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

General Aptitude

10 Questions

GATE→2026→General Aptitude→Verbal Ability

Q1

MCQ[1 Mark]

Suresh said, "I did it yesterday." Which one of the following options is the correct form of this sentence in indirect speech?

(A)

Suresh said that I did it yesterday.

(B)

Suresh says I did it yesterday.

(C)

Suresh says that he did it the day before.

(D)

Suresh said that he had done it the day before.

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q2

MCQ[1 Mark]

To continue the sequence of tiles shown, the tile indicated by the question mark should be

(A)

A

(B)

B

(C)

C

(D)

D

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q3

MCQ[1 Mark]

Consider an art gallery whose walkways are shown as lines in the diagram. A black dot represents a junction of two walkways. A guard may be placed at a junction to watch over the walkways that join at that junction. The minimum number of guards needed to watch all the walkways is

(A)

2

(B)

3

(C)

4

(D)

5

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q4

MCQ[1 Mark]

The 2nd of June is a Thursday in a certain year. Which day of the week is the 3rd of July in that year?

(A)

Thursday

(B)

Friday

(C)

Saturday

(D)

Sunday

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q5

MCQ[1 Mark]

A coin with heads facing up is shown as H and a coin with tails facing up is shown as T. Six coins are placed in the Starting Arrangement (H H H T T T). The minimum number of steps needed to go from the Starting Arrangement to the Final Arrangement (T T T H H H) is

(A)

3

(B)

6

(C)

9

(D)

12

Explanation

GATE→2026→General Aptitude→Verbal Ability

Q6

MCQ[2 Marks]

Exacerbate : Mitigate :: Choose the option with the correct pair of words to fill the blank.

(A)

Aggravate : Alleviate

(B)

Alleviate : Precipitate

(C)

Aggravate : Precipitate

(D)

Emancipate : Exonerate

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q7

MCQ[2 Marks]

A paper shown in Panel I is folded along the dashed lines to construct a cube. Referring to cubes shown in Panel II, which one of the options is correct?

(A)

Only (i) can correspond to the unfolded cube in Panel I.

(B)

Only (ii) can correspond to the unfolded cube in Panel I.

(C)

Both (i) and (ii) can correspond to the unfolded cube in Panel I.

(D)

Neither (i) nor (ii) can correspond to the unfolded cube in Panel I.

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q8

MCQ[2 Marks]

In a population, patients who have high cholesterol also have high blood-pressure (BP). Some patients with high BP also have diabetes. There are no patients who have both high cholesterol and diabetes. Furthermore, 1) total patients with at least one condition = 75, 2) high cholesterol = 10, 3) high BP = 45, 4) only high BP and no other conditions = 20. The number of patients who have both diabetes and high BP is

(A)

0

(B)

15

(C)

20

(D)

10

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q9

MCQ[2 Marks]

Four people P, Q, R, and S, of different ages, make the following observations. P: I am younger than S. Q: I am neither the youngest nor the oldest. R: P is older than me. Based on these observations, the youngest person is

(A)

P

(B)

Q

(C)

R

(D)

S

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q10

MCQ[2 Marks]

Circles $C_1$, $C_2$, and $C_3$, with centers $O_1$, $O_2$, and $O_3$, and radii $r_1$, $r_2$, and $r_3$, respectively, touch each other as shown. Given $r_1=2$ cm, $r_2=1$ cm and the angle $\angle O_1O_3O_2$ is $90^{\circ}$, $r_3=$ cm.

(A)

\frac{1}{2}(-3+\sqrt{17})

(B)

\frac{1}{2}(3+\sqrt{17})

(C)

\frac{1}{2}(-2+\sqrt{17})

(D)

\frac{1}{2}(-3+2\sqrt{17})

Explanation

Engineering Mathematics

9 Questions

GATE→2026→Engineering Mathematics→Linear Algebra

Q11

MCQ[1 Mark]

If $I$ is an identity matrix, the polynomial equation that satisfies the Cayley-Hamilton theorem for the matrix $P = \begin{bmatrix} 2 & 1 \\ 0 & 3 \end{bmatrix}$ is

(A)

