List of top Questions asked in GATE Mining Engineering

Magnitude of error in the determination of the integral, I using Simpson's 1/3 rule, taking step length as 1.0 is
\(I=∫^3_1(x^3+6)\) dx

Matrix A= \(\begin{bmatrix} 1 & 4 & 3\\ 5 & 2 & 1\\6&4&3 \end{bmatrix}\), and B=A-A^T, then B is 

Four identical districts of a mine are ventilated with a quantity of 3500 m³/min at a fan drift pressure of 1.15 kPa. When one of the districts is sealed off, the change in resultant resistance is 0.072 Ns²m^-8. If the fan is stopped, keeping a district sealed, the quantity through the mine becomes 850 m³/min. The natural ventilation pressure in Pa, is

The roof convergence data for 30 days at a monitoring station in a coal mine gallery is given.

Day	Convergence reading (mm)
0	0
5	4.7
10	11.3
16	19.6
22	28.8
30	34.8

The management decides on a Trigger Action Response Plan (TARP) if the following two premises occur simultaneously.
Premise 1: Rate of convergence exceeds 1.5 mm/day between two consecutive measurements. 
Premise 2: Rate of cumulative increase in convergence exceeds 1.0 mm/day. 
Identify the day on which TARP is enforced in that gallery. 

In a closed traverse, ABC, the bearings of two lines AB and BC are given.

Line	Length (m)	Bearing
AB	100	90°
BC	120	150°

The length, in m and bearing of line CA, in degree, respectively, are

A rectangular development heading of dimension 3 m x 2.8 m is to be blasted with holes of 2.4 m in length. If the pull factor is 0.95 and swell factor is 1.20, the volume of blasted rock per round, in m³, is_____.(round off up to 2 decimals)

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

The combined sound pressure level measured at a point in a production bench due to one dumper and one shovel is 95 dB(A). If the sound pressure level of shovel alone is 90 dB(A), the sound pressure level of the dumper alone, in dB(A), at the same point is_____.(round off up to 2 decimals)

For a circular path of radius 300 m, the super elevation is restricted to 0.1 m for a width of 1.6 m. The maximum speed, in m/s, of vehicle to avoid overturn is_____.(round off up to 2 decimals)

A scanline survey between points A and B of a rock mass is shown. Consider
RQD =100×(0.12+1)×exp(−0.1λ), 
where, λ is the frequency of discontinuity per m. The RQD of the rock mass is_____. (round off up to 2 decimals) 

The void ratio of an unconsolidated soil heap of volume 1000 m³ is 1.0. If the soil heap is consolidated to a volume of 800 m3, the corresponding void ratio is_____.(round off up to 2 decimals)

In a VCR stope, blast holes of 165 mm diameter are drilled. For the blast hole to behave as a spherical charge, the maximum charge length, in m, is____.(round off up to 2 decimals)

An explosive with a density of 1.2 g/cm³ has a heat of explosion equal to 900 cal/g. If the heat of explosion of ANFO with density of 0.8 g/cm³ is 950 cal/g, the bulk strength of the explosive relative to ANFO is_____.(round off up to 2 decimals)

A coal washery discharges 300 m³/day of contaminated water in a stream having a flow rate of 0.04 m³/s. The DO level of the stream and the contaminated water are 8.5 mg/L and 4 mg/L, respectively. Neglecting the impact of temperature, the resultant DO, in mg/L, of the stream just after mixing is_____.(round off up to 2 decimals)

The function of District Mineral Foundation established by state governments in India, is to

The magnitude of the curl of the vector F = 2xi + 3yj + 4zk, is

The percentage Fe and corresponding net value for an iron ore mine is given below

Fe (%)	Net value (INR per tonne)
58	4000
62	4500

Assuming net value versus grade curve to be a straight line, and mining cost of waste is INR 1000 /m³; the correct representation of stripping ratio, SR (m³/tonne) versus Fe (%) grade curve is

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

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

Match the following features with the corresponding symbols

	Feature in mine plan		Symbol
P	shaft	1
Q	staple shaft	2
R	Abandoned shaft	3
S	Abandoned staple shaft	4

The ore that is NOT used for commercial extraction of metal is

The spherical semivariogram model (γ(h)) is represented by the following expression, where h is the lag distance.
\(y(h) =   \begin{cases}  C_0,\\ C_0+(C-C_0)[1.5\frac{h}{a}-0.5(\frac{h}{a})^3], &\\C,  \end{cases}\)
The parameters C_o, C and a are respectively known as

If the major (σ₁) and minor (σ₃) principal stresses for a rock element have a relationship as σ₃ = −\(\frac{1}{2}\) σ₁, the maximum shear stress is expressed by

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

In an underground coal mine, two fatalities and three serious bodily injuries occurred during the year 2022. The average daily employment is 1100 and annual working days is 300. The severity index as per DGMS guideline for the mine is

A rectangular mine airway of 2.0 m width and 2.5 m height has a bend with deflection of π/4 radian. If the radius of curvature of the bend is 4.0 m, the shock factor of the bend is (round off to three decimals)