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Type:ALLMCQNATMSQ

General Aptitude(10)Engineering Mathematics(10)Mining Geology, Mine Development and Surveying(8)Geomechanics and Ground Control(14)Mining Methods and Machinery(7)Surface Environment, Mine Ventilation and Underground Hazards(9)Mineral Economics, Mine Planning, Systems Engineering(7)

General Aptitude

10 Questions

GATE→2023→General Aptitude→Verbal Ability

Q1

MCQ[1 Mark]

The line ran ________ the page, right through the centre, and divided the page into two.

(A)

across

(B)

of

(C)

between

(D)

about

Explanation

GATE→2023→General Aptitude→Verbal Ability

Q2

MCQ[1 Mark]

Kind : ________ :: Often : Seldom (By word meaning)

(A)

Cruel

(B)

Variety

(C)

Type

(D)

Kindred

Explanation

GATE→2023→General Aptitude→Quantitative Aptitude

Q3

MCQ[1 Mark]

In how many ways can cells in a $3\times3$ grid be shaded, such that each row and each column have exactly one shaded cell? An example of one valid shading is shown.

(A)

2

(B)

9

(C)

3

(D)

6

Explanation

GATE→2023→General Aptitude→Quantitative Aptitude

Q4

MCQ[1 Mark]

There are 4 red, 5 green, and 6 blue balls inside a box. If N number of balls are picked simultaneously, what is the smallest value of N that guarantees there will be at least two balls of the same colour?

(A)

4

(B)

15

(C)

5

(D)

2

Explanation

GATE→2023→General Aptitude→Quantitative Aptitude

Q5

MCQ[1 Mark]

Consider a circle with its centre at the origin (O), as shown. Two operations are allowed on the circle. Operation 1: Scale independently along the x and y axes. Operation 2: Rotation in any direction about the origin. Which figure among the options can be achieved through a combination of these two operations on the given circle?

(A)

A

(B)

B

(C)

C

(D)

D

Explanation

GATE→2023→General Aptitude→Verbal Ability

Q6

MCQ[2 Marks]

Elvesland is a country that has peculiar beliefs and practices... Based only on the information provided above, which one of the following sets of statement(s) can be logically inferred with certainty? (i) In Elvesland, one always declares one's love by gifting a white flower. (ii) In Elvesland, all emotions are declared by gifting flowers. (iii) In Elvesland, sometimes one expresses one's anger by gifting a flower that is not yellow. (iv) In Elvesland, sometimes one expresses one's love by gifting a white flower.

(A)

only (ii)

(B)

(i), (ii) and (iii)

(C)

(i), (iii) and (iv)

(D)

only (iv)

Explanation

GATE→2023→General Aptitude→Quantitative Aptitude

Q7

MCQ[2 Marks]

Three husband-wife pairs are to be seated at a circular table that has six identical chairs. Seating arrangements are defined only by the relative position of the people. How many seating arrangements are possible such that every husband sits next to his wife?

(A)

16

(B)

4

(C)

120

(D)

720

Explanation

GATE→2023→General Aptitude→Verbal Ability

Q8

MCQ[2 Marks]

Based only on the following passage, which one of the options can be inferred with certainty? [Excerpt from These Hills Called Home by Temsula Ao]

(A)

The mother was embarrassed about her daughter's singing at home.

(B)

The mother's feelings about her daughter's singing at home were only of annoyance.

(C)

The mother was not sure if Apenyo had inherited her love of singing from her father.

(D)

When Apenyo hummed at home, her mother tended to become thoughtful.

Explanation

GATE→2023→General Aptitude→Quantitative Aptitude

Q9

MCQ[2 Marks]

If x satisfies the equation $4^{8^{x}}=256$, then x is equal to

(A)

\frac{1}{2}

(B)

\log_{16}8

(C)

\frac{2}{3}

(D)

\log_{4}8

Explanation

GATE→2023→General Aptitude→Quantitative Aptitude

Q10

MCQ[2 Marks]

Consider a spherical globe rotating about an axis passing through its poles. There are three points P, Q, and R situated respectively on the equator, the north pole, and midway between the equator and the north pole in the northern hemisphere. Let P, Q, and R move with speeds $v_{P}$, $v_{Q}$, and $v_{R}$, respectively. Which one of the following options is CORRECT?