$P^{2}-5P+6I=0$

(B)

$P^{2}-5P+5I=0$

(C)

$P^{2}-6P+5I=0$

(D)

$P^{2}-4P+3I=0$

Explanation

GATE→2026→Engineering Mathematics→Vector Calculus

Q12

MCQ[1 Mark]

Let $\hat{i}$ and $\hat{j}$ be the unit vectors in the $x$ and $y$ direction, respectively. The divergence $(\nabla \cdot \vec{F})$ of $\vec{F} = x^2y\hat{i} + y^3x\hat{j}$ at the point $(3, 2)$ is

(A)

12

(B)

24

(C)

36

(D)

48

Explanation

GATE→2026→Engineering Mathematics→Differential Equations

Q13

MCQ[1 Mark]

Which one of the following is a non-linear, second-order, and first-degree differential equation?

(A)

\frac{d^{2}y}{dx^{2}}+\cos~x\frac{dy}{dx}+e^{x}y=0

(B)

\frac{d^{2}y}{dx^{2}}+\cos~y=0

(C)

\frac{d^{2}y}{dx^{2}}+\sin~x=0

(D)

(\frac{dy}{dx})^{2}+3y=0

Explanation

GATE→2026→Engineering Mathematics→Probability and Statistics

Q14

MCQ[1 Mark]

Match the distribution with its corresponding probability density/mass function.

(A)

P\rightarrow 2, Q \rightarrow 3, R \rightarrow 1, S \rightarrow 4

(B)

P\rightarrow 1, Q \rightarrow 3, R \rightarrow 2, S \rightarrow 4

(C)

P\rightarrow 3, Q \rightarrow 2, R \rightarrow 1, S \rightarrow 4

(D)

P\rightarrow 2, Q \rightarrow 4, R \rightarrow 3, S \rightarrow 1

Explanation

GATE→2026→Engineering Mathematics→Calculus

Q15

MSQ[1 Mark]

Which of the following statements about Fourier series is/are correct?

(A)

The Fourier series of an even function contains only cosine terms

(B)

The Fourier series of an odd function contains only cosine terms

(C)

The Fourier series of an odd function contains only sine terms

(D)

The Fourier series of an even function contains only sine terms

Explanation

GATE→2026→Engineering Mathematics→Calculus

Q16

MCQ[2 Marks]

The value of the determinant of the Hessian of $f(x,y)=x^{2}+y^{2}+xy-8x-7y$ at its stationary point is

(A)

2

(B)

3

(C)

4

(D)

5

Explanation

GATE→2026→Engineering Mathematics→Numerical Methods

Q17

MCQ[2 Marks]

Given the data in the Table, Newton's divided difference interpolation polynomial is $y=b_{0}+b_{1}(x-2)+b_{2}(x-2)(x-2.5)$. If the values of $b_{0}$ and $b_{1}$ are 3 and 1, respectively, then the value of $b_{2}$ is

(A)

3.0

(B)

3

(C)

4

(D)

5

Explanation

GATE→2026→Engineering Mathematics→Linear Algebra

Q18

MCQ[2 Marks]

Given $x=\begin{bmatrix}1\\2\\1\end{bmatrix}, b=\begin{bmatrix}-16\\-3\\7\end{bmatrix}, P^{-1}=\begin{bmatrix}e&-6&-7\\f&9&11\\-1&-2&8\end{bmatrix}$ and $Px=b$. If $Py=d$ and $d=\begin{bmatrix}-16\\0\\7\end{bmatrix}$, the value of $y_{2}$ is

(A)

29

(B)

27

(C)

25

(D)

5

Explanation

GATE→2026→Engineering Mathematics→Probability and Statistics

Q19

NAT[2 Marks]

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

Explanation

Mining Geology, Mine Development and Surveying

10 Questions

GATE→2026→Mining Geology, Mine Development and Surveying→Mining Geology

Q20

MCQ[1 Mark]

As per the Mohs scale of hardness, the correct sequence is

(A)

Topaz > Quartz > Calcite > Talc

(B)

Quartz > Topaz > Calcite > Talc

(C)

