The GATE 2025 MN Question paper with Solution PDF is available to download here. GATE 2025 was conducted by IIT Roorkee. As per the updated exam pattern, the exam consists of 65 questions with 100 marks, with 10 from the General Aptitude section and 55 questions from Engineering Mathematics and Mining Engineering topics.
The difficulty level of GATE 2025 MN was moderate.
GATE 2025 MN Question Paper with Solutions PDF
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GATE 2025 MN Question Paper with Solutions
Even though I had planned to go skiing with my friends, I had to ________ at the last moment because of an injury.
Select the most appropriate option to complete the above sentence.
The President, along with the Council of Ministers, _______ to visit India next week.
Select the most appropriate option to complete the above sentence.
An electricity utility company charges Rs. 7 per kWh. If a 40-watt desk light is left on for 10 hours each night for 180 days, what would be the cost of energy consumption? If the desk light is on for 2 more hours each night for the 180 days, what would be the percentage-increase in the cost of energy consumption?
In the context of the given figure, which one of the following options correctly represents the entries in the blocks labelled (i), (ii), (iii), and (iv), respectively?
A bag contains Violet (V), Yellow (Y), Red (R), and Green (G) balls. On counting them, the following are obtained:
(i) \(Y + 2V = 50\);
(ii) \(V + G = 50\);
(iii) \(Y + R = 50\);
(iv) \(V + 2R = 50\).
Which one of the following Pie charts correctly represents the balls in the bag?
“His life was divided between the books, his friends, and long walks. A solitary man, he worked at all hours without much method, and probably courted his fatal illness in this way. To his own name there is not much to show; but such was his liberality that he was continually helping others, and fruits of his erudition are widely scattered, and have gone to increase many a comparative stranger’s reputation.” (From E.V. Lucas’s “A Funeral”)
Based only on the above passage, which one of the following statements is true?
For the clock shown in the figure, if \(O^* = O\ Q\ S\ Z\ P\ R\ T\) and \(X^* = X\ Z\ P\ W\ Y\ O\ Q\), then which one among the given options is most appropriate for \(P^*\)?
Consider a five-digit number \(PQRST\) with distinct digits \(P,Q,R,S,T\) (chosen from 1–5) satisfying:
\centerline{\(P < Q,\qquad S > P > T,\qquad R < T\).
If integers 1 through 5 are used, the value of \(P\) is:
A trader mixes two potato varieties \(P\) and \(Q\) and sells the mix at Rs. 192 per kg with 8% profit. Given:
Variety \(P\): Rs. 800 for 5 kg; Variety \(Q\): Rs. 800 for 4 kg. Find the ratio \(P:Q\) (by weight).
Three villages P, Q, and R are located such that PQ = 13 km, QR = 14 km, and RP = 15 km. A straight road joins Q and R. It is proposed to connect P to this road QR by constructing another road. What is the \emph{minimum} possible length (in km) of this connecting road? (Figure representative)
A non-transit theodolite does \emph{NOT} have
A steeply dipping metalliferous ore body is non-susceptible to spontaneous heating. The blasted ore is used as the platform to work in a stope. The appropriate mining method is
If \(y=x^x\), then \(\dfrac{dy}{dx}\) is
The rank of a \(3 \times 3\) matrix \(A\) is 2. The determinant of the matrix is
The safety device used to arrest forward runaway tubs in rope haulage is
The metal that belongs to the Rare Earth Element (REE) category is
The major \((\sigma_1)\) and minor \((\sigma_3)\) principal stresses and the maximum shear stress \((\tau_{\max})\) are related as \(|\tau_{\max}|=\sigma_1=-\sigma_3\). The magnitude of normal stress on the plane where \(\tau_{\max}\) acts is
In a Brazilian test, the front view of a homogeneous rock disk is shown. The failure initiates at the point:
Three frictionless pulleys with rope attachment are in static equilibrium as shown. The masses \(m_1\) and \(m_2\) (in kg) are:
Match the source of error with the corresponding correction in surveying with steel tape.
