GATE 2019 ME (ME1) – Previous Year Questions with Solutions
All 65 questions of GATE 2019 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 – “John Thomas, an writer, passed away in 2018.” Choose the correct word.
- Question 2 – “ I permitted him to leave, I wouldn’t have had any problem with him being absent, I?” Choose the correct words.
- Question 3 – A worker notices the factory clock’s hour hand moved 225° during her stay. For how long did she stay?
- Question 4 – Two integers have sum 26 and product 165. Find their difference.
- Question 5 – The minister avoided mentioning women’s reservation in the private sector. He was accused of the issue.
- Question 6 – Under a legal system, prisoners may make one statement. If true, they are hanged; if false, they are shot. One prisoner’s statement left the judge no…
- Question 7 – Rs 100000 is split between schemes earning 10% and 12%. Interchanging the profit percentages would reduce profit by Rs 120. Find the ratio of the…
- Question 8 – Congo was named by Europeans. Congo’s dictator Mobuto later changed the name of the country and the river to Zaire with the objective of Africanising…
- Question 9 – A firm employs workers at five skill levels P, Q, R, S and T. The 2010 shares are shown in the pie chart. Total employment was 600 in 2010 and…
- Question 10 – M and N have four children P, Q, R and S. Only P and R are married; they have children X and Y respectively. Y is a legitimate child of W. Which…
- Question 11 – For P=bmatrix1&1&0\\0&1&1\\0&0&1bmatrix, find the number of distinct eigenvalues.
- Question 12 – The parabola x=y2, 0 x1, bounds the shaded region shown. Find the volume generated by rotating this region through 360° about the x-axis.
- Question 13 – For dy/dx+7x2y=0 with y(0) = 3/7, find y(1).
- Question 14 – Titanium rod lengths are normally distributed with mean 440 mm and standard deviation 1 mm. What percentage lies between 438 mm and 441 mm?
- Question 15 – A flat-faced follower is driven by an eccentric circular cam at constant angular speed ω. At t = 0, y(0) = 0 and the system is positioned as shown.…
- Question 16 – The spring–mass systems I and II shown have natural frequencies I and II. Find their ratio I/ II.
- Question 17 – A 20° full-depth spur gear transmits 20 kW at 200 rad/s. Pitch-circle diameter is 100 mm. Find the radial tooth force magnitude.
- Question 18 – During a non-flow thermodynamic process executed by a perfect gas, heat interaction equals work interaction. Which process gives this equality?
- Question 19 – For hydrodynamically and thermally fully developed laminar flow through a constant-section circular pipe, compare Nusselt numbers at constant wall…
- Question 20 – Order the hydraulic turbines by descending flow rate under common design practice.
- Question 21 – Two slender rods each of length L and diameter d, with L ≫ d, have conductivities k 1,k 2. They are joined end to end into a 2L composite. Neglect…
- Question 22 – An ideal vapour-compression refrigerator replaces throttling by isentropic expansion with all other processes unchanged. Which is true?
- Question 23 – In casting, the vertical passage carrying molten metal downward from pouring basin to runner is called .
- Question 24 – Which welding method gives the highest heat flux (W/mm²)?
- Question 25 – A 400 mm × 40 mm × 20 mm steel sample is reduced uniformly in thickness by 2 mm in one pass using horizontal slab milling. Cutter diameter is 100 mm,…
- Question 26 – Position vector OP for P(20,10) rotates counterclockwise 30° in the XY plane to position Q shown. Find Q’s coordinates (x,y).
- Question 27 – Monthly demand is January 450, February 440, March 460, April 510, May 520, June 495, July 475 and August 560. Using a simple three-month moving…
- Question 28 – Estimate 24x3\,dx using the trapezoidal rule with two equal segments.
- Question 29 – A 10 kg block rests on a horizontal floor. Static-friction coefficient is 0.2 and g = 9.81 m/s². A horizontal 10 N force acts as shown. Find friction…
- Question 30 – A cylindrical rod 10 mm in diameter and 1.0 m long is fixed at one end. A torque twists the other by 10°. Its maximum shear strain is p10-3. Find p,…
- Question 31 – A solid cube of side 1 m is initially at 32°C. Linear thermal-expansion coefficient is 10-5/ C and bulk modulus 200 GPa. It is constrained on all…
- Question 32 – A high-cycle fatigue specimen has mean cyclic stress +140 MPa and minimum stress −70 MPa. Find R-ratio (minimum/maximum stress), to one decimal place.
- Question 33 – Water velocity is V=(4/t+x+y) j m/s, where t > 0 is in seconds and x,y in metres. Find total acceleration magnitude at (x,y) = (1,1), t = 2 s (m/s²).
- Question 34 – One kg air initially at 300 K and 10 bar expands isothermally to 1 bar. Treat it as ideal with R = 0.287 kJ/(kg·K). Find entropy change (kJ/(kg·K)),…
- Question 35 – The stress–strain curve of an ideal elastic–plastic strain-hardening metal is shown. It was loaded from O through initial yield P to Q, unloaded to…
- Question 36 – The equations x+y+z=1, ax-ay+3z=5, 5x-3y+az=6 have infinitely many solutions for which a?