(A)

v_{P}<v_{R}<v_{Q}

(B)

v_{P}<v_{Q}<v_{R}

(C)

v_{P}>v_{R}>v_{Q}

(D)

v_{P}=v_{R}\ne v_{Q}

Explanation

Engineering Mathematics

10 Questions

GATE→2023→Engineering Mathematics→Vector Calculus

Q11

MCQ[1 Mark]

Given two vectors $\vec{A}=3\hat{i}+2\hat{j}$ and $\vec{B}=\hat{i}+\hat{j}$, the magnitude of projection of $\vec{A}$ along $\vec{B}$ is

(A)

\frac{5}{\sqrt{2}}

(B)

\frac{5}{\sqrt{13}}

(C)

\frac{5}{\sqrt{26}}

(D)

5

Explanation

GATE→2023→Engineering Mathematics→Probability and Statistics

Q12

MCQ[1 Mark]

Given two random variables X and Y, the expected value $E(3X-5Y)$ is

(A)

3E(X)-5E(Y)

(B)

3E(X)+5E(Y)

(C)

3E(X)-5E(Y)-15E(XY)

(D)

E(X)-E(Y)-E(XY)

Explanation

GATE→2023→Engineering Mathematics→Calculus

Q13

MCQ[1 Mark]

$x$ and $y$ are functions of independent variables $r$ and $\theta$ as given below: $x=r~cos~\theta$, $y=r~sin~\theta$. The Jacobian of $x, y$ is

(A)

\tan~\theta

(B)

r^{2}\sin~\theta~\cos~\theta

(C)

r^{2}

(D)

r

Explanation

GATE→2023→Engineering Mathematics→Linear Algebra

Q14

MCQ[1 Mark]

Matrix A is negative definite. Which one of the following is NOT the correct statement about the matrix?

(A)

It is symmetric.

(B)

Determinant of A is always less than zero.

(C)

All the eigen values are less than zero.

(D)

Trace of A is always less than zero.

Explanation

GATE→2023→Engineering Mathematics→Probability and Statistics

Q15

MCQ[2 Marks]

In a quality control process of coal supplied to a thermal plant, the 3-sigma control limits for fixed carbon (FC) are defined by $40\%\pm15\%$. The process is termed "out of control" if: Rule 1: 4 out of 5 successive values... Rule 2: Any one value crosses any of the 3-sigma control limits. For the continuous data: 49, 51, 56, 20, 46, 48, 47, 49, 45, 41, 42, 40, the process is

(A)

out of control because of both rules 1 & 2.

(B)

out of control because of rule 1 only.

(C)

out of control because of rule 2 only.

(D)

not out of control.

Explanation

GATE→2023→Engineering Mathematics→Calculus

Q16

MCQ[2 Marks]

The evaluation of the integral $I=\int\frac{e^{x-1}+x^{e-1}}{e^{x}+x^{e}}dx$ yields

(A)

ln(e^{x}+x^{e})

(B)

\frac{1}{e}ln(e^{x}-x^{e})

(C)

\frac{1}{e}ln(e^{x}+x^{e})

(D)

ln(e^{x}-x^{e})

Explanation

GATE→2023→Engineering Mathematics→Calculus

Q17

MCQ[2 Marks]

Given the function $f(x)=|x|+|x-1|$. For all the real values of x, which one of the following statements is CORRECT?

(A)

The function is continuous and not differentiable at one point.

(B)

The function is continuous but not differentiable at two points.

(C)

The function is discontinuous.

(D)

The function is continuous and differentiable.

Explanation

GATE→2023→Engineering Mathematics→Linear Algebra

Q18

MCQ[2 Marks]

The slope and intercept values of three linear equations are given... The above system of equations has

(A)

Trivial solution.

(B)

A single solution.

(C)

Multiple solutions.

(D)

No Solution.

