List of top Questions asked in GATE MN

A truss PQR carries a vertical load of \(10\ \text{kN}\) at Q as shown. The force in member PR, in \(kN\), is . (rounded off to two decimal places)

Two blocks P and Q weighing \(100\ \text{kN}\) and \(200\ \text{kN}\), respectively, are connected by a string passing through a massless and frictionless pulley as shown. The friction coefficient between blocks P and Q is 0.4, and that between block Q and surface is 0.3. The minimum force, F, in kN, required to pull the block Q, is . (answer in integer)

Following observations were taken using a Tacheometer with staff held vertical. The additive and multiplying constants of the instrument are 0 and 100, respectively. The reduced level (RL) of the staff station R, in \(m\), is . (rounded off to two decimal places)

Instrument station	Staff station	Staff reading (m)	Vertical angle	Remarks
P	Q	1.4, 2.7, 3.9	7°	RL of Q = 102 m
P	R	2.1, 2.8, 3.6	5°

In a uniaxial compressive strength test, a \(120\ \Omega\) strain gauge of gauge factor 2.0 is pasted on the rock sample as shown. At the end of the test, the change in resistance of the strain gauge is \(0.5\ \Omega\). The longitudinal deformation of the sample, in \(mm\), is . (rounded off to two decimal places)

A bord and pillar panel has 24 developed pillars of size \(40\ \text{m} \times 40\ \text{m}\) (centre to centre) under extraction. The following information is given:
Gallery width = \(4\ \text{m}\)
Extraction height = \(3\ \text{m}\)
Extraction ratio during depillaring = 80%
Specific gravity of coal = 1.4
Incubation period = 6 months
Average working days per month = 25
In order to extract the panel within the incubation period, the minimum rate of production, in tonne per day, is . (rounded off to one decimal place)

The information for a dragline operation is given:
Bucket capacity: 20 \( \text{m}^3 \)
Bucket fill factor: 0.9
Digging and filling time: 20 s
Swinging (to and fro) time: 32 s
Dumping time: 10 s
Dragline utilization: 90%
The output of the dragline, in \( \text{m}^3\,\text{h}^{-1} \), is . (rounded off to one decimal place)

A coal seam of \(2.4\ \text{m}\) thickness is mined with a DERD shearer at a cutting speed of \(0.6\ \text{km/h}\). The web depth of the cut is \(0.5\ \text{m}\). The average cross-sectional area of coal on the AFC during transportation is \(0.24\ \text{m}^2\). For the evacuation of cut coal from the face with 10% spillage, the required minimum velocity of the AFC, in \(m\ s^{-1}\), is . (rounded off to two decimal places)

A regular shaped cut and fill stope is shown. Pillars of size \(4\ \text{m} \times 4\ \text{m}\) are left at an interval of \(13\ \text{m}\) along the length of the stope. If the density of the mined ore is \(2.5\ \text{tonne/m}^3\), and slices are extracted to the full stope width, the total tonnage of ore recovered from the 1st slice of the stope is \(\times 10^3\). (rounded off to one decimal place)

A turbine pump is designed to generate water head of 60 m. The impeller speed of the pump is 2000 rpm and the manometric efficiency is 70%. Neglecting the impeller blade curvature, the impeller diameter of the pump, in cm, is . (rounded off to two decimal places)

In a bench blasting, as shown, 49 kg of explosive is put in each hole. The detonation time of holes, in millisecond, and the associated scale distance (SD) vs. peak particle velocity (PPV) plot for the given blast pattern is shown.

The PPV at a distance of 100 m, in \( \text{mm}\,\text{s}^{-1} \), is . (rounded off to two decimal places)

A rake of wagons, with inter-wagon gap of 100 cm, is moving at a speed of 0.4 km per hour under a silo loading system. The dimensions of the wagon are 8 m (L) \(\times\) 3 m (W) \(\times\) 3 m (H). The silo stops discharging the material between the wagons. Considering the fill factor of the wagon as 0.95 and the bulk density of coal as 1.2 tonne per cubic meter, the loading rate of the silo, in tonne per hour, is . (rounded off to nearest integer)

