Mining Engineering - MN 2015 GATE Paper (Practice Test) - GATE

Tanya is older than Eric

Cliff is older than Tanya

Eric is older that cliff

if the first two statements are true, the the third statement is :

Five teams have to compete in a league, with every team playing every other team exactly once, before going to the next round. ow many matches will have to be held to complete the league round of matches?

Q. 6 – Q. 10 carry two mark each.

Q.

Select the appropriate option in place of underlines part of the sentence

Increased productivity necessary reflects greater efforts made by the employees.

Given below are two statements followed by two conclusion. Assuming these statements to be true, decide which one logically follows.

Statement:

1  No manager is a leader

2.  All leaders are executives.

Conclusions:

1.  No manager is an executive

2.  No executive is a manager.

In the fiven figure angle Q is a right angle, PS:QS=3:1, RT: QT =5:2 and PU: UR = 1:1 if area of triangle QTS is 20 cm², then the area of triangle PQR in CM² is __________.

(Important : you should answer only the numeric value)

Right triangle PQR is to be constructed in the xy - plane so that the right angle is at P and line PR is parallel to the x-axis. Te x and y coordinates of P, Q and R are to be integers that satisfy the inequalities: -4   x 5 and  6y 16. How many diffrent traingle xould be constructed with these properties ?

A coin is tosssed thrice. Let X be the event that head occurs in each of the first two tosses. Let Y be the event that a tail occurs on the third toss. Let Z be the event that two tails occur in three tosses. Based on the above information, Which one of the following statements is TRUE? 

Q. 1 – Q. 25 carry one mark each.

Q.

Out of the support categories given for an underground coal mine, identify the ‘active support’.

Massive sandstone in immediate roof delays the local fall in goaf of a coal mine. Under this
condition, crushing of the pillars at outbye side is called

A back sight on a bench mark of RL 100.00 m on the floor of a tunnel is 3.25 m. The inverse staff
reading on a roof station of the tunnel is 1.25 m. The RL of the roof station in m is ________

The angle in degrees at which a ridge line intersects contours is

In a drum hoisting system through a vertical shaft, overwinding is prevented by

The temperature of a parcel of air decreases from 30.2^o C to 28.9^o C as it rises from an altitude of
20 m to 120 m. The lapse rate for the atmosphere is

The excess pore pressure in backfill material in a cut-and-fill stope leads to

The primary purpose of cut holes for blasting in an underground drivage is to

In a triangle ABC, the bearings of the sides AB, BC, and CA are 60⁰ , 130⁰, and 270⁰ respectively.
The interior angles A, B, and C in degrees respectively are

In a binomial distribution, the probability of success p →0 and number of trials n → ∞ such that
λ = np approaches to a finite value. The variance of the distribution is

For a function f (x) , it is given that f (0) = 2 and f' (0) = 4 . Ignoring all other higher order
derivative terms, the value of f (0.5) is ________

(Important : you should answer only the numeric value)

The two sides of a parallelogram are given by the vectors   The
area of the parallelogram is

In a BOD test, 5 ml of wastewater is diluted with pure water to fill a 300 ml BOD bottle. The
initial and final dissolved oxygen contents of the mix are 9.0 mg/l and 7.0 mg/l respectively. The
BOD of the wastewater, in mg/l, is

A force of 50 N is applied to a wrench as shown in the figure. The magnitude of the moment in
N-mm of this force about the point P is ________

Dilatancy of rock is associated with

A bord and pillar panel having square pillars is designed for 30% extraction during development. If
the gallery width is 5 m, the side of the pillar in m is ________

Low shock and high gas pressure explosive is generally used for blasting of

The covariance of copper grade for a certain lag distance in an ore body is 6.0 (%)². If the sill is
10 (%)², the semivariogram for the same lag distance in (%)² is

The matrix 

A gas mixture contains CH₄, C₂H₆ and H₂ with respective concentrations of 75%, 15% and 10% by
volume. The lower explosibility limit of CH4, C₂H₆ and H₂ are 5.0%, 3.3% and 4.2% respectively.
The lower explosibility limit of the gas mixture, in percentage, is ________

Intake air containing 0.2% methane enters a section of an underground mine where emission rate of
methane is 0.05 m³/s. Assuming that the threshold limit value of methane is 1.25%, the minimum
quantity of fresh air required in m³/s is ________

In a fully mechanised bord and pillar mining system, winning of coal and its transportation from the
face is commonly carried out with the combination of

An underground coal mine employing 1200 persons experiences 2 fatal injuries, 6 serious injuries
and 8 reportable injuries during the year 2013. The total injury rate per 1000 persons employed for
the year is ________

In self-contained chemical-oxygen self-rescuer, oxygen is produced by

The failure data of an equipment follows an exponential distribution. If the mean time between
failures is 3000 hours, the reliability of the equipment for 750 hours is ________

Q. 36 – Q. 65 carry two marks each.

Q.

In a 4.2 m wide and 3.0 m high gallery in a coal seam, twelve shot holes are blasted per round. The
holes are charged with 2 explosive cartridges of 435 g each. If the powder factor of the blast is 2.2
tonne/kg and specific gravity of coal is 1.4, the pull per round of blast in m is

The stadia readings with horizontal sight on a vertical staff held at 50 m from a tacheometer are
1.285 m and 1.780 m. The focal length of the object glass is 25 cm, and the distance between the
object glass and the vertical axis of the tacheometer is 15 cm. The stadia interval in mm is _______

In a shortwall panel, coal is extracted from the face by a continuous miner having rate of production
30 tonne/h. Coal having specific gravity of 1.4 is transported by shuttle cars of capacity 0.9 m³
each to a feeder breaker located at 60 m from the face. If the average speed of the LHD is 0.5 m/s,
and total loading and unloading time of LHD is 40 s, the number of LHDs required to match the
production of the continuous miner is

Vertical photographs of an area lying 500 m above the mean sea level are to be taken at a scale of
1:20000 from an aircraft. If the camera has a focal length of 210 mm, the flying height of the
aircraft above the mean sea level in m is ________

(Important : you should answer only the numeric value)

Match the following locations with support types in coal mines.

