GATE MN format:nat PYQs & Answers — Page 8

Questions 71–80 of 300. Imported answers require independent review unless marked reviewed.

Topic practice 300 questionsPage 8 of 30

A thermal power plant has an agreement with three mines M1, M2 and M3 to receive ‘Grade 1’ coal, in the proportion of 60%, 25% and 15%, respectively. The probabilities that a wagon supplied coal to the plant containing below ‘Grade 1’ from mines M1, M2 and M3 are 0.02, 0.03 and 0.04, respectively. On a random check, a sample wagon is found to carry below ‘Grade 1’ coal. The probability that the wagon belongs to mine M1, is _____. (round off up to 2 decimals)

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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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Polluted air with particulate matters of diameter 50 μm enter with a horizontal velocity of 1.0 m/s at a height of 0.5 m from the bottom of a dry settling chamber. The density of the particle is 200 kg/m³ and dynamic viscosity of the air is 1.8 × 10⁻⁵ kg/m-s.

Assume streamline flow and the density of air is negligible as compared to particles and uniform horizontal velocity of 1.0 m/s of gas and particles within the chamber.

Considering particle setting follows Stoke’s law, the minimum length in m, of the chamber required for setting of the particle at its bottom is _____. (round off up to 2 decimals)

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In a tacheometry survey, the readings observed are given.

Instrument Station	Staff Station	Bearing of line of sight	Vertical angle	Staff readings (m)
P	A	145°	+8°	1.2, 1.7, 2.2
P	B	205°	+3°	0.8, 1.2, 1.6

The additive and multiplying constants of the instrument are 0 and 100, respectively. The length of the line AB in m, is _____. (round off up to 2 decimals)

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The data obtained from an air sample analysis of an old working in a coal mine are given.

O₂ 17.15%, CO₂ 3.40%, CH₄ 2.20%, and N₂ 77.25%.

Considering atmospheric air contains

O₂ 20.95%, CO₂ 0.03%, and N₂ 79.2%,

the percentage of blackdamp in the old working, is __. (round off up to 2 decimals)

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A rectangular face of 2.0 m × 2.5 m dimension is blasted with 20 kg explosive in a 1000 m long drive. One kilogram of explosive produces 2200 cm³ of nitrous fumes. The face is ventilated with a duct, located 10.0 m away from the face, to dilute the fumes. The quantity of air, in m³/s to be circulated for reducing the concentration of nitrous fumes to 5 ppm within a period of 5 minutes, is ____. (round off up to 2 decimals)

[Use the relation,

, where t = time,

= volume of the tunnel over which the mixing of the gases produced at the face and air delivered by the fan occurs, c = concentration at time t, V = volume of tunnel, Q = quantity of air flow, q = total volume of nitrous fumes produced]

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Data for a centrifugal pump discharging water from a sump to the surface are given.

Head, m : 180 Discharge rate, m

/hr : 320 Operating hours per day for 270 days in a year : 14 Operating hours per day for remaining 95 days : 20 Overall efficiency of the pump system : 0.70 Specific weight of mine water, kN/m

: 10.20

The annual electrical power consumption in GWh, due to pumping operation, is _____. (round off up to 2 decimals)

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The root of the function,

in the interval [0, 1] using bisection method after two iterations, is _____. (round off up to 2 decimals)

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A Bord and Pillar panel is developed at a depth of 250 m in a flat coal seam. The vertical stress gradient is 0.027 MPa/m. If the strength of a square pillar is 12.5 MPa, the extraction ratio of the pillar for a safety factor of 1.5, is _____. (round off up to 2 decimals)

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A Mohr-Coulomb envelop between shear stress,

and normal stress,

of a sandstone rock is given as

(unit of stress is MPa)

A sandstone sample is tested in triaxial mode with confining pressure of 5.0 MPa. The value of the shear stress,

in MPa at the failure, is_____. (round off up to 2 decimals)

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GATE MN format:nat PYQs

Question 45

Question 46

Question 47

Question 48

Question 49

Question 50

Question 51

Question 52

Question 53

Question 54