Explanation

GATE→2023→Engineering Mathematics→Probability and Statistics

Q19

MCQ[2 Marks]

A regression line is constructed between shovel production rate and shovel swing angle for 50 observations as shown below... If residuals are normally distributed and significance tests of the parameters are conducted at 0.05 significance level, the true statement is

(A)

Both intercept and slope are significant.

(B)

Intercept is significant but slope is not significant.

(C)

Intercept is not significant but slope is significant.

(D)

Both intercept and slope are not significant.

Explanation

GATE→2023→Engineering Mathematics→Probability and Statistics

Q20

NAT[2 Marks]

The time between consecutive accidents in days in an underground coal mine in a year are as follows: 10, 15, 6, 18, 12, 14, 16, 9, 21, 15, 26, 18, 22, 25, 13. Assuming exponential distribution, the probability that there will be no accident over a 10-day period is [rounded off to 2 decimal places]

Explanation

Mining Geology, Mine Development and Surveying

8 Questions

GATE→2023→Mining Geology, Mine Development and Surveying→Mining Geology

Q21

MCQ[1 Mark]

The fault pattern shown in the figure is a case of

(A)

Normal fault.

(B)

Reverse fault.

(C)

Strike slip fault.

(D)

Oblique slip fault.

Explanation

GATE→2023→Mining Geology, Mine Development and Surveying→Mine Development

Q22

MCQ[1 Mark]

The blast pattern of a coal face shown in the figure represents

(A)

burn cut.

(B)

pyramid cut.

(C)

wedge cut.

(D)

drag cut.

Explanation

GATE→2023→Mining Geology, Mine Development and Surveying→Mine Surveying

Q23

MCQ[1 Mark]

Match the following items with their respective contours

(A)

P->1, Q->3, R->2

(B)

P->3, Q->1, R->2

(C)

P->2, Q->3, R->1

(D)

P->2; Q->1; R->3

Explanation

GATE→2023→Mining Geology, Mine Development and Surveying→Mine Surveying

Q24

MCQ[1 Mark]

In an astronomical survey at a given station, the pole star is located at an angle of $27^{\circ}$ from the horizon. The latitude of the survey station in degrees is

(A)

27^{\circ}N

(B)

63^{\circ}N

(C)

27^{\circ}S

(D)

63^{\circ}S

Explanation

GATE→2023→Mining Geology, Mine Development and Surveying→Mine Surveying

Q25

MCQ[1 Mark]

The position tracking of a point by GPS is based on the technique of

(A)

Graphical resection.

(B)

Analytical resection.

(C)

Triangulation.

(D)

Trilateration.

Explanation

GATE→2023→Mining Geology, Mine Development and Surveying→Mine Surveying

Q26

MCQ[2 Marks]

Match the following devices with their intended applications.

(A)

P->1; Q->2; R->3; S->4

(B)

P->4; Q->3; R->1; S->2

(C)

P->3; Q->4; R->2; S->1

(D)

P->4; Q->3; R->2; S->1

Explanation

GATE→2023→Mining Geology, Mine Development and Surveying→Mine Surveying

Q27

NAT[2 Marks]

Coordinate of two points A and B are (E 0 m, N 200 m) and (E 300 m, N 200 m), respectively. The bearing of two lines AO and BO are $67^{\circ}$ and $35^{\circ}$, respectively. The easting of point O, in m, is [rounded off to 2 decimal places]

Explanation

GATE→2023→Mining Geology, Mine Development and Surveying→Mine Development

Q28

NAT[2 Marks]

A surface mine blast pattern has spacing 4 m and burden 3 m. The diameter of the drill hole is 110 mm. The drilling length is 8.8 m including subgrade of 10%. The bulk explosive density is $900\text{ kg}/\text{m}^{3}$. If the powder factor is $2.5\text{ m}^{3}/\text{kg}$, the charge length in m is [rounded off to 2 decimal places]

Explanation

Geomechanics and Ground Control

14 Questions

GATE→2023→Geomechanics and Ground Control→Engineering Mechanics

Q29

MCQ[1 Mark]

A shear stress $\tau$ acts tangentially to the upper surface of a block and causes a small deformation $\Delta w$ as shown. The shear strain is calculated by

(A)

\frac{\Delta w}{w}

(B)

