GATE PI format:nat PYQs & Answers — Page 2

Questions 11–20 of 264. Imported answers require independent review unless marked reviewed.

Topic practice 264 questionsPage 2 of 27

A custom pinion, with a width equal to 10 times the module, has 20 full depth teeth and a pressure angle of 20° is being designed. It should transmit a torque of 95 N-m to a corresponding spur gear.

Considering the safe bending stress to be 180 MPa and form factor to be 0.32, the module of the pinion is _____ mm (rounded off to one decimal place).

Note: The Lewis equation gives the tangential force as

, where

is the safe bending stress,

the width,

the form factor, and

the module.

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A company has a fixed cost of INR 3,00,000 and a variable cost of INR 150 per unit for manufacturing of a product. The company sells 5,000 units of that product making a profit equivalent to 20% of the total sales revenue.

The break-even quantity for that product is _____ units (rounded off to the nearest integer).

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A company must allocate oil produced from their two plants to meet all the demands of two markets. The cost per litre of allocation from plant

to market

is denoted by

. The market demand

, plant production capacity

and

values are given in the table.

	Market 1 ( )	Market 2 ( )	Capacity in litres
Plant 1 ( )
Plant 2 ( )
Demand in litres

The company hired an intern to formulate an optimization model to decide on the quantity (

) to be allocated from plant

to market

and the formulation is given below:

Minimize

Subject to

The optimal value of the objective function of the linear programming problem formulated by the intern is _____ (in integer).

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The computer centre (CC) in an institute manages the central server for which researchers queue to run their computer programs. CC processes programs only one at a time. Four computer programs are available at 10:00 am on a given day. The time required to run each program on the central server and their respective promised time of completion (i.e., due date) on that same day are given in the table. If the CC follows shortest processing time (SPT) rule to sequence the computer programs, the number of tardy jobs is _____. Note: Ignore program change-over times.

Program	1	2	3	4
Processing time (in minutes)	60	40	90	100
Promised time (i.e., due date)	12 noon	11:30 am	1:00 pm	1:30 pm

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, and the value of

is 2, then the value of

is _____ (rounded off to two decimal places).

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The number of soldering defects that occur in a semiconductor device follows a discrete Poisson distribution with a probability mass function

. The average number of soldering defects per semiconductor device is 3. The probability that a randomly selected semiconductor device will have at least two soldering defects is _____ (rounded off to two decimal places).

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A time study was carried out for a job broken into two elements. For each element, three iterations of task were observed, and observed time was recorded. The observed times (in seconds) and the rating factor for each element are given in the table.

Work element	Observed time (seconds)	Rating factor
A	20; 25; 21	105%
B	19; 17; 18	90%

If a further 20% needs to be added for allowances, then the standard output of the worker is _____ units per hour (in integer).

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In a hole-shaft assembly, the following are the dimensions and tolerances (all in mm) provided for the hole and shaft:

Hole:

Shaft:

The magnitude of the clearance when the shaft is at the minimum material condition and hole is at the maximum material condition is _____ mm (to three decimal places).

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Consider an assembly line producing an item through a process involving three activities in the following order: cutting, welding, and polishing. There are three workers available: one is assigned only for cutting, one is assigned only for welding, and one is assigned only for polishing.

The activity time per item is given in the table.

Assuming that the process is running in steady state, the total number of items coming out of the assembly line in six hours is _____ (in integer).

Note: Assume that workers, items, and machines/tools are available as and when needed.

Activity name	Cutting	Welding	Polishing
Activity time/item (in minutes)	30	40	25

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In the composite filament winding process as shown in the figure, the mandrel diameter is 70 mm and is rotating at a speed,

rev/min.

If a 45° helical wind angle is needed, the axial velocity,

, of the slider should be _____ m/s (rounded off to two decimal places).

Assume

. Ignore the thickness of the composite layers already wound on the mandrel.

Diagram for Production and Industrial Engineering question 65

Note: Figure is not to scale.

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GATE PI format:nat PYQs

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