GATE 2021 MN – Previous Year Questions with Solutions
All 65 questions of GATE 2021 MN with answers and explanations. Read each question, then practise it by topic or as a full paper.
Practise this paper in The GATE Grind →
- Question 1 – Which sentences are grammatically correct? (i) Arun and Aparna are here. (ii) Arun and Aparna is here. (iii) Arun’s families is here. (iv) Arun’s…
- Question 2 – Which option is the mirror image of PHYLAXIS about the horizontal x-axis shown?
- Question 3 – Two fair six-faced dice numbered 1–6 are rolled independently. Find the probability of an even number on each.
- Question 4 – Define p q=p-q and p q=pq. Evaluate (9(67))(7(65)).
- Question 5 – P, Q, R, S sit in a row, with R forbidden from the second position from the left. How many distinct arrangements are possible?
- Question 6 – From O, travel 3 units east and 4 south to P. Move northeast until reaching a point 6 units east of O, then northwest to Q, which is 8 units north of…
- Question 7 – The author notes that musicians and actors rehearse and says it is no less important for public speakers to rehearse their talks. Which conclusion…
- Question 8 – Some football players play cricket. All cricket players play hockey. Which conclusion necessarily follows?
- Question 9 – In square PQRS of side r, the shaded lens is the overlap of quarter-circles of radius r centred at S and Q. Find the probability that a uniformly…
- Question 10 – In an equilateral triangle, the sides are divided into 4, 6 and 8 equal parts respectively, each part having integer length in cm. Find the minimum…
- Question 11 – A tricone roller bit is used with which drilling system?
- Question 12 – For which deposit is resuing practised?
- Question 13 – Which surface-mining equipment is used for both drop cut and terrace cut?
- Question 14 – Which component does a surface miner NOT have?
- Question 15 – Induced blasting enhances production in which mining method?
- Question 16 – Which set consists only of measures of dispersion?
- Question 17 – Why is NONEL used as a down-the-hole initiator in the context of this question?
- Question 18 – For the coplanar vectors shown, let c=( a+ b)( a- b). Its magnitude equals which quantity?
- Question 19 – Under the MMDR Act 1957, who is authorised to grant permits/leases for minor minerals in the stated allocation context?
- Question 20 – In photogrammetry, what is the tilt of a photograph?
- Question 21 – How should a hydraulic sand-stowing pipeline be laid relative to its hydraulic gradient line?
- Question 22 – Which statement is true for a real symmetric positive-definite square matrix?
- Question 23 – The standard normal distribution is described in the source as which type?
- Question 24 – For independent random variables X, Y, what is Var(X+Y)?
- Question 25 – Which statement distinguishes depreciation and amortisation allowances in the source’s tax/accounting terminology?
- Question 26 – Which is NOT included in a machine’s owning cost?
- Question 27 – Folds primarily result from which deformation process?
- Question 28 – Which plotted curve represents coal-pillar vertical stress versus extraction ratio R in a horizontal bord-and-pillar panel?
- Question 29 – For geometrically similar fans, how does pressure scale with rotational speed n, impeller diameter D and air density ?
- Question 30 – A coal sample has moisture content 8.0% and bulk unit weight 15.6 kN/m³. Find dry unit weight in kN/m³, to two decimals.
- Question 31 – Approximate I= 04x\,dx by Simpson’s 1/3 rule with two subintervals. Round to three decimals.
- Question 32 – The lower and upper frequencies of a 1/1 octave band are 710 Hz and 1420 Hz. Find its centre frequency in Hz, to the nearest integer.
- Question 33 – In the Battelle Environmental Evaluation System, air pollution has PIU 52. Environmental quality falls from 0.8 before the project to 0.6 after it.…
- Question 34 – Four independent components are connected in parallel, with reliabilities 0.40, 0.60, 0.50, 0.40. Find system reliability, to three decimals.
- Question 35 – A vehicle travelling 12 m/s skids without rolling to rest over 15 m on a level road. Deceleration is constant and g=10 m/s². Find the tyre-road…
- Question 36 – Six 10-tonne shuttle cars each carry 80% capacity and make 7 round trips/hour. They feed coal of bulk density 1.2 t/m³ to a belt with effective…
- Question 37 – Match labelled point-attack cutting-tool angles P α, Q β, R δ, S γ with 1 cutting angle, 2 clearance angle, 3 wedge angle, 4 rake angle.
- Question 38 – In the Weisbach triangle shown, CD has bearing 286°00′00″ and length 4.64 m, angle CED=00°00′40″, and DE=5.46 m. Find the bearing of CE.