\begin{tabular{p{0.35\linewidthp{0.55\linewidth
Source of error & Type of correction
(P) Sag & (1) Only Positive (+)
(Q) Temperature & (2) Only Negative (–)
(R) Pull greater than standard pull & (3) Either positive or negative (+ or –)
\end{tabular
The figure shows four environmental lapse-rate profiles. Given the dry adiabatic lapse rate \(= -10^\circ\)C/km, the atmosphere is highly unstable for the profile
In a depillaring face of an underground coal mine, both wet- and dry-bulb temperatures are \(30^\circ\)C. The relative humidity of the face environment, in percentage, is
The chemicals used in a foam type fire extinguisher are
Pressure head characteristic of a mine fan and a mine characteristic curves are shown in the figure below:
Match the points with their corresponding nomenclatures
As per CMR 2017, haulage ropes shall be recapped once at least in every
In a shovel dumper combination, the loading time of a dumper is 3 minutes. The shovel serves 8 dumpers. If the cycle time of a dumper including its loading time is 22 minutes, the waiting time of a dumper, in minute, is (in integer)
An HMX explosive having Velocity of Detonation (VOD) of 10500 m/s is tested by D'Autriche method with a detonating fuse of VOD 7000 m/s. The impression mark on lead plate will be obtained at a distance (L), in meters, from the midpoint of the fuse, is (rounded off to two decimal places)
Hydraulic fracturing method is used to determine the major principal stress (\(\sigma_1\)) in an underground rock strata having tensile strength of 6 MPa. The minor principal stress (\(\sigma_3\)) in the strata is 8 MPa. If fluid pressure of 10 MPa is required to fracture the vertical borehole in that strata, the magnitude of \(\sigma_1\), in MPa, is (rounded off to 2 decimal places)
The value of \(\lim_{x \to 0} \frac{\tan 11x}{\tan 5x}\) is (rounded off to 1 decimal place)
The box plot of a data set is shown below. The interquartile range of the data set is (in integer)
The unadjusted RMR of a tunnel roof is 64. A single joint set exists in the roof as shown in the figure.
Using the abridged RMR table for adjustment orientation, the RMR is ______ (in integer).
In a ventilation network, three airways with resistances of \(4.0 \, Ns^2/m^8\), and \(9.0 \, Ns^2/m^8\) are connected in parallel. The equivalent resistance of the network in \( Ns^2/m^8\) is ______ (rounded off to 2 decimal places)
In a bord and pillar panel, the following data are obtained:
Number of blasting rounds per shift = 8
Face dimension (m × m) = 4.2 × 2.5
Average pull (m) = 1.2
Specific gravity of coal = 1.4
Manpower per shift = 100
The OMS (output per manshift) of the panel, in tonne, is ______ (rounded off to 2 decimal places)
If the in-situ density of coal is 1320 kg/m³ and the density of blasted coal is 952 kg/m³, the swell factor is ______ (rounded off to 3 decimal places)
The relevant information on metal extraction from a copper mine are given below:
Selling price of copper (Rs./kg) = 900
Mining cost (Rs./tonne of ore) = 500
Processing cost (Rs./tonne of ore) = 2000
Overall recovery of copper metal (%) = 70
Ignoring all other costs, the breakeven cutoff grade of copper, in %, is _________ (rounded off to 2 decimal places)
Match the type of deposit with the corresponding process of formation.
Transportation (NW-corner): Three suppliers S, O, I to Mines 1–3 with costs (Rs/tonne) as below. Find the transportation cost of the initial basic feasible solution using the North–West corner method.
Triaxial test on sandstone at confining pressure \(10\) MPa (\(\sigma_2=\sigma_3=10\) MPa). At axial stress \(50\) MPa, \(\varepsilon_1=4.2\times10^{-3}\) and \(\varepsilon_v=2.0\times10^{-3}\). Find \(E\) (GPa) and \(\nu\).