\frac{\Delta w}{h}

(C)

\frac{2\Delta w}{w}

(D)

\frac{2\Delta w}{h}

Explanation

GATE→2023→Geomechanics and Ground Control→Geomechanics

Q30

MCQ[1 Mark]

Axial stress versus axial strain curves for two test results of a porous rock from triaxial undrained compression tests are shown in the figure. The pore pressure for the curve B can be the best explained by

(A)

U < 0

(B)

U = 0

(C)

U > 10

(D)

0 < U < 10

Explanation

GATE→2023→Geomechanics and Ground Control→Geomechanics

Q31

NAT[1 Mark]

A slope stability radar shows that the position of a point P in a mine dump shifts from (200, 700, -60) m to (200.05, 700.1, -60.75) m over a time $\Delta t$. The net displacement in cm of the point P is [rounded off to 2 decimal places]

Explanation

GATE→2023→Geomechanics and Ground Control→Geomechanics

Q32

NAT[1 Mark]

A Mohr-Coulomb failure envelop of a sandstone rock is given as $\sigma_{1}=30+3.5\sigma_{3}$ where $\sigma_{1}$ and $\sigma_{3}$, measured in MPa, are the major and minor principal stresses respectively. The angle ofキュリティ the failure plane with the $\sigma_{3}$ axis in degree is [rounded off to 1 decimal place]

Explanation

GATE→2023→Geomechanics and Ground Control→Geomechanics

Q33

NAT[1 Mark]

A punch hole of diameter 10 mm is to be made in a 5 mm thick rock plate as shown. If the yield strength of rock plate is 25 MPa, the punch force P required in kN is [rounded off to 1 decimal place]

Explanation

GATE→2023→Geomechanics and Ground Control→Subsidence

Q34

NAT[1 Mark]

Critical subsidence has occurred on the surface due to mining of a flat longwall panel at a depth of 200 m. The width of the panel is 150 m. The maximum width of the panel in m that can be mined at a depth of 300 m, to reach critical subsidence is [rounded off to 1 decimal place]

Explanation

GATE→2023→Geomechanics and Ground Control→Geomechanics

Q35

MCQ[2 Marks]

A tunnel of diameter 8 m is to be driven in a rock mass having quality index, Q of 1.0. Assume the excavation support ratio (ESR) of the tunnel is 1.0. The support requirement of the tunnel wall using fibre reinforced shotcrete (based on the chart prepared by Grimstad and Barton, 1993) is

(A)

A

(B)

B

(C)

Shotcrete of thickness 9-12 cm, bolt length of 3.0-3.2 m

(D)

D

Explanation

GATE→2023→Geomechanics and Ground Control→Geomechanics

Q36

NAT[2 Marks]

A circular tunnel is developed in a biaxial in situ stress field as shown in the figure. If the ratio between tangential stress at the boundary point A and that at the boundary point B is 2.0, the value of k is [rounded off to 2 decimal places]

Explanation

GATE→2023→Geomechanics and Ground Control→Ground Control

Q37

NAT[2 Marks]

Strength of a rectangular coal pillar in MPa is given by $S_{p}=S_{1}(0.64+0.54\frac{w}{h}-0.18\frac{w^{2}}{lh})$ where w, $l(\ge w)$ and h are width, length and height of the pillar, respectively. A 30 m square pillar is split into two halves as shown. The height of the pillar is 3 m. The ratio of safety factors between one half-pillar and the original square pillar is [rounded off to 2 decimal places]

Explanation

GATE→2023→Geomechanics and Ground Control→Engineering Mechanics

Q38

NAT[2 Marks]

A dozer pushes up a 100 kg spool of cable along a $20^{\circ}$ incline road at a constant velocity as shown in the figure. The coefficient of static friction between the dozer bucket and the spool (Point B) is 0.45, and coefficient of kinetic friction between road and the spool (Point A) is 0.15. Consider the spool only slides up the incline. The maximum normal force in N acting at Point B, is [rounded off to 1 decimal place]

Explanation

GATE→2023→Geomechanics and Ground Control→Geomechanics

Q39

NAT[2 Marks]