Quartz > Topaz > Talc > Calcite

(D)

Topaz > Calcite > Quartz > Talc

Explanation

GATE→2026→Mining Geology, Mine Development and Surveying→Mine Development

Q21

MCQ[1 Mark]

The best combination of explosive and initiation system for underwater blasting for rock breakage is

(A)

ANFO and electric detonator

(B)

emulsion and non-electric detonator

(C)

HANFO and safety fuse

(D)

PETN and electronic detonator

Explanation

GATE→2026→Mining Geology, Mine Development and Surveying→Mine Development

Q22

MCQ[1 Mark]

The firing sequence in a drivage is shown. The charge per hole for Sections 1, 2, and 3 are 2.0 kg, 3.0 kg, and 1.0 kg, respectively, and the delay between each section is 25 milliseconds. The maximum charge per delay, in kg, is

(A)

8.0

(B)

12.0

(C)

20.0

(D)

28.0

Explanation

GATE→2026→Mining Geology, Mine Development and Surveying→Mining Geology

Q23

MCQ[1 Mark]

The igneous intrusion along the bedding plane of the coal seam, as indicated by P, is known as

(A)

dyke

(B)

washout

(C)

sill

(D)

seam split

Explanation

GATE→2026→Mining Geology, Mine Development and Surveying→Mine Surveying

Q24

MCQ[1 Mark]

In remote sensing, the order of the wavelength bands of electromagnetic radiation used for data acquisition is

(A)

Visible < Near Infrared < Thermal Infrared < Microwave

(B)

Thermal Infrared < Near Infrared < Visible < Microwave

(C)

Microwave < Near Infrared < Thermal Infrared < Visible

(D)

Near Infrared < Thermal Infrared < Microwave < Visible

Explanation

GATE→2026→Mining Geology, Mine Development and Surveying→Mine Surveying

Q25

NAT[1 Mark]

A circular curve having radius of curvature 1000 m is set out by connecting two straights with a deflection angle of $60^{\circ}$. The apex distance, in m, is

Explanation

GATE→2026→Mining Geology, Mine Development and Surveying→Mining Geology

Q26

MCQ[2 Marks]

Match the type of rock with its metamorphic form.

(A)

P \rightarrow 4, Q \rightarrow 3, R \rightarrow 1, S \rightarrow 2

(B)

P \rightarrow 3, Q \rightarrow 1, R \rightarrow 4, S \rightarrow 2

(C)

P \rightarrow 4, Q \rightarrow 3, R \rightarrow 2, S \rightarrow 1

(D)

P \rightarrow 3, Q \rightarrow 4, R \rightarrow 2, S \rightarrow 1

Explanation

GATE→2026→Mining Geology, Mine Development and Surveying→Mine Development

Q27

MCQ[2 Marks]

Match the shaft sinking method with its applicability.

(A)

P \rightarrow 2, Q \rightarrow 3, R \rightarrow 4, S \rightarrow 1

(B)

P \rightarrow 4, Q \rightarrow 1, R \rightarrow 2, S \rightarrow 3

(C)

P \rightarrow 2, Q \rightarrow 1, R \rightarrow 4, S \rightarrow 3

(D)

P \rightarrow 4, Q \rightarrow 3, R \rightarrow 2, S \rightarrow 1

Explanation

GATE→2026→Mining Geology, Mine Development and Surveying→Mine Surveying

Q28

MCQ[2 Marks]

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

(A)

215^\circ 19^\prime 59.6^{\prime\prime}

(B)

35^\circ 19^\prime 59.6^{\prime\prime}

(C)

215^\circ 20^\prime 1.4^{\prime\prime}

(D)

35^\circ 20^\prime 1.4^{\prime\prime}

Explanation

GATE→2026→Mining Geology, Mine Development and Surveying→Mine Surveying

Q29

NAT[2 Marks]

Following observations were taken using a Tacheometer with staff held vertical. Additive and multiplying constants are 0 and 100. The reduced level (RL) of staff station R, in m, is

Explanation

Geomechanics and Ground Control

9 Questions

GATE→2026→Geomechanics and Ground Control→Engineering Mechanics

Q30

MCQ[1 Mark]