A ground reaction curve (GRC) of a 3 m radius circular tunnel is shown. The tunnel is supported by a 300 mm shotcrete lining. The uniaxial compressive strength (\(\sigma_c\)), modulus of elasticity (\(E_k\)), and Poisson’s ratio (\(\nu\)) of shotcrete material are 20 MPa, 15 GPa, and 0.25 respectively. The maximum capacity (\(P_{max}\)) of the lining and its stiffness (\(k\)) are given as: \[ P_{max} = \frac{1}{2} \sigma_c \left(1 - \left(\frac{a}{r}\right)^2 \right) \] \[ E_k = \frac{E \left( a^2 - (a - t)^2 \right)}{(1 + \nu)\left[(1-\nu)(a^2) + (a - t)^2 \right]} \]
where \(a\) is the radius of the unlined tunnel and \(t\) is the thickness of the lining.
If the lining is constructed after 5 mm radial deformation, the support reaction is best represented by the line:
A fixed quantity of air must pass through a duct whose cross section is a rectangle of width \(2r\) and height \(h\) with a semicircular roof of radius \(r\) (common width \(2r\)). The total perimeter is \(20\) m. The radius \(r\) (in m) that \emph{minimizes air velocity (i.e., \emph{maximizes area for fixed perimeter) is:
Based on the theodolite survey for a closed traverse PQRS, the following bearings are
observed for the sides of the traverse.
The interior angles at P and R respectively are
The CORRECT statement(s) of dragline operation is/are:
A constant feed of 400 mL/s is maintained by a Xanthate column of height H as shown in the figure. The outlet cross section area is \(1.0 \times 10^{-4} \, m^2\). The acceleration due to gravity is 10 m/s². Neglecting friction and other losses, the value of H, in cm, is _________ (rounded off to 2 decimal places)
A continuous miner serves two shuttle cars of 12 tonne capacity each. Shuttle cars I and II operate with a total cycle time of 12 minutes and 15 minutes respectively, which includes loading time of 8 minutes for each car. The production rate of the continuous miner, in tonne/hour, is _______ (rounded off to 2 decimal places)
In a sublevel stope, a ringhole blast round is designed for winning 2500 tonne of ore with 8.0 % metal content. The blast results into breakage of 90.0 % of the design blast round. Overbreak of 250 tonne wallrock with 0.5 % metal content dilutes the blasted ore. The total metal content, in tonne, considering 95 % recovery of the blasted muck from the stope, is _______ (rounded off to 2 decimal places)
In a surface mine, blasting is carried out using electronic detonator and cartridge emulsion explosive with following details:
Burden = 3.5 m
Spacing = 4.5 m
Bench height = 10.0 m
Subgrade drilling = 1.0 m
Stemming = 4.0 m
Linear charge concentration = 16 kg/m
Cost of one detonator = Rs. 800
Cost of explosive = Rs. 30/kg
The cost of blasting material per cubic meter of blasted rock, in Rs., is _________ (rounded off to 2 decimal places)
A pit slope has the following information:
Number of benches = 5
Height of each bench = 8 m
Bench slope angle = 70 degree
If width of one bench is 24 m and that of other four benches is 10 m each, the overall pit slope angle, in degree, is _________ (rounded off to 2 decimal places)
A direct rope haulage has the following details:
Output = 24 tonne/hour
Length of trip = 610 m
Gradient = 1 in 12
Capacity of mine car = 1.0 tonne
Tare weight of mine car = 0.5 tonne
Average rope speed = 1.694 m/s
Change over time of cars = 3 minute
Acceleration due to gravity = 10.0 m/s²
Neglecting all frictional resistance and mass of the rope, the minimum power required, in kW, to raise the loaded mine cars is _________ (rounded off to 3 decimal places)
A mine void of dimension 100.0 m × 2.0 m × 1.2 m is to be filled in 3 hours by hydraulic stowing. The sand to slurry ratio is 0.4. If the hydraulic fill factor is 0.9, the hourly consumption of water for the operation, in m³, is _________ (rounded off to 2 decimal places)
A 2.5 tonne diesel locomotive hauls 5 mine cars upslope having a gradient of 1 in 20. The constant tractive force of the locomotive is 1800 kN. The gross weight of a car is 3 tonne. Acceleration due to gravity is 10.0 m/s². If the acceleration of the system is 0.5 m/s², the rolling resistance in kN/tonne is _________ (rounded off to 3 decimal places)
A longwall panel is to be developed in a flat seam at a depth of H m. The surface subsidence profile (s) of the area with the horizontal distance x is estimated as \[ s = \frac{S_{max}}{2} \left[ 1.002 - \tanh \left( \frac{4.8x}{H} \right) \right] \]
where, \(S_{max}\) is the maximum subsidence at the centre of the panel, x is measured from the inflection point. The value of x is negative towards the panel centre and positive towards the panel boundary. The ratio between the critical width of the panel and the depth is _________ (rounded off to 2 decimal places)
The percent Fe content of a random sample consisting of five observations is shown.
