Mining Engineering - MN 2014 GATE Paper (Practice Test) - GATE

In any given year, the probability of an earthquake greater than Magnitude 6 occurring in the
Garhwal Himalayas is 0.04. The average time between successive occurrences of such earthquakes
is ____ years.

(Important : you should answer only the numeric value)

The population of a new city is 5 million and is growing at 20% annually. How many years would
it take to double at this growth rate?

Q. 6 – Q. 10 carry two marks each.

Q.

In a group of four children, Som is younger to Riaz. Shiv is elder to Ansu. Ansu is youngest in the
group. Which of the following statements is/are required to find the eldest child in the group?
Statements
1. Shiv is younger to Riaz.
2. Shiv is elder to Som.

Moving into a world of big data will require us to change our thinking about the merits of
exactitude. To apply the conventional mindset of measurement to the digital, connected world of
the twenty-first century is to miss a crucial point. As mentioned earlier, the obsession with
exactness is an artefact of the information-deprived analog era. When data was sparse, every data
point was critical, and thus great care was taken to avoid letting any point bias the analysis.
From “BIG DATA” Viktor Mayer-Schonberger and Kenneth Cukier
The main point of the paragraph is:

The total exports and revenues from the exports of a country are given in the two pie charts below.
The pie chart for exports shows the quantity of each item as a percentage of the total quantity of
exports. The pie chart for the revenues shows the percentage of the total revenue generated through
export of each item. The total quantity of exports of all the items is 5 lakh tonnes and the total
revenues are 250 crore rupees. What is the ratio of the revenue generated through export of Item 1
per kilogram to the revenue generated through export of Item 4 per kilogram?

X is 1 km northeast of Y. Y is 1 km southeast of Z. W is 1 km west of Z. P is 1 km south of W. Q is
1 km east of P. What is the distance between X and Q in km?

10% of the population in a town is HIV+. A new diagnostic kit for HIV detection is available; this
kit correctly identifies HIV⁺ individuals 95% of the time, and HIV⁻ individuals 89% of the time. A
particular patient is tested using this kit and is found to be positive. The probability that the
individual is actually positive is _______

Q. 11 – Q. 25 carry one mark each.

Q.

A block of weight 100 kN rests on a floor as shown in the figure. The coefficient of static friction
between the block and the floor is 0.5. A force of 45 kN is applied horizontally on the block. The
static frictional force in kN is

A spring of constant stiffness k is stretched from point A to point B (displacement u in the figure)
by a force F. The potential energy of the spring is expressed by

If σ_s is the induced stress and σ_i is the insitu stress at a point below ground, the ‘stress
concentration’ at that point is

The components of state of stress at a point in x−y plane are given as 

and  The sum of the principal stresses acting on the x−y plane in MPa is _______

(Important : you should answer only the numeric value)
 

The andgle 5^o 15' 25" is expressed in hours, minutes and seconds as 

A circular curve has a radius of 200 m and deflection angle of 65⁰. The length of the curve in m is

The weight strength of ANFO of specific gravity 0.8 is 912 kcal/kg. The weight strength of an
emulsion explosive of specific gravity 1.2 is 850 kcal/kg. Bulk strength of the emulsion explosive
relative to ANFO in percentage is _________

In a cut-and-fill stope, the main purpose of back filling is to

Bypass valve in a compressed oxygen type self-contained breathing apparatus is meant to

Given S is the setting load and Y is the yield load of a hydraulic prop, the correct relationship is

Solution of the differential equation dy/dx= ky follows exponential decay ( where k is a constant) for

The value of k for which the vectors a = 2i - 3j and b = k i + 4j are orthogonal to each other is _______

(Important : you should answer only the numeric value)

Which one of the following is the most likely mode of slope failure for waste dump

The occurrence of head in a single toss of an unbiased coin is given by a random variable X. The
variance of X is _______________

(Important : you should answer only the numeric value)

The divergence of the vector v = (x + y)(−yi + xj) is

The 

For Indian coal mines, the ‘maximum allowable concentration’ of respirable dust containing 7.5%
free silica in mg/m³ is

Given ???? is the thermal conductivity, ?? is density and ?? is specific heat of a rock sample, the thermal
diffusivity of the rock sample is

Cyclone, bag filter and scrubber can be used for control of

A mine waste dump of pH 5.2 can be neutralized by adding

A flat coal seam of thickness (t) 3 m is excavated and broken roof rock has completely filled the
space created due to extraction as shown in the figure. If the bulking factor of roof rock is 1.2, the
caving height (H) in m is ______________

(Important : you should answer only the numeric value)

A piece of coal sample weighs 10 kg in air and 2 kg when immersed in water. The specific gravity
of the coal sample is ______________________

(Important : you should answer only the numeric value)

In a borehole log of 1.2 m in length, recovery of rock cores in cm is given below
20, 8, 15, 8, 8, 4, 3, 9, 10, 1, 5, 10
The RQD in percentage is

An underground coal mine panel produces 520 tonnes per day deploying 220, 200 and 192 persons
in three shifts. As per CMR 1957, the minimum quantity of air in m3/min to be delivered at the last
ventilation connection of the panel is ______________

(Important : you should answer only the numeric value)

In a PERT network, the activities on the critical path are a, b and c. The standard deviations of the
durations of these activities are 2, 2 and 1 respectively. The variance of the project duration is

Q. 36 – Q. 65 carry two marks each.

Q

A particle P is in equilibrium as shown in the figure. The magnitude in kN and the orientation θ in
degrees of the force F respectively are

A distributed load of 4 kN/m acts on a beam of 6 m length supported by a hinge and a roller as
shown in the figure. The distance in m of the point of zero shear in the beam from the point A is __