A simply supported beam is shown. The location at which the zero shear force is acting on the beam is

(A)

P

(B)

Q

(C)

R

(D)

S

Explanation

GATE→2026→Geomechanics and Ground Control→Geomechanics

Q31

MCQ[1 Mark]

In a Slake Durability Index (SDI) test, a rock sample of 500 g undergoes two standard cycles of wetting and drying. The mass of the sample retained after the test is 400 g. The SDI of the sample, in %, is

(A)

10

(B)

40

(C)

20

(D)

80

Explanation

GATE→2026→Geomechanics and Ground Control→Geomechanics

Q32

MCQ[1 Mark]

Results from the permeability test of rock samples, E, F, and G are shown. The correct order of hydraulic conductivity (k) of the rock samples is

(A)

k_E > k_F > k_G

(B)

k_E < k_F < k_G

(C)

k_E = k_F = k_G

(D)

k_F > k_G > k_E

Explanation

GATE→2026→Geomechanics and Ground Control→Geomechanics

Q33

MCQ[2 Marks]

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

(A)

\frac{\sigma_{P}+\sigma_{Q}}{2}

(B)

\frac{\sigma_{P}-\sigma_{Q}}{2}

(C)

-(\frac{\sigma_{P}+\sigma_{Q}}{2})

(D)

-(\frac{\sigma_{P}-\sigma_{Q}}{2})

Explanation

GATE→2026→Geomechanics and Ground Control→Ground Control

Q34

NAT[2 Marks]

A plug dam is to be constructed in a mine gallery of size $3.5\text{ m} \times 2.5$ m. The interfacial shear strength between 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

Explanation

GATE→2026→Geomechanics and Ground Control→Ground Control

Q35

NAT[2 Marks]

In a bench blasting, 49 kg of explosive is put in each hole. The PPV at a distance of 100 m, in $\text{mm s}^{-1}$, is

Explanation

GATE→2026→Geomechanics and Ground Control→Engineering Mechanics

Q36

NAT[2 Marks]

A truss PQR carries vertical load of 10 kN at Q as shown. The force in member PR, in kN, is

Explanation

GATE→2026→Geomechanics and Ground Control→Engineering Mechanics

Q37

NAT[2 Marks]

Two blocks P and Q weighing 100 kN and 200 kN, respectively, are connected by a string passing through a frictionless pulley. Friction coefficient between P and Q is 0.4, and between Q and surface is 0.3. The minimum force, F, in kN, required to pull the block Q, is

Explanation

GATE→2026→Geomechanics and Ground Control→Geomechanics

Q38

NAT[2 Marks]

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

Explanation

Mining Methods and Machinery

9 Questions

GATE→2026→Mining Methods and Machinery→Mining Machinery

Q39

MCQ[1 Mark]

The ideal load - deformation characteristic curve of a hydraulic prop is

(A)

P

(B)

Q

(C)

R

(D)

S

Explanation

GATE→2026→Mining Methods and Machinery→Mining Methods

Q40

MCQ[1 Mark]

A 20 m thick orebody is dipping at an angle of $75^{\circ}$. The orebody and host rock are strong. It is proposed to deploy a 150-200 mm diameter drill for production. The suitable stoping method is

(A)

block caving

(B)

long hole stoping

(C)

shrinkage stoping

(D)

post and pillar stoping

Explanation

GATE→2026→Mining Methods and Machinery→Mining Machinery

Q41

NAT[1 Mark]

The shaft of a motor rotating at 50 rev s$^{-1}$ is uniformly retarded to 20 rev s$^{-1}$ in 15 s. The number of complete rotations the shaft makes in the given time is

Explanation

GATE→2026→Mining Methods and Machinery→Mining Machinery

Q42

NAT[1 Mark]

A belt is wrapped around a pulley as shown. The coefficient of friction between the belt and pulley is 0.3. If there is no slippage between the belt and pulley, the angle of wrap ($\theta$), in degrees, is

Explanation

GATE→2026→Mining Methods and Machinery→Mining Machinery

Q43

NAT[2 Marks]

