical Path and expected project completion time.
(ii) Calculate the probability that the project will be completed in 61 days.
(iii) When the company wants to be 95% sure that the system will be installed by a certain date, how many days prior to that should it start the work ? 20
Answer approach & key points
This numerical question demands precise calculations across five sub-parts: allocate ~30% time to 3(a) EOQ with holding cost breakdown (15 marks), ~25% to 3(b) aggregate planning with transportation method (15 marks), and ~45% to 3(c) PERT network with probability analysis (20 marks). Structure as: clear formula statement → step-wise computation → final answer with units → brief interpretation where asked.
- 3(a)(i): Correct EOQ formula application with total holding cost = 18%+1%+1.5% of ₹70 + ₹2.50+₹3.40+₹7.0 = ₹12.60+₹12.90 = ₹25.50/unit/year; EOQ = √(2×1600×100/25.50) ≈ 112 units; total cost calculation
- 3(a)(ii): Total variable cost at Q=250 vs EOQ, showing cost penalty for batch constraint; compare ordering + holding costs
- 3(a)(iii): Modified EOQ under storage constraint (max 100 units); optimal policy becomes ordering at capacity limit with adjusted cost analysis
- 3(b): Transportation method/linear programming formulation for aggregate planning; month-wise production allocation across regular, overtime, subcontracting minimizing total cost (production + inventory carrying); show inventory balance constraints
- 3(c): PERT network construction with AOA or AON; ES/EF/LS/LF calculations; critical path identification; variance and Z-score for probability; 95% confidence time calculation using normal distribution
Q4 50M discuss Information systems and expert systems
4.(a) (i) "Expert Systems play a significant role in Organisations." Discuss it giving at least four benefits of Expert Systems. 10
(ii) Elaborate the different components of Expert Systems giving suitable examples. 10
(b) (i) "Information Resource Management is a strategic plan of an organisation." Elaborate. 10
(ii) What are the important components that must be considered for implementation of Information Resource Management. 5
(c) (i) Explain the fundamental role of Information Systems in business and organisations. 5
(ii) State at least eight evaluation factors for an excellent information system. 10
Answer approach & key points
The directive 'discuss' demands a balanced treatment with elaboration and critical examination across all sub-parts. Allocate approximately 40% of effort to part (a) [20 marks] covering expert systems benefits and components with examples; 30% to part (b) [15 marks] on IRM as strategic plan and implementation components; and 30% to part (c) [15 marks] on fundamental roles of IS and evaluation factors. Structure with a brief introduction, systematic part-wise treatment, and a synthesizing conclusion linking information systems to organizational competitiveness.
- Part (a)(i): Four+ benefits of Expert Systems—preservation of expertise, 24/7 availability, consistency in decision-making, and training/learning support—with organizational context
- Part (a)(ii): Five components of Expert Systems—knowledge base, inference engine, user interface, explanation facility, and knowledge acquisition subsystem—each with domain-specific examples
- Part (b)(i): IRM as strategic plan—alignment with business objectives, resource optimization, competitive advantage, and governance framework
- Part (b)(ii): Implementation components—top management commitment, IT infrastructure, human resource development, change management, and performance metrics
- Part (c)(i): Fundamental roles of IS—operational efficiency, decision support, strategic management, and communication/coordination
- Part (c)(ii): Eight evaluation factors—reliability, timeliness, accuracy, completeness, relevance, usability, security, and cost-effectiveness
Q5 50M Compulsory critically examine Chambers of Commerce, Strategic Intent, Turnaround, Foreign Trade, E-business
(a) "Have various Chambers of Commerce and other Industry Associations played their desired role effectively ?" Critically examine. (10 marks)
(b) What is meant by 'Strategic intent' ? Give brief explanation of each of these concepts :
(i) Stretch
(ii) Leverage
(iii) Fit (10 marks)
(c) Define Turnaround strategies. Discuss conditions for turnaround strategies. Also discuss types of turnaround actions. (2+4+4 marks)
(d) Critically evaluate India's foreign trade since independence and identify constraints in India's Exports Growth. (5+5 marks)
(e) Elucidate the conceptual framework of e-business. Identify the significant changes it has brought to business processes. (5+5 marks)
Answer approach & key points
Critically examine demands balanced analysis with evidence-based judgment across all five parts. Allocate time proportionally: ~20% for (a) Chambers of Commerce, ~20% for (b) Strategic Intent concepts, ~20% for (c) Turnaround strategies, ~20% for (d) India's foreign trade, and ~20% for (e) E-business. Structure each part with definition, analysis, and critical evaluation; use Indian examples throughout.