Stress waves are sent from the transmitter A to the receiver B through an isotropic and elastic cylindrical rock specimen as shown in the figure. The length of the specimen is 100 mm. The travel time of longitudinal and shear waves are 0.025 ms and 0.04 ms, respectively. The Poisson's ratio of the rock specimen is [rounded off to 2 decimal places]

Explanation

GATE→2023→Geomechanics and Ground Control→Geomechanics

Q40

NAT[2 Marks]

A jointed rock sample is subjected to 20 MPa vertical stress as shown in the figure. The modulus of elasticity of the rock is 10 GPa and the normal stiffness of the joint surface is $5\text{ GPa/m}$. Assuming one-dimensional elastic behaviour of rock and joint, the displacement in mm of the loading surface AB is [rounded off to 1 decimal place]

Explanation

GATE→2023→Geomechanics and Ground Control→Geomechanics

Q41

NAT[2 Marks]

An irregular shaped rock sample of mass 60 g displaces 27 g of brine when submerged in a filled jar. The specific gravity of brine is 1.05. The unit weight of the rock sample in $\text{kN/m}^{3}$ is [rounded off to 2 decimal places]

Explanation

GATE→2023→Geomechanics and Ground Control→Geomechanics

Q42

NAT[2 Marks]

A rock slope is intercepted by a joint plane at an angle $30^{\circ}$ as shown in figure... Unit weight of rock = $20\text{ kN/m}^{3}$, Cohesion of joint = 30 kPa, Friction angle of joint = $22^{\circ}$. The factor of safety of the rock slope to slide along the joint plane is [rounded off to 2 decimal places]

Explanation

Mining Methods and Machinery

7 Questions

GATE→2023→Mining Methods and Machinery→Mining Methods

Q43

MCQ[1 Mark]

A tabular, near-flat ($dip<30^{\circ}$), and less than 2 m thick copper orebody having erratically located grade is to be mined underground. Wall rock and orebody are competent. The most suitable mining method is

(A)

Cut and fill stoping.

(B)

Sub-level stoping.

(C)

Underhand open stoping.

(D)

Breast stoping.

Explanation

GATE→2023→Mining Methods and Machinery→Mining Machinery

Q44

NAT[1 Mark]

A coal seam of 3.0 m height is mined with a double-ended ranging drum shearer (DERDS) for a web depth of 0.5 m. The coal density is $1.4\text{ tonne}/\text{m}^{3}$. If the panel width is 150 m, the production per cycle in tonne is [rounded off to 1 decimal place]

Explanation

GATE→2023→Mining Methods and Machinery→Mining Machinery

Q45

NAT[2 Marks]

Data related to a surface miner operation are given below: Drum width = 3.0 m, Average cutting depth = 20 cm, Average cutting speed = 25 m/min, Length of pit = 500 m, Turning time = 2 min, Truck exchange time = 30 s, Truck capacity = 15 m^3. Considering in situ volume, the production rate of the surface miner in m^3/hr, is [rounded off to 1 decimal place]

Explanation

GATE→2023→Mining Methods and Machinery→Mining Methods

Q46

NAT[2 Marks]

A continuous miner served by two shuttle cars produces $240\text{ tonne/hr}$. The capacity of each shuttle car is 10 tonne. When a single shuttle car operates, the cycle time becomes 4 min. In case one of the shuttle cars is under break-down, the reduction in hourly production from that of two cars in percent is [rounded off to 1 decimal place]

Explanation

GATE→2023→Mining Methods and Machinery→Mining Machinery

Q47

NAT[2 Marks]

An unmanned aerial vehicle (UAV) with payload of 2 kg reaches vertically 100 m in 10 s at uniform velocity. The self-weight of the UAV is 1.2 kg. The power required in lifting in kW is [rounded off to 2 decimal places]

Explanation

GATE→2023→Mining Methods and Machinery→Mining Methods

Q48

NAT[2 Marks]

A mine void of width 20 m, length 50 m and height 30 m is to be filled with mill tailings based cemented paste backfill (CPB). The CPB contains tailings:cement:water as 1.0:0.1:0.2 by weight. The specific gravity of tailings and cement are 2.8 and 2.4 respectively. Assuming 20% of the original volume of water is retained in the final backfill, the amount of cement in tonne required so as to fill the void completely is [rounded off to nearest integer]