- Question 39 – A 250-tonne truck moves uphill at 5° with constant tractive force 800 kN and rolling resistance 545 kN. Take g=10 m/s². How many seconds are required…
- Question 40 – Longwall shields have yield capacity 460 tonnes each, canopy length 3.25 m and width 1.5 m, and setting capacity 80% of yield. Tip-to-face distance…
- Question 41 – A 10 mL wastewater sample is diluted to 300 mL with BOD-free water. Initial dissolved oxygen is 9.0 mg/L and the original wastewater’s BOD₅ is 60…
- Question 42 – The initial dry-rock Mohr circle has principal stresses σ₃ and σ₁. With full saturation and uniform pore pressure p, which plotted effective-stress…
- Question 43 – The failure criterion is σ₁=4σ₃+28 MPa. At A, (σ₃, σ₁)=(10, 90) MPa; at B, (40, 160) MPa. Find safety factors A and B using available…
- Question 44 – Match roof-bolt cost/revenue lines: P line A, R line B, S line C, with 1 total cost, 2 indirect operating cost, 3 revenue.
- Question 45 – For a fixed real constant b, evaluate x(xx2+b2-x4+b4).
- Question 46 – Test H₀:mean Fe=62% against Hₐ:mean Fe<62%. A sample of five grades is 58%, 56%, 60%, 64%, 62%. Find the one-sample t statistic.
- Question 47 – A three-year quarry mines 3 million tonnes ore each year. Waste volumes in years 1, 2, 3 are 5.0, 5.5, 5.0 million m³. Ore sells at₹1500/t; ore mining…
- Question 48 – A simply supported 2 m beam carries a triangular UDL increasing from zero at A to 5 kN/m at B. Find maximum bending moment in kN·m, to two decimals.
- Question 49 – A dumpy-level bubble has sensitivity 40″ per division. At a staff distance 60 m, the bubble is two divisions off centre. Find staff-reading error…
- Question 50 – A 1:1000 old mine plan measures 802 cm² by planimeter. An original 10 cm line has shrunk to 9.8 cm. Find true ground area in m², to the nearest…
- Question 51 – CO is emitted at ground level at 25 g/s. Wind speed is 5 m/s; horizontal and vertical Gaussian dispersion coefficients are 150 m and 200 m. Find…
- Question 52 – The hypothetical daily-infection quantity c follows 100\,dc/dt-7c=0, with t in days. Find its doubling time in days, to the nearest integer.
- Question 53 – A single 7-tonne-payload skip hoists from 620 m. Acceleration/deceleration are 1 m/s² and full speed 10 m/s. Loading takes 120 s and unloading 60 s;…
- Question 54 – Blast fragments have mean-size parameter 60 cm and uniformity index 1.25. Using the Rosin–Rammler form used in the paper, find cumulative mass percent…
- Question 55 – A single-acting reciprocating ram pump runs at 120 rpm and delivers 10 L/s. Ram diameter is 150 mm and stroke 300 mm. Find volumetric efficiency in…
- Question 56 – A stowing slurry contains 35% sand by volume. Sand specific gravity is 2.6. Find sand concentration by mass in percent, to one decimal.
- Question 57 – Fly rock is launched at 45° from the third bench above the pit bottom. Each bench is 8 m wide, 6 m high, with 80° faces, as shown. With g=10 m/s²,…
- Question 58 – Of 25 roof-bolter operators, 13 were injured and 12 not injured. Of 107 loader operators, 35 were injured and 72 not injured. Find injury odds ratio…
- Question 59 – X takes−2, 3, 1 with probabilities 1/3, 1/2, 1/6 respectively. Find E(X²), to one decimal.
- Question 60 – A project has activities(duration days; predecessors): A(3; none), B(4; none), C(5; A, B), D(6; B), E(7; D), F(8; C, E), G(9; D), H(X; F, G). Total…
- Question 61 – A truck travelling at x km/h consumes fuel at 20+x²/50 L/hour. Fuel costs₹70/L and other costs₹500/hour. It travels 100 km. Find the speed minimising…
- Question 62 – Three cement factories supply 600, 100, 1000 t/day. Demands at D 1, D 2, D 3, D 4 are 700, 500, 300, 200 t/day. Unit transport costs are F 1:[20, 30,…
- Question 63 – Ultimate-pit cumulative million tonnes below Cu grades 0.1%, 0.4%, 0.5%, 0.6%, 0.7%, 0.9%+ are 0, 15, 17, 18, 19, 23. Mill cutoff is 0.5% Cu. Mining…
- Question 64 – A three-shift coal mine produces 400 t/day from panel A and 200 t/day from B, both with face OMS 1.0. Parallel-panel resistances are 0.6 and 0.5…
- Question 65 – Three collinear steel-bar segments have lengths 250, 500, 250 mm and equal area 0.01 m². E=200 GPa. Axial forces at successive nodes are 400 kN right,…