GATE 2026 MN – Previous Year Questions with Solutions
All 65 questions of GATE 2026 MN with answers and explanations. Read each question, then practise it by topic or as a full paper.
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- Question 1 – Suresh said, “I did it yesterday.” Which one of the following options is the correct form of this sentence in indirect speech?
- Question 2 – To continue the sequence of tiles shown, which tile should replace the question mark?
- Question 3 – 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…
- Question 4 – The 2nd of June is a Thursday in a certain year. Which day of the week is the 3rd of July in that year?
- Question 5 – A coin with heads facing up is denoted by H, and a coin with tails facing up is denoted by T. Six coins have the starting arrangement H H H T T T and…
- Question 6 – Exacerbate : Mitigate :: Choose the option with the correct pair of words to fill the blank.
- Question 7 – A paper shown in Panel I is folded along the dashed lines to construct a cube. The shaded regions shown in Panel I appear on the outer surface of the…
- Question 8 – 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…
- Question 9 – 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…
- Question 10 – 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 in the figure. Given r…
- Question 11 – For P=pmatrix2&1\\0&3pmatrix and identity I, which polynomial identity follows from Cayley–Hamilton?
- Question 12 – Find the divergence of F=x2y i+y3x j at (3,2).
- Question 13 – Which differential equation is nonlinear, second order and first degree?
- Question 14 – Which decreasing Mohs-hardness order is correct?
- Question 15 – Match P binomial,Q Poisson,R normal,S exponential to these probability laws. (1) f(x)=e-(x-)2/(22)/(2); (2) f(x)= nx px(1-p)n-x for x=0,…,n; (3)…
- Question 16 – In the UNFC mineral-resource classification used by this question, which code denotes the highest category?
- Question 17 – Which listed combination is most suitable for underwater rock blasting?
- Question 18 – The drivage diagram assigns2.0,3.0 and1.0 kg per hole to Sections1,2 and3 respectively. Consecutive sections have25 ms delay. What is the maximum…
- Question 19 – What is the igneous intrusion P, which follows the coal seam’s bedding plane?
- Question 20 – Which is the increasing-wavelength order used in remote sensing?
- Question 21 – For the simply supported beam and loads shown, at which labelled location does the shear-force diagram cross zero?
- Question 22 – A500 g rock sample retains400 g after the two standard wetting/drying cycles of a slake-durability test. Find the Slake Durability Index in percent.
- Question 23 – The graph plots discharge Q against Ah/L for rock samples E,F,G. Here A is cross-sectional area,h the hydraulic head and L sample length. Which…
- Question 24 – Which curve is the ideal load–deformation characteristic of a hydraulic prop?
- Question 25 – A20 m thick orebody dips75°. Both ore and host rock are strong, and production drilling of150–200 mm diameter is proposed. Which stoping method fits?
- Question 26 – What is the mining term for the gradually expanding duct fitted to an exhaust fan’s outlet?
- Question 27 – Which condition is associated in this mining-health question with a cobweb-like appearance on a miner’s lung radiograph?
- Question 28 – Air is79% nitrogen and21% oxygen by volume. Find methane’s volume percentage in a stoichiometric methane–air mixture.
- Question 29 – For Fourier series on a symmetric interval, which statements are correct?
- Question 30 – A circular curve of radius1000 m joins two straights with deflection angle60°. Find apex(external) distance in m, to three decimals.
- Question 31 – Activities in the project network are labelled(expected days,standard deviation in days). Find the standard deviation of project completion time to…
- Question 32 – A shaft slows uniformly from50 to20 revolutions/s over15 s. How many rotations occur? Give an integer.
- Question 33 – A500 m long circular airway of diameter5 m carries30 m³/s. With unchanged surface roughness and length, find diameter needed to double flow at the…
- Question 34 – A Kata thermometer takes60 s to fall from38°C to35°C. Its factor is480 millicalories/cm². Find cooling power in W/m², to one decimal.
- Question 35 – The belt has tight-side tension5.0 kN and slack-side tension2.5 kN as shown. Friction coefficient is0.3. At limiting no-slip equilibrium, find wrap…
- Question 36 – For f(x,y)=x2+y2+xy-8x-7y, find the determinant of the Hessian at its stationary point.
- Question 37 – Data are (x,y)=(2,3),(2.5,3.5),(3,5). Newton’s polynomial is y=b 0+b 1(x-2)+b 2(x-2)(x-2.5). Given b₀=3 and b₁=1, find b₂.
- Question 38 – Let x=(1,2,1)T, b=(-16,-3,7)T, and P-1=pmatrixe&-6&-7\&9&11\\-1&-2&gpmatrix. Given Px=b and Py=d with d=(-16,0,7)T, find y₂.
