GATE PI exam:gate PYQs & Answers — Page 57

Questions 561–570 of 650. Imported answers require independent review unless marked reviewed.

In a service centre, cars arrive according to Poisson distribution with a mean of 2 cars per hour. The time for serving a car is exponential with a mean of 15 minutes. The expected waiting time (in minute) in the queue is

Your answerChoose one option.

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Actual and forecasted demands of a product are as follows: | Period: 1, 2, 3, 4, 5 | Actual demand: 180, 170, 165, 170, 200 | Forecasted demand: 190, 190, 190, 190, 190 | The forecast error measured in terms of mean absolute deviation (MAD) and mean absolute percentage error (MAPE), respectively, are

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13 and 7.84%

13 and 9.85%

17 and 7.84%

17 and 9.85%

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In a mass production firm, measurements are carried out on 1000 pairs of shaft and hole. The mean diameters of the shaft and the hole are 37.53 mm and 37.59 mm, respectively. The corresponding standard deviations are 0.03 mm and 0.04 mm. The mean clearance and its standard deviation (both in mm), respectively, are

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0.06 and 0.07

0.06 and 0.06

0.06 and 0.05

0.07 and 0.01

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A pressure die casting set-up was tested by injecting water (density 1000 kg/m

) at a pressure of 200 bar. Mould-filling time was found to be 0.05 s. Afterward, the actual casting is made by injecting the liquid metal (density 2000 kg/m

) at an injection pressure of 400 bar. Neglect all losses (friction, viscous-effect, etc.). The approximate mould-filling time (in s) is

Your answerChoose one option.

0.05

0.075

0.1

0.2

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The value of the surface integral

over the surface S of the sphere

, where n is the unit outward normal to the surface element dS, is _____

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Consider the differential equation

with initial conditions: at

and

. The value of y (up to two decimal places) at

is _____

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One kg of air (that can be considered a calorically perfect gas with characteristic gas constant R = 287 J/kg-K and specific heat ratio

) undergoes a constant-volume process from an initial static pressure of 1 bar to a final static pressure of 4 bar. The increase in entropy (in J/kg-K) of air is _____

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and

represent the x- and y-components of the two-dimensional velocity field of an incompressible flow, the value of the constant a is _____

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A spherical pressure vessel (made of mild steel) of internal diameter 500 mm and thickness 10 mm is subjected to an internal gauge pressure of 400 kPa. If the yield stress of mild steel is 200 MPa, the factor of safety (up to one decimal place) is _____

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A square cross-section wooden column of length 3140 mm is pinned at both ends. For the wood, Young’s modulus of elasticity is 12 GPa and allowable compressive stress is 12 MPa. The column needs to support an axial compressive load of 200 kN. Using a factor of safety of 2.0 in the computation of Euler’s buckling load, the minimum cross-sectional area (in mm

) of the column is _____

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GATE PI exam:gate PYQs

Question 31

Question 32

Question 33

Question 34

Question 35

Question 36

Question 37

Question 38

Question 39

Question 40