GATE 2018 ME (ME1) – Previous Year Questions with Solutions
All 65 questions of GATE 2018 ME (ME1) with answers and explanations. Read each question, then practise it by topic or as a full paper.
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- Question 1 – “Going by the that many hands make light work, the school involved all the students in the task.” Choose the best words.
- Question 2 – “Her should not be confused with miserliness; she is ever willing to assist those in need.” Choose the best word.
- Question 3 – Seven machines take 7 minutes to make 7 identical toys. At the same rate, how many minutes do 100 machines take to make 100 toys?
- Question 4 – A rectangle becomes a square after its length and breadth decrease by 10 m and 5 m respectively. It loses 650 m² of area. What was its original area?
- Question 5 – A two-digit number has digit sum 9. Subtracting 45 interchanges its digits. What is the number?
- Question 6 – For integers a, b, c with a + b + c =0, find the minimum and maximum of a+b+c respectively.
- Question 7 – Integers a and b satisfy that a+a2b3 is odd. Which is correct?
- Question 8 – At constant speed 54 km/h, 25 seconds elapse between a train’s front entering and rear leaving a platform. At the same speed it passes a man running…
- Question 9 – Which function describes the plotted graph?
- Question 10 – Consider (i) Some roses are red. (ii) All red flowers fade quickly. (iii) Some roses fade quickly. Which inference is valid?
- Question 11 – A box contains four red, four green and four blue balls. Three are drawn successively at random without replacement. Probability that all three are…
- Question 12 – Find the rank of bmatrix-4&1&-1\\-1&-1&-1\\7&-3&1bmatrix.
- Question 13 – For continuous f on [a,b], the integral mean-value theorem gives some ξ in the interval such that abf(x)\,dx equals .
- Question 14 – For z=x+iy, F(z)=iz+kRe(z)+iIm(z). Which k makes F satisfy the Cauchy–Riemann equations?
- Question 15 – A uniform bar weighing 100 N is held horizontally by massless inextensible strings S1 and S2 as shown. Their tensions are .
- Question 16 – For algebraically largest and smallest principal stresses 1, 3, maximum shear stress is .
- Question 17 – A spring–mass system obeys M x+Kx=F( t), with mass M, stiffness K, force amplitude F and excitation angular frequency ω. Resonance occurs at ω = .
- Question 18 – For an Oldham coupling between two shafts, which are correct? I. Torsional load transfers along the shaft axis. II. It provides shaft velocity ratio…
- Question 19 – For two-dimensional incompressible velocity u=A(x i-y j), A > 0, which is FALSE?
- Question 20 – Which is correct for superheated vapour?
- Question 21 – Beyond initial yield in a linearly hardening plastic material, true stress .
- Question 22 – The shaded weld shown is a weld.
- Question 23 – Taylor tool-life exponent is n = 0.5. If cutting speed is reduced by 50%, new tool life divided by original tool life is .
- Question 24 – A grinding ratio of 200 implies .
- Question 25 – A CNC interpolator .
- Question 26 – Which forecasting method equally weights each of the m most recent observations?
- Question 27 – For an FCC crystal, atoms per unit cell and slip systems respectively are .
- Question 28 – A fair six-faced die is rolled five times. Probability, in percent, of obtaining ONE at least four times is .
- Question 29 – A 15 mm × 10 mm rectangular steel column is 1.5 m long and simply supported at both ends. With E = 200 GPa, critical axial load, to two decimals, is…
- Question 30 – A four-bar mechanism has link lengths 100, 200, 300 and 350 mm. With the 350 mm link fixed, the number of links able to rotate fully is .
- Question 31 – A compression helical spring’s wire diameter increases by 2%. The change in stiffness, to two decimals, is %.
- Question 32 – A plate of width L = 1 m moves towards a wall at U = 0.01 m/s, squeezing fluid out as shown. Assume two-dimensional incompressible flow, with the…
- Question 33 – An ideal gas changes from 300 K, 100 kPa to 600 K, 500 kPa. Specific heats cp = 1 and cv = 0.7 kJ/kg K. Specific entropy change, to two decimals, is…
- Question 34 – For a given Pelton-wheel water-jet speed, bucket-speed/jet-speed ratio for maximum output power, to two decimals, is .
- Question 35 – For a 125 mm sine bar measuring a flat-workpiece taper of 27°32′, required height, to three decimals, is mm.
- Question 36 – Independent normal variables X₁ and X₂ have means 1,1 and standard deviations 1,2 respectively. For Y = X₁ − X₂, which is correct?
- Question 37 – For position vector r=x i+y j+z k and outward normal n, evaluate S r n\,dS on the closed boundary S of volume V.
