GATE PI discipline:mechanical-and-production-engineering PYQs & Answers — Page 6

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Questions 51–60 of 650. Imported answers require independent review unless marked reviewed.

Topic practice 650 questionsPage 6 of 65

Which ONE or MORE among the following work materials is/are NOT commonly machined using diamond cutting tools?

Your answerSelect all correct options. You can choose more than one.

Mild steel

Stainless steel

Silicon

Aluminium alloy

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A linear slot is to be milled in a single pass from the point

on XY plane by a CNC machine. The actual velocity along the Y-axis is 5% less than the intended value. The programmed feed rate along the intended slot is 150 mm/min.

The magnitude of the positional error along the Y-axis when the X-coordinate reaches 180 mm is _____ mm (in integer).

Note: All coordinates are in mm.

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In laser beam machining, the time (

) required for the material to attain the melting temperature from a room temperature (

) of 32 °C is expressed by the following expression,

where

is thermal diffusivity,

is melting temperature,

is thermal conductivity,

is heat flux.

If a uniformly distributed 1 kW power laser beam with a beam diameter of 0.1 mm is used for machining tungsten carbide, and 10% of beam absorption is assumed, the time

is _____ μs (rounded off to one decimal place).

Note: Thermal properties of tungsten carbide: melting temperature = 3400 °C; thermal conductivity = 2.15 Wcm⁻¹°C⁻¹; diffusivity = 0.79 cm²s⁻¹; assume

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In the measurement of surface roughness using a 2D stylus profilometer, a surface profile measured over a length of 0.8 mm was recorded on a graph paper. During recording, vertical magnification of 10,000 and horizontal magnification of 100 were used. The areas in the as-recorded graph above and below the datum line are as follows:

Above (mm²): 140, 60, 150, 50 Below (mm²): 70, 50, 120, 160

The average surface roughness (

) of the surface is _____ μm (rounded off to two decimal places).

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A cylindrical metal component of 10 mm diameter is subjected to uniform uniaxial tension during operation. It was observed that a force of 14 kN produces a uniform reduction of

mm in diameter. Assume that material behaviour is homogeneous, isotropic, and linear elastic.

If its Young’s modulus is 150 GPa, the Poisson’s ratio of the material is _____ (rounded off to two decimal places).

Note: Assume

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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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GATE PI discipline:mechanical-and-production-engineering PYQs

Question 51

Question 52

Question 53

Question 54

Question 55

Question 56

Question 57

Question 58

Question 59

Question 60