62, 64, 63, 60, 61
If mean grade of the stockpile is estimated using the above data, the standard error of mean grade, in %, is _________ (rounded off to 3 decimal places)
In a bord and pillar panel, a square pillar of size 35 m × 35 m (centre to centre) is extracted to form four equal square-shaped stooks as shown. The width of each gallery and crosscut is 5 m. The height of the working seam is 3 m. The reduction in safety factor after pillar splitting by using Bieniawski’s pillar strength formula, in %, is _________ (rounded off to 2 decimal places)
A five-member truss system is shown in the figure. The maximum vertical force P in kN that can be applied so that loads on the member CD and BC do NOT exceed 50 kN and 30 kN, respectively, is _________ (rounded off to 2 decimal places)
The characteristic polynomial of a third-order matrix, A, is given by \[ f(x) = x^3 - 6x^2 + 11x - 6 \]
If one of the eigenvalues of A is 1, then sum of the other two eigen values is _________ (in integer)
The directional derivative of a function \(f(x, y, z) = 4x^2 + 8y^2 + 9z^2\) at the point P(3, 4, 5) in the direction vector \(\mathbf{b} = 2\hat{i} - 3\hat{j} + 4\hat{k}\) is _________ (rounded off to 1 decimal place)
Average noise level at a working place is 80 dB(A) for the first 10 minutes and 60 dB(A) for the next 30 minutes. The energy equivalent continuous noise level at the place for the entire period of 40 minutes, in dB(A), is _________ (rounded off to 2 decimal places)
The area bounded by the curves, \(y = \sqrt{x}\), and \(y = 8x^2\) is _________ (rounded off to 3 decimal places)
Data from a borehole log with collar elevation at 590 mRL are given below. Composite grade is calculated using cores of 5 m above and below the reference bench at 580 mRL. The composite grade, in %, is _________ (rounded off to 1 decimal place).
The information of a mining project for a life of three years is given below: Year Revenue (Crore Rupees) Capital cost (Crore Rupees) Operating cost (Crore Rupees) Tax rate = 30%. NPV calculation?
In a longwall panel, air flows at a velocity of 1.2 m/s through a 900 m long gate road of 2.5 m height and 3 m width. The coefficient of friction is 0.022 Ns²m⁻⁴. The frictional pressure drop, in Pa, between two ends of the gate road is _________ (rounded off to 3 decimal places).
SO₂ is emitted at a rate of 20 kg/s from a 10 km × 10 km airshed in an industrial area. Wind blows at a speed of 4 m/s from one direction. The steady state SO₂ concentration in the airshed, in \(\mu g/m^3\), is _________ (rounded off to 2 decimal places).
Reciprocal levelling is performed for points P and Q by placing the same levelling instrument at A and B. The observations of staff readings are tabulated as below.
A wastewater sample has an ultimate BOD of 300 mg/L. BOD reaction rate constant is 0.22 per day at 20 °C. If the temperature coefficient is 1.05, the 5-day BOD at 25 °C, in mg/L, is _________ (rounded off to 2 decimal places).
A double ended ranging drum (DERD) shearer uni-directionally cuts coal in a longwall panel having the following details. The number of days required for complete extraction of the panel is _________ (in integer).
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