GATE PI year:2021 PYQs & Answers — Page 5

Questions 41–50 of 65. Imported answers require independent review unless marked reviewed.

The eigenvalues of matrix

are 5 and 10. For matrix

, where

is a constant and

is a 2×2 identity matrix, its eigenvalues are

Your answerChoose one option.

5, 10

5 + α, 10 + α

5 - α, 10 - α

5α, 10α

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A company manufactures two products P and Q with unit profit of 4 and 5, respectively. The production requires manpower and two kinds of raw materials R1 and R2. The following table summarizes the requirement and availability of resources.

Resource	Resource usage per unit of production P	Q	Amount of resource available
manpower	1	1	10
R1	1	2	18
R2	2	1	18

The maximum profit the company can make is

Your answerChoose one option.

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A tool of an NC machine has to move along a circular arc from (20,20) to (10,10), while performing an operation. The center of the arc is at (20,10). Which one of the following NC tool commands performs the above mentioned operation?

Your answerChoose one option.

N20 G03 X20 Y20 X10 Y10 R10

N20 G02 X20 Y20 X10 Y10 R10

N20 G02 X10 Y10 X20 Y20 R10

N20 G01 X20 Y20 X10 Y10 R10

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In a shaft-hole assembly, the hole is specified as 30^_ mm. The mating shaft has a clearance fit with minimum clearance of 0.01 mm. The tolerance on the shaft is 0.03 mm. The maximum clearance in mm between the hole and the shaft is

Your answerChoose one option.

0.04

0.05

0.08

0.10

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‘GO’ and ‘NO GO’ snap gauges are to be designed for a shaft 36.000^_ mm. Gauge tolerance can be taken as 5% of the hole tolerance. Following the ISO system of gauge design, the respective sizes of ‘GO’ and ‘NO GO’ gauges are

Your answerChoose one option.

36.013 mm and 36.067 mm

36.015 mm and 36.065 mm

36.018 mm and 36.062 mm

36.020 mm and 36.060 mm

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A circular tank of 4 m diameter is filled up to a height of 3 m. Assuming almost steady flow and neglecting losses, the time taken in seconds to empty the tank through a 5 cm diameter hole located at the center bottom (take acceleration due to gravity g = 9.81 m/s²) is [round off to the nearest integer]

Your answerChoose one option.

505

187

897

354

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The probability mass function

of a discrete random variable X is given by

, where x = 1, 2, ···, ∞. The expected value of X is _________. [in integer]

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The time to pass through a security screening at an airport follows an exponential distribution. The mean time to pass through the security screening is 15 minutes. To catch the flight, a passenger must clear the security screening within 15 minutes. The probability that the passenger will miss the flight is _________. [round off to 3 decimal places]

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A machine shop has received four jobs A, B, C and D for processing on a single CNC machine. All jobs are available for processing on the first day of the production schedule calendar, and processing times and due dates as applicable on the first day are given below. Using earliest due date rule, the average tardiness (in days) is ________. [in integer]

Job	Processing time (in days)	Due date (day)
A	8	14
B	5	10
C	7	12
D	9	19

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A time study is carried out for a spot welding operation which is being performed by an operator. The time taken (in seconds) for five observations are recorded as 40, 35, 45, 37 and 43, respectively. If the standard time and the allowance for this operation are 45 seconds and 9 seconds, respectively, then the performance rating (in percentage) of the operator is ________. [in integer]

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GATE PI year:2021 PYQs

Question 31

Question 32

Question 33

Question 34

Question 35

Question 36

Question 37

Question 38

Question 39

Question 40