Production and Industrial Engineering
GATE PI year:2025 PYQs
Build your understanding with focused practice from past exam papers.
Questions 51–60 of 65. Imported answers require independent review unless marked reviewed.
Question 51
Open questionPINAT2 marksNeeds review
In the iron-carbon equilibrium phase diagram, the eutectoid reaction occurs at 723 °C with the eutectoid composition of 0.83 weight % carbon. Ferrite and cementite phases are considered to contain 0.022 weight % carbon and 6.67 weight % carbon, respectively. If a steel specimen with 0.7 weight % carbon is cooled from 950 °C to below 723 °C, the fraction of eutectoid ferrite is________. (Rounded off to two decimal places)
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During orthogonal cutting with a tool of 10° rake angle, the cutting and thrust forces are 900 N and 275 N, respectively. The coefficient of friction on the rake surface of the tool is________. (Rounded off to two decimal places)
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In casting a cube of 80 mm side, the volumetric shrinkages due to solidification and solid contraction are 4.5% and 2%, respectively. Assume uniform cooling in all directions. The side (in mm) of the cube pattern for getting the required size casting is________. (Rounded off to two decimal places)
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The solidification of a casting starts at 10 AM. However, the solidification of the molten metal at the center-line of the mold starts at 10:03 AM and ends at 10:10 AM. The casting is considered solidified completely when the solidification is completed at the center-line of the mold. The center-line feeding resistance (CFR) in percentage is________. (Answer in integer)
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A link OA of length 200 mm is rotating counter clockwise about O in x-y plane with a constant angular velocity of 100 rad/s, as shown in the figure. The absolute value of the x-component of the linear velocity (in m/s) of point A at the instant shown in the figure is________. (Rounded off to one decimal place)
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A force of 1000 N is acting at point A on a bracket fixed at point B as shown in the figure. The magnitude of the moment of the force about B (in N·m) is________. (Rounded off to one decimal place)
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A steel plate is fastened to a channel using three identical bolts as shown in the figure. The bolts are made of carbon steel of permissible yield strength in shear as 400 N/mm
. The plate is subjected to a force of 12 kN. Neglect the weight of the plate. The magnitude of the resultant shear force (in N) on bolt 2 is ________. (Answer in integer) 
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The annual profit of a company depends on its annual marketing expenditure. The information of preceding 3 years’ annual profit and marketing expenditure is given in the table. Based on linear regression, the estimated profit (in units) of the 4
year at a marketing expenditure of 5 units is ________. (Rounded off to two decimal places)Log in to check the answer
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Three plants P₁, P₂ and P₃ produce 6, 1 and 9 thousand liters of fruit juice, respectively. The produced fruit juice is transported to three distribution centers D₁, D₂ and D₃ with requirement of 7, 5 and 4 thousand liters of juice, respectively. The transportation cost (in hundreds of Rupees) from each plant to each distribution center is given in the table. The total transportation cost (in hundreds of Rupees) in initial basic feasible solution using Vogel’s approximation method is ________. (Answer in integer)
| D₁ | D₂ | D₃ | Supply |
|---|---|---|---|---|
P₁ | 2 | 3 | 11 | 6 |
P₂ | 1 | 0 | 6 | 1 |
P₃ | 5 | 8 | 15 | 9 |
Demand | 7 | 5 | 4 | |
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A company purchases items in bulk for getting quantity discount in the item’s price. The price break-up is given in the table. The annual demand for the item is 5000 units. The ordering cost is Rupees 400 per order. The annual inventory carrying cost is 30 percent of the purchase price per unit. The optimal order size (in units) is ________. (Answer in integer)
Quantity of item (Q in units) | Unit price of item (Rupees) |
|---|---|
0 ≤ Q < 1200 | 10 |
1200 ≤ Q < 2000 | 8 |
2000 ≤ Q | 7 |
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