GATE 2021 ME (ME1) – Previous Year Questions with Solutions
All 65 questions of GATE 2021 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 – Consider the following sentences: (i) After his surgery, Raja hardly could walk. (ii) After his surgery, Raja could barely walk. (iii) After his…
- Question 2 – Ms. X came out of a building through its front door to find her shadow due to the morning sun falling to her right side with the building to her back.…
- Question 3 – In the above figure, O is the center of the circle and, M and N lie on the circle. The area of the right triangle MON is 50 cm². What is the area of…
- Question 4 – If “⊕” means “−”, “⊗” means “÷”, “Δ” means “+”, “∇” means “×”, then, the value of the expression 23((42)4)=
- Question 5 – "The increased consumption of leafy vegetables in the recent months is a clear indication that the people in the state have begun to lead a healthy…
- Question 6 – Oxpeckers and rhinos manifest a symbiotic relationship in the wild. The oxpeckers warn the rhinos about approaching poachers, thus possibly saving the…
- Question 7 – A jigsaw puzzle has 2 pieces. One of the pieces is shown above. Which one of the given options for the missing piece when assembled will form a…
- Question 8 – The number of hens, ducks and goats in farm P are 65, 91 and 169, respectively. The total number of hens, ducks and goats in a nearby farm Q is 416.…
- Question 9 – The distribution of employees at the rank of executives, across different companies C1, C2, …, C6 is presented in the chart given above. The ratio of…
- Question 10 – Five persons P, Q, R, S and T are sitting in a row not necessarily in the same order. Q and R are separated by one person, and S should not be seated…
- Question 11 – If y(x) satisfies the differential equation dydx x+y x=1, subject to the condition y(/2)=/2, then y(/6) is
- Question 12 – The value of x01- xx2 is
- Question 13 – The Dirac-delta function (t-t 0) for t,t 0 R has the following property: ab(t-t 0)\,dt=1 if a<t 0<b, and 0 otherwise. The Laplace transform of the…
- Question 14 – The ordinary differential equation dydt=- y subject to an initial condition y(0)=1 is solved numerically using the following scheme: y(t n+1)-y(t…
- Question 15 – Consider a binomial random variable X. If X 1,X 2,,X n are independent and identically distributed samples from the distribution of X with sum Y=…
- Question 16 – The loading and unloading response of a metal is shown in the figure. The elastic and plastic strains corresponding to 200 MPa stress, respectively,…
- Question 17 – In a machining operation, if a cutting tool traces the workpiece such that the directrix is perpendicular to the plane of the generatrix as shown in…
- Question 18 – The correct sequence of machining operations to be performed to finish a large diameter through hole is
- Question 19 – In modern CNC machine tools, the backlash has been eliminated by
- Question 20 – Consider the surface roughness profile as shown in the figure. The center line average roughness (R a, in m) of the measured length (L) is
- Question 21 – In which of the following pairs of cycles, both cycles have at least one isothermal process?
- Question 22 – Superheated steam at 1500 kPa, has a specific volume of 2.75 m³/kmol and compressibility factor (Z) of 0.95. The temperature of steam is °C (round off…
- Question 23 – A hot steel spherical ball is suddenly dipped into a low temperature oil bath. Which of the following dimensionless parameters are required to…
- Question 24 – An infinitely long pin fin, attached to an isothermal hot surface, transfers heat at a steady rate of Q 1 to the ambient air. If the thermal…
- Question 25 – The relative humidity of ambient air at 300 K is 50% with a partial pressure of water vapour equal to p v. The saturation pressure of water at 300 K…
- Question 26 – Consider a reciprocating engine with crank radius R and connecting rod of length L. The secondary unbalance force for this case is equivalent to…
- Question 27 – A cantilever beam of length, L, and flexural rigidity, EI, is subjected to an end moment, M, as shown in the figure. The deflection of the beam at…
- Question 28 – A prismatic bar PQRST is subjected to axial loads as shown in the figure. The segments having maximum and minimum axial stresses, respectively, are
- Question 29 – Shear stress distribution on the cross-section of the coil wire in a helical compression spring is shown in the figure. This shear stress distribution…
- Question 30 – Robot Ltd. wishes to maintain enough safety stock during the lead time period between starting a new production run and its completion such that the…
- Question 31 – A pressure measurement device fitted on the surface of a submarine, located at a depth H below the surface of an ocean, reads an absolute pressure of…
- Question 32 – Consider fully developed, steady state incompressible laminar flow of a viscous fluid between two large parallel horizontal plates. The bottom plate…
- Question 33 – A rigid insulated tank is initially evacuated. It is connected through a valve to a supply line that carries air at a constant pressure and…