A shovel costing (P) Rs. 20 crores has a salvage value (S) of Rs. 2 crores with a useful life (n) of 10 years. The annual depreciation is evaluated using the declining balance method as given by
\[ \text{Depreciation rate} = 1 - (S/P)^{1/n} \]
The depreciated cost of the shovel, in crores, in its 2nd year is Rs. . (rounded off to two decimal places)

A plug dam is to be constructed in a mine gallery of size 3.5 m \(\times\) 2.5 m. The interfacial shear strength between the surrounding rock and plug dam is 1.0 MPa. The minimum thickness of the dam, in m, to withstand a water pressure of 10.0 MPa, is . (rounded off to two decimal places)

A main mechanical ventilator installed for an underground mine develops a pressure of 25 mm wg. A natural ventilation pressure (NVP) of 15 mm wg acting in the mine aids the ventilator, and a total 500 \( \text{m}^3\,\text{min}^{-1} \) of air is circulated in the mine. Considering the same NVP aiding the ventilator, the pressure required, in mm wg, to be generated by the ventilator to circulate 1000 \( \text{m}^3\,\text{min}^{-1} \) of air, is . (answer in integer)

An economic block model along with extraction sequence is shown. The numbers given at the centre of the block represent the year of extraction, and that at the corners represent the block economic value in Rs. (lakhs). If the discount rate is 10%, the net present value (NPV), in lakhs, is Rs. . (rounded off to two decimal place)

Dust particles from a blasting operation rise up in the atmosphere to a height of 500 m. The viscosity of air is \( 1.80 \times 10^{-5}\ \text{kg}\,\text{m}^{-1}\,\text{s}^{-1} \). Assume the particles have quiescent settling (no turbulence) in atmosphere. Neglecting air density, the settling time, in days, of a dust particle of 2.5 \(\mu\)m diameter and 3600 \( \text{kg}\,\text{m}^{-3} \) density is . (rounded off to two decimal places)

In a biochemical oxygen demand (BOD) test, 15 ml of wastewater sample was diluted with distilled water to completely fill a 300 ml BOD bottle and incubated at 20 \(^{\circ}\text{C}\) for 5 days. The dissolved oxygen (DO) level before and after incubation are 9.2 mg liter\(^{-1}\) and 4.4 mg liter\(^{-1}\), respectively. The BOD of the sample, in mg liter\(^{-1}\), is . (answer in integer)

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

The borehole data for resource estimation for an iron ore deposit are shown.

The average grade of the deposit, in %, is . (rounded off to two decimal places)

The in-situ stresses are determined by the Flat-jack method by making three slots (P, Q, and R) on the wall (ABCD) of a mine gallery as shown. The in-situ stresses \( \sigma_P \), \( \sigma_Q \), and \( \sigma_R \) are determined at slot-P, slot-Q, and slot-R, respectively. If \( \sigma_P > \sigma_Q \), and \( \sigma_R = 0 \), the shear stress on the wall is

The observations from a correlation survey are shown. If the coordinates of points C and D are (East: 375 m, North: 1120 m) and (East: 376 m, North: 1121 m), respectively, the whole circle bearing of the line EF is

CD = 3.0 m
CE = 4.2 m
\( \angle DEC = 1'' \)
\( \angle DEF = 170^{\circ} 20' \)

A closed-circuit self-contained breathing apparatus (SCBA) contains 2 liters of \(O_2\) at 200 bar. If a miner uses \(O_2\) at a rate of 2 liters \(\text{min}^{-1}\), the maximum duration that the apparatus can supply \(O_2\), in min, is . (answer in integer)

Using linear regression (least squares), the best-fit line for the given dataset is \(y = 2.2x + 2.3\). Given the residual sum of squares is 25.8, the coefficient of determination \((r^2)\) is . (rounded off to two decimal places)

x	2	3	4	5
y	8	9	7	16

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	800	8
S2	850	9
S3	920	10
S4	1000	11

Match the type of rock with its metamorphic form.

Igneous/Sedimentary rock	Metamorphic rock
(P) Shale	(1) Gneiss
(Q) Limestone	(2) Quartzite
(R) Granite	(3) Marble
(S) Sandstone	(4) Slate