GATE MN topic:systems-engineering PYQs & Answers

Questions 1–10 of 38. Imported answers require independent review unless marked reviewed.

The expected time (P days) and standard deviation (Q days) of the different activities (A to F) in a project are indicated in the network diagram as (P, Q). The standard deviation of the project completion time, in days, is ____________. (rounded off to one decimal place)

Diagram for Mining Engineering question 31

Network diagram activity labels and nodes: A (12, 0) from 1 to 2; B (23, 4) from 1 to 3; C (15, 1) from 2 to 4; D (18, 2) from 4 to 5; E (27, 3) from 3 to 6; F (6, 2) from 5 to 6.

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A shovel needs to be selected from four models of different capacities, S1 to S4, for loading of dumpers. The operational data for the shovel-dumper combination are provided. The mean arrival rate of the dumpers at the loading point is 5 per hour and the waiting cost of dumper is ₹ 200 per hour. The inter-arrival time of dumpers and loading time of shovel follows exponential distribution. Ignoring the shovel hiring cost, the shovel type that will have minimum total cost (waiting and operating cost) is

Model	Operating cost of shovel (₹ per hour)	Mean loading rate of shovel (number of dumpers per hour)
S1	80	8
S2	85	9
S3	90	10
S4	100	11

Your answerChoose one option.

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A mine workshop needs to assign 4 jobs to 4 service engineers. The cost for performing a job by an individual service engineer is given. A typical job can be assigned to only one service engineer. If the service engineer S1 cannot perform the job J3, and S3 cannot perform the job J4, the optimal cost for completion of jobs is ____________. (answer in integer)

Service Engineer	J1	J2	J3	J4
S1	50	50	---	20
S2	70	40	20	70
S3	90	30	50	---
S4	70	20	60	30

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Following information are given for three mines of a company receiving explosives from three suppliers.

Explosive suppliers	Mine-1	Mine-2	Mine-3	Supply capacity (tonne)
Supplier - S	10	15	50	2500
Supplier - O	5	2	100	2500
Supplier - I	30	40	20	3000
Explosive demand (tonne)	1000	2000	500

Considering the initial basic feasible solution of this transportation problem, using North-West corner method, the transportation cost of explosives supplied to the company, in Rs., is

Your answerChoose one option.

9000

19000

29300

38500

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In a M/M/1 system, the inter-arrival time of dumpers to a shovel follows exponential distribution with a mean arrival rate of 9 dumpers per hour. The service time of the shovel follows exponential distribution with a mean service rate of 12 dumpers per hour. The probability that exactly one dumper is available to the shovel is

Your answerChoose one option.

1/16

3/16

3/4

1/4

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A project network with the sequence of five activities is shown.

Diagram for Mining Engineering question 20

The crashing costs of activities are

Activity	A	B	C	D	E
Duration (week)	5	6	8	3	4
Crashing cost per week (lakh INR)	4.0	2.5	2.0	3.0	4.0

If the project is crashed by one week, the increase in project cost, in lakh INR, is

Your answerChoose one option.

2.0

2.5

3.0

4.0

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Data from two production faces of an open pit iron ore mine are given.

Item description	Face 1	Face 2
Maximum production capacity (tonne/day)	1600	2000
Fe (%)	63	58
Production cost of ores (in INR/tonne)	1500	1200

Ores from two different faces are blended and supplied with Fe grade not less than 60 %. Based on the demand, the combined production is limited to a maximum of 2500 tonne/day. If the selling price of blended iron ores is INR 4500 /tonne, the optimal production from two faces in tonne/day, for maximizing the profit, respectively are

Your answerChoose one option.

1000.0 and 1500.0

1333.3 and 1166.7

1600.0 and 900.0

500.0 and 2000.0

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A transportation system for carrying ore from stock pile to railway siding through an ore bin is shown. The time between failure of each conveyor belt follows an exponential distribution with mean time between failure of 700 hours. The system is considered to be a ‘success’ if ore transports from stock pile to siding by any combination of belts. The reliability of the system for 350 hours of continuous successful operation is _____. (round off up to 2 decimals)

Diagram for Mining Engineering question 46

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A linear programming problem is given as: Maximize

Subject to:

The problem has

Your answerChoose one option.

Unbounded solution.

Infeasible solution.

Multiple optimal solutions.

Unique optimal solution.

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In project scheduling techniques, the CORRECT statement is

Your answerChoose one option.

Both CPM and PERT are deterministic.

Both CPM and PERT are probabilistic.

CPM is deterministic and PERT is probabilistic.

CPM is probabilistic and PERT is deterministic.

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GATE MN topic:systems-engineering PYQs

How to practice topic:systems-engineering

Question 31

Question 42

Question 47

Question 37

Question 19

Question 20

Question 36

Question 46

Question 19

Question 22