- (a) Chambers of Commerce: Evaluate effectiveness of FICCI, CII, ASSOCHAM in policy advocacy, MSME support, and dispute resolution; cite limitations like elite capture and weak regional presence
- (b) Strategic Intent: Define Hamel & Prahalad's concept; explain Stretch (ambitious goals beyond resources), Leverage (resource multiplication), Fit (alignment with environment) with Indian corporate examples
- (c) Turnaround: Define as performance recovery strategies; conditions (declining profits, market share loss, cash crunch); types (cost reduction, asset reduction, revenue generation, combination)
- (d) Foreign Trade: Trace evolution from import substitution to liberalization (1991); identify export constraints (infrastructure, transaction costs, NTBs, product concentration)
- (e) E-business: Framework (B2B, B2C, C2C, G2C); process changes (supply chain digitization, CRM transformation, disintermediation, 24/7 operations)
Q6 50M critically evaluate Small-Scale Industries, Government in Business, Privatisation, Consumer Protection Act
(a) (i) "Small-Scale Industries play a vital role in the growth of economic activities of a country." Explain giving examples. (10 marks)
(ii) How can Government initiatives expedite the growth and success of small-scale industries ? Discuss. (5 marks)
(b) (i) "Government should not enter into business activities." Do you agree ? Explain with examples. (10 marks)
(ii) "Privatisation of Industries has not achieved its objectives." Give your critical comments. (10 marks)
(c) "Consumer Protection Act 2019 (CPA) has changed the business scenario in India." Do you agree ? Describe at least eight features of CPA giving suitable examples. (15 marks)
Answer approach & key points
The directive 'critically evaluate' demands balanced judgment with evidence. Allocate approximately 25% time/words to (a)(i) on SSI role, 12% to (a)(ii) on government initiatives, 20% each to (b)(i) on government in business and (b)(ii) on privatisation critique, and 23% to (c) on CPA 2019. Structure: brief introduction acknowledging SSI importance, then systematic treatment of each sub-part with examples, ending with synthesized conclusion on state-market-consumer balance.
- (a)(i) Economic roles of SSI: employment generation, regional dispersion, export contribution, entrepreneurship development—illustrated with Khadi clusters, Coimbatore textile SMEs, or Moradabad brassware
- (a)(ii) Government initiatives: PMEGP, CGTMSE, MUDRA, MSME Development Act 2006, single-window clearance, technology upgradation through MSME-Technology Centres
- (b)(i) Balanced view on government in business: arguments for (market failure, strategic sectors, social welfare) and against (inefficiency, political interference)—examples from Air India, BSNL, vs. successful PSUs like ISRO or SAIL
- (b)(ii) Critical assessment of privatisation: achievements (disinvestment proceeds, efficiency gains in Maruti, VSNL) versus shortcomings (job losses, asset stripping, strategic sale controversies, limited revenue generation)
- (c) CPA 2019 transformation: eight features—e-commerce inclusion, product liability, mediation, enhanced pecuniary jurisdiction, CCPA establishment, strict liability, misleading advertisement penalties, and class action suits—with examples like Amazon/Flipkart consumer disputes or Maggi case implications
Q7 50M discuss Strategic alliances, mergers, acquisitions and BCG matrix
(a) Define Strategic Alliances. Discuss the reasons for strategic alliances. Also discuss types of strategic alliances with suitable examples. (5+5+5=15 marks)
(b) Define Mergers and Acquisitions. Discuss the types of mergers and acquisitions. Also discuss the important issues in mergers and acquisitions with suitable examples. (5+5+5=15 marks)
(c) What do you understand by BCG Matrix ? Describe the four Quadrants of it and also discuss its Strategic Implications and Limitations with suitable examples. (5+7+8=20 marks)
Answer approach & key points
The directive 'discuss' requires a comprehensive, analytical treatment across all three sub-parts. Allocate approximately 30% time/words to part (a) on strategic alliances, 30% to part (b) on M&A, and 40% to part (c) on BCG Matrix given its higher 20-mark weightage. Structure with brief introductions for each sub-part, detailed body covering definitions, types, and issues/examples, and a synthesizing conclusion that connects these strategic tools to contemporary Indian business challenges.