- Question 39 – Match P shale,Q limestone,R granite,S sandstone to metamorphic forms1 gneiss,2 quartzite,3 marble,4 slate.
- Question 40 – Two parallel ventilation districts A and B initially have common pressure drop ΔP and flows QA,QB. A booster increases B flow to Q′B while A flow…
- Question 41 – Match sinking methods P piling,Q caisson,R cementation,S freezing to applications:1 alternating strong/loose strata where the drum sinks under its…
- Question 42 – Dumpers arrive exponentially at5/hour and loading times are exponential. Waiting cost is₹200 per dumper-hour. Shovels S1,S2,S3,S4 have operating…
- Question 43 – The flat-jack slots P,Q,R on the gallery wall measure σP,σQ,σR. Slot R is at45° as drawn, σP>σQ and σR=0. Find wall shear stress with the displayed…
- Question 44 – The correlation-survey geometry is shown. C has(E375 m,N1120 m) and D has(E376 m,N1121 m). Determine the whole-circle bearing of EF.
- Question 45 – A closed-circuit breathing apparatus has2 L of oxygen at200 bar. Consumption is2 L/min at ambient pressure. Under the ideal capacity approximation,…
- Question 46 – The exploratory boreholes and their influence polygons are shown. With equal density assumed, estimate average deposit grade in percent to two…
- Question 47 – Assign four jobs J1–J4 to engineers S1–S4, one job each. Costs by row are S1:(50,50,unavailable,20); S2:(70,40,20,70); S3:(90,30,50,unavailable);…
- Question 48 – For data x=(2,3,4,5),y=(8,9,7,16), the least-squares line is y=2.2x+2.3 and residual sum of squares25.8. Find coefficient of determination r² to two…
- Question 49 – A plug dam seals a3.5×2.5 m gallery. Rock–dam interfacial shear strength is1.0 MPa. Find minimum dam thickness resisting10.0 MPa water pressure, in m…
- Question 50 – A shovel costs P=₹20 crore, has salvage S=₹2 crore and life n=10 years. Declining-balance rate is r=1-(S/P)1/n. Find its second-year depreciated cost…
- Question 51 – In the economic block model, centre labels give extraction year and corner labels give block economic values in lakh rupees. At10% annual discount,…
- Question 52 – A mine fan generates25 mm water gauge and an aiding natural-ventilation pressure is15 mm water gauge, producing500 m³/min. With the same aiding…
- Question 53 – A2.5 μm dust particle of density3600 kg/m³ settles500 m through still air of viscosity1.80×10⁻⁵ kg/(m s). Neglect air density and turbulence. Find…
- Question 54 – A15 mL wastewater sample is diluted to300 mL and incubated for5 days at20°C. Dissolved oxygen drops from9.2 to4.4 mg/L. Find sample BOD in mg/L as an…
- Question 55 – Wagons8 m long,3 m wide and3 m high move at0.4 km/h under a silo, with1 m gaps. Filling stops between wagons. At fill factor0.95 and coal density1.2…
- Question 56 – A turbine pump generates60 m water head at2000 rpm with manometric efficiency70%. Neglect impeller-blade curvature. Find impeller diameter in cm to…
- Question 57 – A dragline bucket holds20 m³ with fill factor0.9. Digging/filling takes20 s, total outward-and-return swing32 s and dumping10 s. Utilisation is90%.…
- Question 58 – Each hole in the displayed bench-blast pattern contains49 kg explosive. Hole labels give delay times in milliseconds. Using the supplied…
- Question 59 – The cut-and-fill stope dimensions are shown. Pillars are4×4 m, separated by clear13 m intervals along the stope. Ore density is2.5 tonne/m³ and slices…
- Question 60 – A DERD shearer cuts a2.4 m seam at0.6 km/h with web depth0.5 m. Coal occupies0.24 m² of AFC cross-section. With10% spillage, find minimum AFC speed in…
- Question 61 – A bord-and-pillar panel has24 pillars of40×40 m centre-to-centre spacing,4 m galleries and3 m extraction height. Coal specific gravity is1.4 and…
- Question 62 – A tacheometer has multiplying constant100 and additive constant0; the staff is vertical. From P, Q has readings1.4,2.7,3.9 m and vertical angle7°; R…
- Question 63 – The pin-jointed triangular truss PQR has span PR=5 m, angles60° at P and30° at R, and a10 kN vertical downward load at Q. Find the force magnitude in…
- Question 64 – Blocks P and Q weigh100 and200 kN. They are connected over a fixed frictionless pulley as drawn. Friction coefficient P–Q is0.4 and Q–floor0.3. Find…
- Question 65 – A120 Ω strain gauge with gauge factor2.0 is bonded longitudinally to the110 mm rock specimen shown. Resistance-change magnitude at the end of the…