Explanation

GATE→2023→Mining Methods and Machinery→Mining Machinery

Q49

NAT[2 Marks]

Data related to a water turbine pump with backward bladed impellers are given below: Impeller diameter = 35 cm, RPM = 1200, Angle of curvature of blade = $30^{\circ}$, Radial velocity of discharge = $2\text{ m/s}$, Manometric efficiency = 0.8. The number of impellers required in the pump to lift water by a height 300 m is [rounded off to higher integer]

Explanation

Surface Environment, Mine Ventilation and Underground Hazards

9 Questions

GATE→2023→Surface Environment, Mine Ventilation and Underground Hazards→Surface Environment

Q50

MCQ[1 Mark]

The reaction products of calcium hydroxide with acidic ferruginous mine water are

(A)

FeO, $Ca^{+}$ and $H^{+}$

(B)

FeO, CaO and $H_{2}O$

(C)

FeH_{3}, $Ca^{3+}$ and $OH^{-}$

(D)

$Fe(OH)_{3}$, $Ca^{2+}$ and H_{2}O

Explanation

GATE→2023→Surface Environment, Mine Ventilation and Underground Hazards→Underground Hazards

Q51

MCQ[1 Mark]

An underground coal mine experienced 5 serious injuries, 15 reportable injuries, and 25 minor injuries during 2020. If the average employment in the mine is 1200, then the total injury rate per 1000 persons employed is

(A)

54.0

(B)

20.83

(C)

37.5

(D)

60.0

Explanation

GATE→2023→Surface Environment, Mine Ventilation and Underground Hazards→Underground Hazards

Q52

MCQ[1 Mark]

As per DGMS guidelines, the risk score in Safety Management Plan for a hazard is computed as

(A)

Consequence \times Exposure

(B)

Consequence \times Exposure \times Probability

(C)

Exposure \times Probability

(D)

Consequence \times Probability

Explanation

GATE→2023→Surface Environment, Mine Ventilation and Underground Hazards→Mine Ventilation

Q53

NAT[1 Mark]

To increase the resistance of a mine roadway by $1.5\text{ Ns}^{2}\text{m}^{-8}$, the size in $\text{m}^{2}$ of the regulator to be installed is [rounded off to 2 decimal places]

Explanation

GATE→2023→Surface Environment, Mine Ventilation and Underground Hazards→Underground Hazards

Q54

NAT[1 Mark]

In a panel with 50 workers, a miner typically consumes $2.5\times10^{-3}\text{ m}^{3}/\text{min}$ of oxygen. The percentage of oxygen in the intake air is 20.95%. To ensure minimum permissible oxygen in the return air as per CMR 2017 the quantity of ventilating air in $\text{m}^{3}/\text{min}$ to be supplied to the panel is [rounded off to 2 decimal places]

Explanation

GATE→2023→Surface Environment, Mine Ventilation and Underground Hazards→Mine Ventilation

Q55

MCQ[2 Marks]

A duct of diameter 0.60 m with an exhausting fan has -97.5 mm wg static pressure behind the fan when the air flow rate is $4.0\text{ m}^{3}/\text{s}$. If an evasee with inlet to outlet area ratio of 1:4 and efficiency 60% is attached to the outlet of the fan, the static pressure of the fan in mm of wg becomes

(A)

-104.26

(B)

- 99.13

(C)

-90.73

(D)

-80.6

Explanation

GATE→2023→Surface Environment, Mine Ventilation and Underground Hazards→Surface Environment

Q56

NAT[2 Marks]

In a sample of groundwater, the concentration of $Ca^{2+}$ is $200\text{ mg/l}$. The corresponding calcium carbonate hardness in $\text{mg/l}$ is [rounded off to 1 decimal place]

Explanation

GATE→2023→Surface Environment, Mine Ventilation and Underground Hazards→Surface Environment

Q57

NAT[2 Marks]