- Part (a): Precise definition of strategic alliances distinguishing from M&A; reasons including risk-sharing, market access, resource complementarity; types (joint ventures, equity alliances, non-equity alliances) with examples like Maruti-Suzuki JV or Tata-Starbucks alliance
- Part (b): Clear differentiation between mergers (voluntary combination) and acquisitions (purchase of control); types (horizontal, vertical, conglomerate, congeneric) with Indian examples like HDFC-HDFC Bank merger or Tata-Tetley acquisition; critical issues including valuation, cultural integration, regulatory hurdles (CCI approval), due diligence
- Part (c): BCG Matrix definition as portfolio planning tool; detailed description of four quadrants (Stars, Cash Cows, Question Marks, Dogs) with Indian corporate examples like ITC's portfolio or Reliance's business units
- Part (c continued): Strategic implications for resource allocation decisions; limitations including market share-reliance, snapshot nature, ignoring synergies between SBUs
- Synthesis: Integration of how these three strategic tools serve different purposes in corporate strategy—alliances for flexibility, M&A for control, BCG for portfolio optimization—relevant to Make in India and Atmanirbhar Bharat contexts
Q8 50M elucidate Joint ventures, foreign direct investment and foreign exchange risk
(a) Explain Joint Venture with suitable examples. Discuss the Life Cycle of a Joint Venture. (7+8=15 marks)
(b) What is Foreign Direct Investment ? Describe with suitable examples the different factors that influence Foreign Direct Investment. (5+10=15 marks)
(c) Elucidate the concept of Foreign Exchange Risks and Exposure. Discuss the techniques included in Managing Foreign Exchange Risks with suitable examples. (10+10=20 marks)
Answer approach & key points
The directive 'elucidate' for part (c), the highest-mark section, demands clear explanation with examples; secondary directives are 'explain' for (a) and 'describe' for (b). Structure: brief introduction defining international business expansion → part (a): JV definition with Maruti-Suzuki/Tata Starbucks examples, then formation-growth-maturity-decline lifecycle → part (b): FDI definition, then Dunning's OLI framework or push-pull factors with Walmart-Flipkart/Foxconn-Vedanta examples → part (c): transaction/translation/economic exposure with Tata Motors-JLR or Infosys hedging examples, then forward contracts, options, swaps, natural hedging → conclusion on integrated risk management for Indian MNCs. Allocate ~30% time/words to (a), ~30% to (b), ~40% to (c) based on marks.
- Part (a): Joint Venture definition, characteristics (shared ownership/control/risk), suitable examples (Maruti Suzuki, Tata Starbucks, Hero Honda), and detailed Life Cycle stages: Formation/Negotiation, Growth/Development, Maturity/Stabilization, Decline/Renegotiation/Dissolution with triggers at each stage
- Part (b): FDI definition distinguishing from FPI, greenfield vs brownfield; factors influencing FDI using Dunning's OLI paradigm or eclectic theory (Ownership, Location, Internalization advantages) with examples (Walmart-Flipkart, Samsung India, Foxconn-Vedanta semiconductor plant)
- Part (c): Foreign Exchange Risk types—Transaction exposure (payables/receivables), Translation exposure (consolidation), Economic/Operating exposure (long-term competitiveness); Exposure measurement techniques
- Part (c): Risk management techniques—Forward contracts, Futures, Options (currency), Swaps, Money market hedging, Natural hedging (local borrowing, matching currency cash flows), Leading and Lagging, Netting with Indian corporate examples (TCS, Infosys, Tata Motors, Reliance)
- Integration: Link between FDI mode choice and JV formation, how forex risk management affects JV stability across lifecycle stages, and policy implications for India's FDI regime and RBI's forex management framework