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 $8\text{ m} (L) \times 3\text{ m} (W) \times 3\text{ m} (H)$. Considering fill factor 0.95 and bulk density 1.2 tonne/m$^3$, the loading rate of the silo, in tonne per hour, is

Explanation

GATE→2026→Mining Methods and Machinery→Mining Machinery

Q44

NAT[2 Marks]

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 impeller blade curvature, the impeller diameter of the pump, in cm, is

Explanation

GATE→2026→Mining Methods and Machinery→Mining Methods

Q45

NAT[2 Marks]

The information for a dragline operation is given: Bucket capacity: $20\text{ m}^3$, Fill factor: 0.9, Digging and filling time: 20 s, Swinging time: 32 s, Dumping time: 10 s, Utilization: 90%. The output of the dragline, in $\text{m}^3\text{h}^{-1}$, is

Explanation

GATE→2026→Mining Methods and Machinery→Mining Methods

Q46

NAT[2 Marks]

A regular shaped cut and fill stope is shown. Pillars of size $4\text{ m} \times 4$ m are left at an interval of 13 m along the length of the stope. If density is 2.5 tonne/m$^3$, the total tonnage of ore recovered from the $1^{\text{st}}$ slice of the stope (in $\times 10^3$ tonnes) is

Explanation

GATE→2026→Mining Methods and Machinery→Mining Machinery

Q47

NAT[2 Marks]

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

Explanation

Surface Environment, Mine Ventilation and Underground Hazards

10 Questions

GATE→2026→Surface Environment, Mine Ventilation and Underground Hazards→Mine Ventilation

Q48

MCQ[1 Mark]

A gradually expanding duct fitted to the outlet of an exhaust fan is known as

(A)

chimney

(B)

diffuser

(C)

evasee

(D)

equivalent orifice

Explanation

GATE→2026→Surface Environment, Mine Ventilation and Underground Hazards→Underground Hazards

Q49

MCQ[1 Mark]

The cobweb-like appearance in the radiograph of the lung of a miner can be diagnosed as

(A)

silicosis

(B)

asbestosis

(C)

talcosis

(D)

coal workers' pneumokoniosis

Explanation

GATE→2026→Surface Environment, Mine Ventilation and Underground Hazards→Underground Hazards

Q50

MCQ[1 Mark]

In firedamp explosion, the methane concentration in the stoichiometric methane-air mixture, in % by volume, is (Assume air contains 79% nitrogen and 21% oxygen, by volume).

(A)

5.4

(B)

9.5

(C)

10.8

(D)

14.8

Explanation

GATE→2026→Surface Environment, Mine Ventilation and Underground Hazards→Mine Ventilation

Q51

NAT[1 Mark]

In an underground mine, an airflow of $30\text{ m}^3/\text{s}$ is delivered through a circular opening having a diameter of 5 m and a length of 500 m. Assuming that there is no change in the surface characteristics, the diameter of the opening, in m, required to double the quantity of airflow at same pressure loss is

Explanation

GATE→2026→Surface Environment, Mine Ventilation and Underground Hazards→Mine Ventilation

Q52

NAT[1 Mark]

In an underground mine atmosphere, the alcohol of a Kata thermometer took 60 s to fall from $38^{\circ}\text{C}$ to $35^{\circ}\text{C}$. The Kata factor of the thermometer is 480 milli-calories $\text{cm}^{-2}$. The Kata cooling power, in $\text{W m}^{-2}$, is

Explanation

GATE→2026→Surface Environment, Mine Ventilation and Underground Hazards→Mine Ventilation

Q53

MCQ[2 Marks]

In an underground coal mine, the air quantities $Q_A$ and $Q_B$ pass through ventilation districts A and B, respectively, with a pressure drop of $\Delta P$ across them. The air quantity in district B is to be increased to $Q_B^{\prime}$ by installing a booster fan without affecting district A. The capacity of booster fan ($P_B$) can be expressed as

(A)

P_{B}=\Delta P(\frac{Q_{B}}{Q_{B}^{\prime}})^{2}-\Delta P

(B)

P_{B}=\Delta P(\frac{Q_{B}^{\prime}}{Q_{B}})^{2}-\Delta P

(C)