A dry rock sample of diameter 50 mm and length 100 mm weighs 300 g. After saturating in brine
solution of specific gravity 1.05, its weight increased to 330 g. The porosity of the rock sample in
percentage is __________

A joint plane of length L and dip δ intersects the toe of a slope as shown in the figure. The weight
of the shaded block is W. Uniform water pressure P acts normal to the joint plane. If the cohesion
and angle of internal friction of the joint surface are c and φ respectively, then the expression for
‘safety factor’ of the shaded block is

The lengths and standard errors of three sections AB, BC, and CD of a straight line AD are given
below

The standard error in total length AD in m is

The bearing of side AB of a regular hexagon ABCDEF is ??50⁰10′ ?? . If the station C is easterly
from the station B, the whole circle bearing of the side BC is

In a room-and-pillar stope, bench blasting is conducted using ANFO having density of 800 kg/m³.
The specific gravity of rock is 2.5, hole diameter is 100 mm and spacing to burden ratio is 1.3. The
charge length of each blast hole is 80% of the hole length. For a desired powder factor of 0.48
kg/tonne, the spacing and burden of the blast pattern in m respectively are

Match the following for ore handling operations in an underground metal mine

The following characteristic curves (P, Q, R, S) pertain to rotary drilling in rock.

Title of the curve
I: Torque versus RPM
II: Rate of penetration versus uniaxial compressive strength of rock
III: Rate of penetration versus weight on bit
IV: Specific energy versus weight on bit
Match the curves with their titles

The height H of a drawpoint in a sublevel caving stope is 3.0 m. If the angle of repose (??) of
broken ore is 350, the digging depth y of the loader as shown in the figure in m is _______

For an explosives company, the probability of producing a defective detonator is 0.02. The
probability that a lot of 50 detonators produced by the company contains at most 2 defective
detonators is __________

The area enclosed by the curves y = x² and y = x³  for x∈[0,∞] is

The value of a, for which the function below is continuous at x = 1 is

The sum of the infinite series a + ar + ar² + ar³ +...+ arⁿ⁻¹ +..... for r <1 is

A centrifugal pump has a discharge rate of 2000 L of water per min against a total head of 200 m. If
the pump efficiency is 75%, the input power to the pump in kW is

A dragline is required to remove 3,00,000 m³ of rock per month on the bank volume basis.
Consider the following data for the dragline operation.
Effective working hours per month = 450
Bucket fill factor = 0.8
Cycle time = 65 s
Swell factor of the rock = 1.25
The minimum bucket capacity of the dragline in m³ is

A direct rope haulage pulls 8 tubs loaded with coal through an incline of length 500 m having an
inclination of 1 in 6. Consider the following additional data.
Capacity of tub = 1.0 tonne
Tare weight of tub = 500 kg
Hauling speed = 9 km per hour
Coefficient of friction between wheel and rail = 1/60
Coefficient of friction between rope and drum = 1/10
Mass of rope per meter = 1.5 kg
The minimum power required to haul the tubs in kW is

A coal mine receives two bids for purchase of a new dragline. The first bid quotes Rs. 150 crore as
a price to be paid in full on delivery. The second bid quotes Rs. 180 crore as a price payable at the
end of the third year after delivery. If the discount rate is 12%, the difference in NPV between the
first and second bids in crore of rupees is __________

(Important : you should answer only the numeric value)

Match the following in the context of underground mine environment

A mine airway having cross-section of 2.2 m × 2.2 m and length 500 m contains a bend. Given that
the airway friction factor is 0.01 Ns²m⁻⁴, shock loss factor for the bend is 0.07 and density of air is
1.2 kg/m³, the equivalent length of the airway in m is __________

In order to estimate the NVP in a mine, measurements are made at the main fan as shown below.

The NVP in Pa is ___________

The resistances of two splits A and B are 0.35 Ns²m⁻⁸ and 0.05 Ns2m−8 respectively. The combined
resistance of the shafts and trunk airways is 0.4 Ns²m⁻⁸. A booster fan is planned to be installed in
split A to increase the quantity flowing through it. Assuming that the surface fan continues to
operate at a constant pressure of 1000 Pa, the critical pressure of the booster fan in Pa is _______

A pitot tube is inserted in a ventilation duct with the nose facing the air flow. A vertical U-tube
manometer filled with alcohol (specific gravity 0.8) has been used for pressure measurements such
that 10.2 mm is read as the total pressure and 8.8 mm as the static pressure. Given the density of air
to be 1.2 kg/m3, the air velocity at the nose of the pitot tube in m/s is ____________

An illumination source S shown in the figure emits light equally in all directions. At a point A on
the floor, the illuminance is 5.0 lux. The illuminance at point B on the floor in lux is ________

Two machines A and B while operating simultaneously produce a sound pressure level of 85 dBA
at a point. When the machine A stops, the sound pressure level at that point reduces to 80 dBA. The
sound pressure level at the same point due to machine A operating alone in dBA is

A waste water effluent has BOD5 of 80 mg/L and the reaction rate constant is 0.16 per day. The
ultimate BOD in mg/L is

A series of tri-axial compression tests conducted on sandstone samples reveal the following
relationship between major and minor principal stresses
??1 = 50 + 3??₃ [stresses are in MPa]
The cohesion in MPa and angle of internal friction in degrees of sandstone respectively are

Six detonators each having resistance of 1.5 ohm are connected in parallel. A 15 V exploder is
connected to the detonators by two single-core cables of resistance 3 ohm each. The current in the
circuit in Ampere is __________

The failure and the repair rates of a shovel are 0.06 hr⁻¹ and 0.04 hr⁻¹ respectively. The availability
of the shovel in percentage is ____________

(Important : you should answer only the numeric value)

The individual reliability values of four sub-systems are given in the figure below. The reliability of
the system is _________