The value of 

A rectangular field of area 20000 m² is to be divided into 6 different plots by fencing as shown in
the figure. The value of L in m for which the total length of fencing becomes minimum is _______

Match the following for a drilling system.

For the ventilation system shown, the combined resistance of the trunk airways and the shafts is
2.2 Ns²m^-8. The resistances of splits A and B are 0.5 Ns²m^-8 and 0.8 Ns²m^-8 respectively. A
regulator of size 2.0 m² is placed in split A. Considering the fan generates a pressure of 1000 Pa,
the air flow in m3/s in split B is ________

A mine fan running at 300 rpm delivers 150 m³/s of air at a pressure of 900 Pa. Fan and motor
efficiencies are 75% and 90% respectively. If the fan speed is reduced to 250 rpm, the saving in
electric power input to the motor in kW is ________

Subsidence profile function, s(x), along the lateral cross-section over a flat longwall panel is given
as

where x = distance (m) from the inflection point and D = depth (m) of the seam. Considering that
the inflection point lies vertically above the edge of the panel, the angle of draw in degrees for a
depth of 250 m is ________

A goaf void of 250 m³ is filled in 3 hours by hydraulic sand stowing method. Density of the sand is
2.6 tonne/m³. If the filling factor of goaf void is 0.9 and sand to water ratio in the stowing mixture
is 1.0 tonne to 1.1 m³ , the stowing rate in m³/h is ________

A single-acting reciprocating pump delivers 0.018 m³/s of water when running at 45 cycles per
minute. The piston diameter is 300 mm and stroke length is 400 mm. The volumetric efficiency of
the pump in % is ________

Match the method of mining with strength of orebody, type of support and orebody geometry.

A mine air sample contains CH₄, CO, H₂, N₂ and O₂. The mine air analysis using Haldane apparatus
gives the following results expressed in percentage of total sample volume.

The percentage of CH₄ in the sample analysed is ________

The initial investment for a small scale mining project is Rs. 5.0 crore. Annual cash inflow for a life
period of 4 years is given below.

The net present value of the project at an annual discount rate of 10% in Rs. crore is ________

Given the following linear programming problem,

the corner point feasible solution in terms of (x₁,x₂) is

The 3-period torque-time diagram of a statically balanced hoist is shown in the figure.

The rms torque for the motor in kN-m is ________

Airborne PM₁₀ concentration in a residential area is monitored for 24 hours by a respirable dust
sampler. Initial and final weights of the filter paper are 2.3125 g and 2.6996 g respectively. The
average airflow rate during sampling is 1.2 m³/min. The PM₁₀ concentration of the area in
μg m^-3 is ______

The assignment problem given requires four different jobs to be done on four different machines.

The minimum cost of assignment is ________

Acceleration of a particle moving in a straight line is expressed by

where, s denotes distance (m) and t, time (s). At time t = 0, the distance and velocity of the particle
are 0 m and 3 m/s respectively. The distance travelled by the particle in m after 3 s is

Rock bolts have length L = (150 + X) cm, where X is a random variable with probability density
function

If 95% of the bolt lengths (L) lie in the interval 150 - c cm to 150 + c cm, the value of c is _______

The properties for a bivariate distribution of two random variables X and Y are given below.

E(X) = 24, E(Y ) = 36, E(X² ) = 702, E(Y² ) =1524, E(XY) =1004

The correlation coefficient between X and Y is ________

Biaxial stresses at a point inside a pillar are shown in the figure.

The magnitude of the maximum shear stress in MPa and its direction with the x-axis in degrees at
the same point respectively are

A circular tunnel is constructed in a biaxial far field stress (vertical stress p₀ and horizontal stress
Kp₀ ) as shown in the figure.

If the ratio of the tangential stress measured at the boundary points A and B is 3:1, the value of K is
_______

(Important : you should answer only the numeric value)

Peak particle velocity (PPV) at points A and B are measured for a blast pattern as shown in the
figure.

where D (in m) denotes the distance from the blast row to the measuring point and Q (in kg),
maximum charge per delay. The site constants K and n respectively are

Copper ore of average grade 0.65% is mined, milled, smelted and then refined. The following
information is available:

The amount of refined copper obtained per tonne of ore in kg is

The ratio of horizontal to vertical in-situ stresses, K, at a mine field varies with depth, D (in m) as

If the unit weight of overburden rock is 25 kN/m³, the horizontal stress in MPa at a depth of 400 m
is ________

A coal seam of 2 m thickness is extracted by a longwall retreating panel with face length of 120 m.
Web depth of the shearer is 0.6 m. Average manpower in the longwall face in a shift is 20. The
specific gravity of in-situ coal is 1.4. If the shearer makes 4 full-face cuts in 3 shifts, the face OMS
in tonne is ________

A loaded dumper of total mass 75 tonne, having wheel diameter 1250 mm, runs on a haul road
which offers an average specific rolling resistance of 260 N/tonne. The engine develops an axle
torque of 15 kN-m. The starting acceleration of the dumper in m/s² is ________