- Question 37 – A harmonic function satisfies Laplace’s equation. For u(x,y)=2x2-2y2+4xy, find its conjugate harmonic function v(x,y).
- Question 38 – Variables x and y are uniformly distributed on 0 to 10 and 0 to 20 respectively. Find the probability x + y > 20.
- Question 39 – A car of weight W accelerates at a in the shown direction. Its centre of gravity is height h above ground, midway between front and rear axles…
- Question 40 – The four-bar mechanism shown has AB = 5 cm, AD = 4 cm and DC = 2 cm. At this instant AB and DC are both perpendicular to AD. AB rotates at 10 rad/s.…
- Question 41 – An aircraft turbojet rotor has mass 180 kg and polar moment 10 kg·m² about its axis. It spins at 1100 rad/s clockwise viewed from the aircraft front.…
- Question 42 – A 1 m constant-diameter pipe is heated with uniform wall heat flux. Flow enters hydrodynamically fully developed, is incompressible, steady and…
- Question 43 – Gas flows over a resistance heater supplied with 101 kW electrical power. It enters the duct at 100 kPa, 27°C and 15 m³/s; 51 kW is lost to…
- Question 44 – The plane-strain forging block shown has zero z strain and uniaxial-compression yield strength 300 MPa, obeying Tresca’s criterion. The entire block…
- Question 45 – In orthogonal turning of a cylindrical tube of wall thickness 5 mm, axial and tangential cutting forces are 1259 N and 1601 N. Measured chip thickness…
- Question 46 – A turned shaft diameter is 65.00+0.01 -0.05 mm. It receives 50 μm TiN coating with allowed variation ±5 μm. Find minimum hole diameter (mm) just…
- Question 47 – Match casting defects P: blow hole, Q: misrun, R: hot tearing, S: wash with causes 1: poor collapsibility, 2: mould erosion, 3: poor permeability, 4:…
- Question 48 – The shown truss comprises AB, BC, CD, AD and BD and carries 10 kN vertically downward at D. Find BC axial force magnitude (kN).
- Question 49 – An elastic straight beam of length 10π m has square cross-section of side 5 mm and E = 200 GPa. It is bent so the ends meet, forming a circle of mean…
- Question 50 – The prismatic beam shown is pinned at both ends, length π m, square side 6 mm, E = 200 GPa and =310-6\ K-1. Find minimum uniform temperature rise…
- Question 51 – A 100 mm tensile specimen fails at 40 kN and cross-head displacement 15 mm. UTM compliance is constant at 510-8 m/N. Find specimen failure strain (%).
- Question 52 – At a component point, xx=100 MPa, yy=220 MPa and xy= yx=80 MPa; all other stress components are zero. Yield strength is 468 MPa. Find safety factor by…
- Question 53 – A uniform thin disc of mass 1 kg and radius 0.1 m rolls without slipping as shown. Spring k1 = 400 N/m attaches to centre A; spring k2 = 100 N/m…
- Question 54 – The shown single-block short-shoe brake has torque capacity 250 N·m. Its cylindrical drum rotates anticlockwise at 100 rpm; friction coefficient is…
- Question 55 – Two immiscible incompressible viscous fluids of equal density occupy the shown 2 m gap between infinite horizontal plates. Bottom plate is fixed; top…
- Question 56 – A cube of side 100 mm and density 800 kg/m³ rests on one face at the bottom of an empty container. Liquid of density 1000 kg/m³ is added. Find minimum…
- Question 57 – Three slabs are joined as shown without contact resistance. Each is 1 m thick and has conductivity 5 W/(m·K). The centre slab has nonuniform heat…
- Question 58 – One mole of H₂ in a rigid 1000 L vessel is heated from 27°C to 37°C. With ideal gas behavior and R = 8.314 J/(mol·K), find pressure increase (Pa), to…
- Question 59 – The regenerative steam cycle shown uses one open feedwater heater. Turbine expansion is isentropic; bleed enters the heater from state 2. Process 3–4…
- Question 60 – An air turbine has isentropic efficiency 0.70 at pressure ratio 3. The ratio increases to 5 with inlet conditions and actual specific work unchanged.…
- Question 61 – Evaluate 1e x x\,dx, to three decimal places.
- Question 62 – A sharp ASA turning tool has side and end cutting-edge angles 45° and 10°. Feed is 0.1 mm/rev. Find generated surface centre-line average roughness…
- Question 63 – Taylor’s tool-life equation is VTn=C, with V in m/min and T in min. Tool X has n = 0.3, C = 60; tool Y has n = 0.6, C = 90. Find the cutting speed…
- Question 64 – Assign each of five jobs to a distinct machine to minimize total processing time. Times in minutes for M1, M2, M3, M4, M5 are: J1: 40, 30, 50, 50, 58.…
- Question 65 – A project has activities with immediate predecessors and durations (weeks): P: none, 5; Q: none, 1; R: Q, 2; S: P and R, 4; T: P, 6; U: S and T, 3.…