- Question 34 – The figure shows an arrangement of a heavy propeller shaft in a ship. The combined polar mass moment of inertia of the propeller and the shaft is 100…
- Question 35 – Consider a single degree of freedom system comprising a mass M, supported on a spring and a dashpot as shown in the figure. If the amplitude of the…
- Question 36 – Consider a vector p in 2-dimensional space. Let its direction (counter-clockwise angle with the positive x-axis) be . Let p be an eigenvector of a 22…
- Question 37 – Let C represent the unit circle centered at origin in the complex plane, and complex variable, z=x+iy. The value of the contour integral C3z2z\,dz…
- Question 38 – A set of jobs A, B, C, D, E, F, G, H arrive at time t = 0 for processing on turning and grinding machines. Each job needs to be processed in sequence…
- Question 39 – The fundamental thermodynamic relation for a rubber band is given by dU=T\,dS+\,dL, where T is the absolute temperature, S is the entropy, is the…
- Question 40 – Consider a two degree of freedom system as shown in the figure, where PQ is a rigid uniform rod of length, b and mass, m. Assume that the spring…
- Question 41 – A right solid circular cone standing on its base on a horizontal surface is of height H and base radius R. The cone is made of a material with…
- Question 42 – A tappet valve mechanism in an IC engine comprises a rocker arm ABC that is hinged at B as shown in the figure. The rocker is assumed rigid and it…
- Question 43 – Customers arrive at a shop according to the Poisson distribution with a mean of 10 customers/hour. The manager notes that no customer arrives for the…
- Question 44 – Let f(x)=x2-2x+2 be a continuous function defined on x[1,3]. The point x at which the tangent of f(x) becomes parallel to the straight line joining…
- Question 45 – Activities A, B, C and D form the critical path for a project with a PERT network. The means and variances of the activity duration for each activity…
- Question 46 – A true centrifugal casting operation needs to be performed horizontally to make copper tube sections with outer diameter of 250 mm and inner diameter…
- Question 47 – The resistance spot welding of two 1.55 mm thick metal sheets is performed using welding current of 10000 A for 0.25 s. The contact resistance at the…
- Question 48 – An orthogonal cutting operation is performed using a single point cutting tool with a rake angle of 12° on a lathe. During turning, the cutting force…
- Question 49 – In a grinding operation of a metal, specific energy consumption is 15 J/mm³. If a grinding wheel with a diameter of 200 mm is rotating at 3000 rpm to…
- Question 50 – A 200 mm wide plate having a thickness of 20 mm is fed through a rolling mill with two rolls. The radius of each roll is 300 mm. The plate thickness…
- Question 51 – The XY table of a NC machine tool is to move from P(1,1) to Q(51,1); all coordinates are in mm. The pitch of the NC drive leadscrew is 1 mm. If the…
- Question 52 – Consider a single machine workstation to which jobs arrive according to a Poisson distribution with a mean arrival rate of 12 jobs/hour. The process…
- Question 53 – An uninsulated cylindrical wire of radius 1.0 mm produces electric heating at the rate of 5.0 W/m. The temperature of the surface of the wire is 75°C…
- Question 54 – A solid sphere of radius 10 mm is placed at the centroid of a hollow cubical enclosure of side length 30 mm. The outer surface of the sphere is…
- Question 55 – Consider a steam power plant operating on an ideal reheat Rankine cycle. The work input to the pump is 20 kJ/kg. The work output from the high…
- Question 56 – In the vicinity of the triple point, the equation of liquid-vapour boundary in the P-T phase diagram for ammonia is P=24.38-3063/T, where P is…
- Question 57 – A cylindrical jet of water (density = 1000 kg/m³) impinges at the center of a flat, circular plate and spreads radially outwards, as shown in the…
- Question 58 – A single jet Pelton wheel operates at 300 rpm. The mean diameter of the wheel is 2 m. Operating head and dimensions of jet are such that water comes…
- Question 59 – An air-conditioning system provides a continuous flow of air to a room using an intake duct and an exit duct, as shown in the figure. To maintain the…
- Question 60 – Two smooth identical spheres each of radius 125 mm and weight 100 N rest in a horizontal channel having vertical walls. The distance between vertical…
- Question 61 – An overhanging beam PQR is subjected to uniformly distributed load 20 kN/m as shown in the figure. The maximum bending stress developed in the beam is…
- Question 62 – The Whitworth quick return mechanism is shown in the figure with link lengths as follows: OP = 300 mm, OA = 150 mm, AR = 160 mm, RS = 450 mm. The…
- Question 63 – A short shoe drum (radius 260 mm) brake is shown in the figure. A force of 1 kN is applied to the lever. The coefficient of friction is 0.4. The…
- Question 64 – A machine part in the form of cantilever beam is subjected to fluctuating load as shown in the figure. The load varies from 800 N to 1600 N. The…
- Question 65 – A cantilever beam of rectangular cross-section is welded to a support by means of two fillet welds as shown in figure. A vertical load of 2 kN acts at…