- Question 38 – A point mass is launched vertically upwards at 4 m/s from ground at t = 0. After each ground impact it loses 20% of its impact speed. With g = 10 m/s²…
- Question 39 – The plane-stress state shown has σx = 100 kPa and τxy = 50 kPa. If the minimum principal stress is 10 kPa, σy is .
- Question 40 – In the gear train shown, tooth counts are A = 20, B = 30, D = 20; C has 80 internal and 100 external teeth. Carrier AB is fixed. If A rotates…
- Question 41 – Two cylindrical wooden logs are bonded at the θ = 30° interface shown. Glue fails if normal stress exceeds 2.5 MPa (criterion 1) or shear stress…
- Question 42 – A self-aligning ball bearing has dynamic rating C₁₀ = 35 kN for one million revolutions. Equivalent radial load is 45 kN. Expected life in millions of…
- Question 43 – An open tank contains water to depth 1 m. A smooth hole 0.5 m above the floor emits a horizontal free jet, as shown. Horizontal distance X to the…
- Question 44 – A Lagrangian particle trajectory is x=x 0e-kt, y=y 0ekt, where x 0,y 0,k are constants. The flow is .
- Question 45 – Maximum cross-sectional reduction per cold wire-drawing pass is R=1-e-(n+1), where n is the strain-hardening exponent. For a perfectly plastic…
- Question 46 – A continuous sheet-metal strip is blanked into circular pieces of diameter D as shown, with D/5 spacing between circles and D/5 margins on both edges.…
- Question 47 – Use explicit forward Euler on dy/dt=y with step 0.1 and y(0) = 1. The computed y(1), to two decimals, is .
- Question 48 – F(s) is the Laplace transform of f(t)=2t2e-t. F(1), to two decimals, is .
- Question 49 – A simply supported beam is 100 mm wide, 200 mm high and 4 m long, carrying a 10 kN/m UDL. Maximum bending stress, to one decimal, is MPa.
- Question 50 – A 200 kg machine rests on two mounts, each of stiffness 10 kN/m. Applied force is F(t)=505t N. Assume only vertical translation. Dynamic force…
- Question 51 – The slider–crank shown has crank angle 45°, crank length 30 mm and connecting rod length 70 mm. A 40 N leftward force acts on the slider. Neglect…
- Question 52 – The sprinkler shown rotates horizontally about a frictionless hinge. Total water flow is 1 litre/s, shared equally by two arms with outlet areas 1 cm²…
- Question 53 – A 2 kg block slides steadily down a vertical wall, lubricated by an oil film 0.15 mm thick over area 0.04 m². Film velocity varies linearly as shown.…
- Question 54 – A 0.05 m³ tank contains saturated water and steam at 200°C, with 8 kg liquid. Saturation pressure is 1.5538 MPa; vf = 0.001157 m³/kg, vg = 0.12736…
- Question 55 – Steam passes through a nozzle at 0.1 kg/s with heat loss 5 kW. Inlet and outlet enthalpies are 2500 and 2350 kJ/kg. Inlet speed is negligible. Exit…
- Question 56 – An air-standard Otto engine receives air at 0.1 MPa and 35°C. Compression ratio is 8; heat input is 500 kJ/kg. Air cp = 1.005, cv = 0.718 and R =…
- Question 57 – A slab is 20 cm thick with conductivity 2.5 W/m K. Side Q is maintained at 25°C; side P is exposed to fluid at 45°C with h = 10 W/m² K, as shown.…
- Question 58 – The true stress–true strain curve shown loads a strain-hardening material to A at 500 MPa and strain 0.5, then unloads to B at 100 MPa. With E = 200…
- Question 59 – In orthogonal cutting, uncut thickness is 0.010 mm, cutting speed 130 m/min, rake angle 15° and width 6 mm. Chip thickness is 0.015 mm, cutting force…
- Question 60 – A bar is compressed to half its original length. True-strain magnitude, to two decimals, is .
- Question 61 – Minimize 3x+5y subject to 3x+5y15, 4x+9y8, 13x+2y2 and x,y0. The minimum is .
- Question 62 – Six jobs have (processing time including setup; due date) in days: A (3;8), B (7;16), C (4;4), D (9;18), E (5;17), F (13;19). Using shortest…
- Question 63 – The clockwise external drum shown engages a short shoe at Y on rigid lever XYZ, hinged at X. A 100 N force acts at Z as shown. With friction…
- Question 64 – A 2 kg block P slides down a surface and passes the lowest point Q at 20 m/s. Local radius of curvature is 2 m as shown. With g = 10 m/s², normal…
- Question 65 – ECM cuts a 10 mm × 30 mm rectangular through-hole in a 12 mm aluminium plate in 2 minutes at 90% efficiency. Aluminium specific removal rate is…