P_{B}=\Delta P-\Delta P(\frac{Q_{B}^{\prime}}{Q_{B}})^{2}

(D)

P_{B}=\Delta P+\Delta P(\frac{Q_{B}^{\prime}}{Q_{B}})^{2}

Explanation

GATE→2026→Surface Environment, Mine Ventilation and Underground Hazards→Underground Hazards

Q54

NAT[2 Marks]

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

Explanation

GATE→2026→Surface Environment, Mine Ventilation and Underground Hazards→Mine Ventilation

Q55

NAT[2 Marks]

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. Considering the same NVP aiding, the pressure required, in mm wg, to be generated by the ventilator to circulate $1000\text{ m}^3\text{min}^{-1}$ of air is

Explanation

GATE→2026→Surface Environment, Mine Ventilation and Underground Hazards→Surface Environment

Q56

NAT[2 Marks]

Dust particles from a blasting operation rise up in the atmosphere to a height of 500 m. The viscosity of air is $1.80 \times 10^{-5}\text{ kg m}^{-1}\text{s}^{-1}$. Assume quiescent settling. The settling time, in days, of a dust particle of $2.5\,\mu\text{m}$ diameter and $3600\text{ kg m}^{-3}$ density is

Explanation

GATE→2026→Surface Environment, Mine Ventilation and Underground Hazards→Surface Environment

Q57

NAT[2 Marks]

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 $\text{mg liter}^{-1}$ and 4.4 $\text{mg liter}^{-1}$, respectively. The BOD of the sample, in $\text{mg liter}^{-1}$, is

Explanation

Mineral Economics, Mine Planning, Systems Engineering

8 Questions

GATE→2026→Mineral Economics, Mine Planning, Systems Engineering→Mineral Economics

Q58

MCQ[1 Mark]

As per the UNFC mineral resources classification system, the highest category of resource is indicated by

(A)

111

(B)

122

(C)

333

(D)

334

Explanation

GATE→2026→Mineral Economics, Mine Planning, Systems Engineering→Systems Engineering

Q59

NAT[1 Mark]

The expected time ($P$ days) and standard deviation ($Q$ days) of the different activities (A to F) in a project are indicated in the network diagram as $(P, Q)$. The standard deviation of the project completion time, in days, is

Explanation

GATE→2026→Mineral Economics, Mine Planning, Systems Engineering→Systems Engineering

Q60

MCQ[2 Marks]

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. Mean arrival rate = 5 per hour, dumper waiting cost = 200 per hour. Shovel type with minimum total cost is

(A)

S1

(B)

S2

(C)

S3

(D)

S4

Explanation

GATE→2026→Mineral Economics, Mine Planning, Systems Engineering→Mine Planning

Q61

NAT[2 Marks]

The borehole data for resource estimation for an iron ore deposit are shown. The average grade of the deposit, in %, is

Explanation

GATE→2026→Mineral Economics, Mine Planning, Systems Engineering→Systems Engineering

Q62

NAT[2 Marks]

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. If service engineer S1 cannot perform J3, and S3 cannot perform J4, the optimal cost for completion of jobs is

Explanation

GATE→2026→Mineral Economics, Mine Planning, Systems Engineering→Mineral Economics

Q63

NAT[2 Marks]

A shovel costing $P = 20$ crores has a salvage value $S = 2$ crores with a useful life $n = 10$ years. The annual depreciation is evaluated using declining balance method. The depreciated cost of the shovel, in crores, in its $2^{\text{nd}}$ year is

Explanation

GATE→2026→Mineral Economics, Mine Planning, Systems Engineering→Mine Planning

Q64

NAT[2 Marks]

An economic block model along with extraction sequence is shown. If the discount rate is 10%, the net present value (NPV), in lakhs, is

Explanation

GATE→2026→Mineral Economics, Mine Planning, Systems Engineering→Mine Planning

Q65

NAT[2 Marks]

A bord and pillar panel has 24 developed pillars of size $40\text{ m} \times 40$ m (centre to centre) under extraction. Gallery width = 4 m, extraction height = 3 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

Explanation