A thermal power station receives coal of calorific value $4000\text{ kcal/kg}$ and uses 7000 tonnes of coal every day. Assuming 860 kcal is the heat equivalent of $1.0\text{ kWh}$, for a thermal efficiency of 40% and electrical efficiency of 85% the power generation per day in MWh is [rounded off to 1 decimal place]

Explanation

GATE→2023→Surface Environment, Mine Ventilation and Underground Hazards→Mine Ventilation

Q58

NAT[2 Marks]

A fan installed in a mine ventilation system circulates $30\text{ m}^{3}/\text{s}$ of air to two districts A and B as shown in Figure below. It is desired to increase the quantity of air by 20% in the district B using a booster fan in it. Assuming that the main fan pressure is unchanged, the pressure of the booster fan, in Pa, is [rounded off to 2 decimal places]

Explanation

Mineral Economics, Mine Planning, Systems Engineering

7 Questions

GATE→2023→Mineral Economics, Mine Planning, Systems Engineering→Systems Engineering

Q59

MCQ[1 Mark]

A linear programming problem is given as: Maximize $Z=4x_{1}+2x_{2}$ Subject to: $2x_{1}-2x_{2}\le20$, $4x_{1}\le80$, $x_{1}\ge0$, $x_{2}\ge0$. The problem has

(A)

Unbounded solution.

(B)

Infeasible solution.

(C)

Multiple optimal solutions.

(D)

Unique optimal solution.

Explanation

GATE→2023→Mineral Economics, Mine Planning, Systems Engineering→Systems Engineering

Q60

MCQ[1 Mark]

In project scheduling techniques, the CORRECT statement is

(A)

Both CPM and PERT are deterministic.

(B)

Both CPM and PERT are probabilistic.

(C)

CPM is deterministic and PERT is probabilistic.

(D)

CPM is probabilistic and PERT is deterministic.

Explanation

GATE→2023→Mineral Economics, Mine Planning, Systems Engineering→Mineral Economics

Q61

NAT[1 Mark]

The average ore grade of a copper deposit is 0.9%. The recovery of the metal after processing, smelting and refining is 85%. If the selling price of refined copper is Rs $640/kg$, the sale value in Rs. from mining one tonne of ore is [rounded off to 1 decimal place]

Explanation

GATE→2023→Mineral Economics, Mine Planning, Systems Engineering→Systems Engineering

Q62

NAT[2 Marks]

The reliability function of a pump is given as $R(t)=exp[-(\frac{t}{1000})^{0.5}]$ where t stands for time in years. If the pump comes with a six-month warranty, the number of years for the pump to attain a reliability of 0.9 is [rounded off to 2 decimal places]

Explanation

GATE→2023→Mineral Economics, Mine Planning, Systems Engineering→Systems Engineering

Q63

NAT[2 Marks]

A coal company has three mines which transport coal to four washeries. The daily production from each mine, the demand at each washery and unit transportation cost from each mine to each washery are given in table... The cost of initial basic feasible solution using Vogel's approximation method is [rounded off to 1 decimal place]

Explanation

GATE→2023→Mineral Economics, Mine Planning, Systems Engineering→Systems Engineering

Q64

NAT[2 Marks]

A workshop has four tasks and equal number of machines to perform the tasks. Each of the machines can perform only one of the four tasks. The estimated cost at each of the machines to complete each task is given in table... The total cost of optimal assignment is [rounded off to 1 decimal place]

Explanation

GATE→2023→Mineral Economics, Mine Planning, Systems Engineering→Mineral Economics

Q65

NAT[2 Marks]

A mining company makes an initial investment of Rs 200 crore on a project. The following data are available: Production life: 3 years; Year wise production after gestation period (Mtonne): 1.0, 2.0, and 1.0; Stripping ratio: $1.5\text{ m}^{3}/\text{tonne}$; Selling price of ore: Rs. 2000 per tonne; Ore mining cost: Rs. 500 per tonne; Waste mining cost: Rs. 500 per $\text{m}^{3}$; Discount rate: 10%. By ignoring any other cash-flows, if the NPV of the project becomes Rs. 5.367 crore, the gestation period of the project, in years, is [rounded off to the nearest integer]

Explanation