Mechanical Engineering 2025 Paper I 50 marks Calculate

Q8

(a) What are the various computer languages used for NC machines? Explain the merits and limitations of each language. (10 marks) (b) A small manufacturing unit produces bolts and the weight of each bolt is measured. The target weight for a bolt is 60 grams. A sample of 5 bolts is taken every day for 30 days. The weight (in grams) for first 5 days is given below: Calculate the control limits for the X̄ (X-bar) chart. The constant A₂ for a sample size of 5 is 0·577. (20 marks) (c) A certain component can be manufactured either by welding or by forging process. The factory has an order for 5,00,000 units. The costs involved for both methods of manufacturing are as follows: | Cost | Welding | Forging | | Fixed cost | ₹ 15,000 | ₹ 94,000 | | Variable cost/unit | ₹ 5 | ₹ 4·25 | (i) Which is the most economical method of manufacturing the component? Draw the indicative graph also for BEP. (ii) What will be the loss if a wrong choice is made? (20 marks)

हिंदी में प्रश्न पढ़ें

(a) NC मशीनों के लिए उपयोग की जाने वाली विभिन्न कंप्यूटर भाषाएं कौन-सी हैं? प्रत्येक भाषा के लाभ एवं सीमाएं स्पष्ट कीजिए। (10 marks) (b) एक छोटी विनिर्माण इकाई में बोल्ट का उत्पादन होता है तथा प्रत्येक बोल्ट का भार मापा जाता है। एक बोल्ट का लक्षित भार 60 ग्राम है। प्रतिदिन 5 बोल्ट के नमूने 30 दिन तक लिए गए हैं। पहले 5 दिनों का भार (ग्राम में) नीचे दिया गया है: X̄ (X-bar) चार्ट के लिए नियंत्रण सीमाएं परिकलित कीजिए। नमूना आकार 5 के लिए स्थिरांक A₂ 0·577 है। (20 marks) (c) एक निश्चित घटक को या तो वेल्डन से या फिर फोजन (फोर्जिंग) प्रक्रिया से निर्मित किया जा सकता है। कारखाने के पास 5,00,000 इकाइयों का एक आदेश है। निर्माण की दोनों विधियों में संलग्न लागत इस प्रकार है: | लागत | वेल्डन | फोजन | | अचल लागत | ₹ 15,000 | ₹ 94,000 | | परिवर्तनीय लागत/इकाई | ₹ 5 | ₹ 4·25 | (i) घटक का उत्पादन करने का सबसे किफायती तरीका कौन-सा है? BEP के लिए सांकेतिक ग्राफ भी बनाइए। (ii) गलत चुनाव करने पर क्या नुकसान होगा? (20 marks)

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Directive word: Calculate

This question asks you to calculate. The directive word signals the depth of analysis expected, the structure of your answer, and the weight of evidence you must bring.

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How this answer will be evaluated

Approach

Calculate requires systematic treatment of all three parts: for (a) enumerate NC languages with comparative merits/limitations; for (b) compute X̄ chart control limits using given A₂ constant with proper statistical steps; for (c) determine BEP by equating total costs, compare at 5,00,000 units, sketch cost-revenue graph, and quantify wrong-choice loss. Allocate roughly 20% time to (a), 35% to (b), and 45% to (c) given mark distribution.

Key points expected

  • Part (a): APT, G-code/M-code, and conversational languages identified with specific merits (APT for complex 3D contours, G-code universal compatibility, conversational for shop-floor ease) and limitations (APT needs post-processor, G-code low-level tedious, conversational limited flexibility)
  • Part (b): Correct calculation of grand mean X̿ from sample data, average range R̄ computation, UCL = X̿ + A₂R̄ and LCL = X̿ - A₂R̄ with A₂ = 0.577 applied, final control limits numerically stated
  • Part (c)(i): BEP calculation by equating total costs: 15000 + 5Q = 94000 + 4.25Q yielding BEP = 1,12,000 units; welding economical below BEP, forging above; at 5,00,000 units forging is cheaper
  • Part (c)(i): Indicative BEP graph with fixed cost lines (horizontal), total cost lines (sloping), intersection at BEP, and 5,00,000 unit point marked showing forging advantage
  • Part (c)(ii): Loss calculation: Cost at wrong choice (welding at 5,00,000) minus cost at correct choice (forging at 5,00,000) = ₹2,65,00,000 - ₹2,21,50,000 = ₹43,50,000 loss

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness20%10Correctly identifies APT/G-code/conversational NC languages with accurate technical descriptions; applies X̄ chart theory with proper understanding of A₂ constant usage; sets up correct cost equations and BEP concept for make-or-break analysisIdentifies major NC languages but conflates some features; understands X̄ chart basics but confuses R-chart constants; sets up cost equations but BEP concept slightly muddledConfuses NC languages with general programming languages; applies wrong control chart type (p-chart or c-chart); treats BEP as revenue-based rather than cost-comparison based
Numerical accuracy20%10X̿ and R̄ computed correctly from given data; UCL/LCL values accurate to 2 decimal places; BEP = 1,12,000 units exact; total costs at 5,00,000 units: welding ₹26,50,000 and forging ₹22,15,000; loss ₹4,35,000 correctly derivedMinor arithmetic slips in X̿ or R̄ but method correct; BEP calculation shows correct algebra but final value off by small margin; cost comparison directionally correctMajor calculation errors in control limits (forgetting A₂ or using wrong formula); BEP calculation yields impossible negative or extremely high values; wrong-choice loss computed incorrectly or ignored
Diagram quality20%10Clean BEP graph with axes labelled (Quantity vs Cost in ₹), fixed cost lines at ₹15,000 and ₹94,000, diverging total cost lines, clear intersection at 1,12,000 units, and 5,00,000 unit point marked with cost values showing forging advantageBEP graph shows correct general shape but missing labels or scale; intersection point approximate rather than marked at calculated BEP; axes not clearly identifiedNo BEP graph drawn; or graph shows revenue lines (break-even with sales) instead of cost comparison; or lines drawn without any intersection logic
Step-by-step derivation20%10Shows all sample means and ranges for part (b); explicit formulas X̿ = ΣX̄/k and R̄ = ΣR/k; clear substitution into UCL/LCL formulas; for (c) shows algebraic solution 0.75Q = 79,000; all steps traceable with proper mathematical notationShows key formulas but skips some intermediate steps; final answers correct but working condensed; BEP derivation present but algebraic steps partially impliedFinal answers stated without derivation; or jumps from problem statement to answer; no visible working for control limits or BEP calculation
Practical interpretation20%10Interprets X̄ chart limits for quality control decision-making (when to investigate process); explains why forging wins at high volume (economies of scale absorbing fixed cost) with Indian MSME context; quantifies wrong-choice loss as significant managerial risk; suggests when welding would be preferred (small batches, prototype runs)States which process is cheaper without explaining volume economics; mentions loss amount without contextualizing significance; limited connection to real manufacturing decisionsNo interpretation of results; treats all parts as purely academic exercises; no discussion of practical implications for production planning or quality management

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