GATE ME 2023
Paper was held on Sat, Feb 4, 2023 9:00 AM
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## GATE ME

A machine produces a defective component with a probability of 0.015. The number of defective components in a packed box
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The figure shows the plot of a function over the interval [-4, 4]. Which one of the options given CORRECTLY identifies t
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A vector field π(π₯, π¦, π§) = π₯ πΜ + π¦ jΜ β 2π§ kΜ is defined over a conical region having height β = 2, base rad
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A linear transformation maps a point (π₯, π¦) in the plane to the point (π₯Μ, π¦Μ) according to the rule π₯Μ = 3π¦, π¦Μ
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The value of k that makes the complex-valued function π(π§) = πβππ₯&nbsp;(cos 2π¦ β π sin 2π¦) analytic, where π§
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Which one of the options given is the inverse Laplace transform of&nbsp;$\rm \frac{1}{s^3-s}$? π’(π‘) denotes the unit-s
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The smallest perimeter that a rectangle with area of 4 square units can have is ______ units. (Answer in integer)
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Consider the second-order linear ordinary differential equation $\rm x^2\frac{d^2y}{dx^2}+x\frac{dy}{dx}-y=0, x\ge1$ w
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The initial value problem $\rm \frac{dy}{dt}+2y=0, y(0)=1$ is solved numerically using the forward Eulerβs method with
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The options show frames consisting of rigid bars connected by pin joints. Which one of the frames is non-rigid?&nbsp;
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A spherical ball weighing 2 kg is dropped from a height of 4.9 m onto an immovable rigid block as shown in the figure. I
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Air (density = 1.2 kg/m3, kinematic viscosity = 1.5 Γ 10-5 m2/s) flows over a flat plate with a free-stream velocity of
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Consider an isentropic flow of air (ratio of specific heats = 1.4) through a duct as shown in the figure. The variation
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The velocity field of a certain two-dimensional flow is given by V(π₯, π¦) = π(π₯πΜ β π¦πΜ) where π = 2 s-1. The c
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Consider a unidirectional fluid flow with the velocity field given by V(π₯, π¦, π§, π‘) = π’(π₯, π‘) πΜ where π’(0,π‘
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The figure shows two fluids held by a hinged gate. The atmospheric pressure is Pa = 100 kPa. The moment per unit width a
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An explosion at time t = 0 releases energy πΈ at the origin in a space filled with a gas of density&nbsp;Ο. Subsequently
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Consider incompressible laminar flow of a constant property Newtonian fluid in an isothermal circular tube. The flow is
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Consider a laterally insulated rod of length L and constant thermal conductivity. Assuming one-dimensional heat conducti
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Consider a counter-flow heat exchanger with the inlet temperatures of two fluids (1 and 2) being T1, in = 300 K and T2,
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A cylindrical rod of length β and diameter π is placed inside a cubic enclosure of side length πΏ. π denotes the inner
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A very large metal plate of thickness π and thermal conductivity π is cooled by a stream of air at temperature πβ&nbs
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With reference to the Economic Order Quantity (EOQ) model, which one of the options given is correct?&nbsp;
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Which one of the options given represents the feasible region of the linear programming model: πππ₯ππππ§π 45π1 +
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A solid part (see figure) of polymer material is to be fabricated by additive manufacturing (AM) in square-shaped layers
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The S-N curve from a fatigue test for steel is shown. Which one of the options gives the endurance limit?
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The braking system shown in the figure uses a belt to slow down a pulley rotating in the clockwise direction by the appl
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Two surfaces P and Q are to be joined together. In which of the given joining operation(s), there is no melting of the t
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In a metal casting process to manufacture parts, both patterns and moulds provide shape by dictating where the material
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In an ideal orthogonal cutting experiment (see figure), the cutting speed V is 1 m/s, the rake angle of the tool Ξ± = 5Β°,
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A CNC machine has one of its linear positioning axes as shown in the figure, consisting of a motor rotating a lead screw
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The atomic radius of a hypothetical face-centered cubic (FCC) metal is (β2/10) nm. The atomic weight of the metal is 24.
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A steel sample with 1.5 wt.% carbon (no other alloying elements present) is slowly cooled from 1100 Β°C to just below the
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A part, produced in high volumes, is dimensioned as shown. The machining process making this part is known to be statist
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A coordinate measuring machine (CMM) is used to determine the distance between Surface SP and Surface SQ of an approxima
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An optical flat is used to measure the height difference between a reference slip gauge A and a slip gauge B. Upon viewi
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The effective stiffness of a cantilever beam of length L and flexural rigidity EI subjected to a transverse tip load W i
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A beam is undergoing pure bending as shown in the figure. The stress (π)-strain (π) curve for the material is also giv
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The principal stresses at a point P in a solid are 70 MPa, β70 MPa and 0. The yield stress of the material is 100 MPa. W
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Which of the plot(s) shown is/are valid Mohrβs circle representations of a plane stress state in a material? (The center
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A beam of length πΏ is loaded in the π₯π¦ βplane by a uniformly distributed load, and by a concentrated tip load paralle
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The figure shows a thin-walled open-top cylindrical vessel of radius π and wall thickness π‘. The vessel is held along
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Cylindrical bars P and Q have identical lengths and radii, but are composed of different linear elastic materials. The Y
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Ignoring the small elastic region, the true stress (π) β true strain (π) variation of a material beyond yielding follo
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The area moment of inertia about the y-axis of a linearly tapered section shown in the figure is _____________ m4 . (An
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A cylindrical bar has a length πΏ = 5 π and cross section area π = 10 π2 . The bar is made of a linear elastic materi
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A cylindrical transmission shaft of length 1.5 m and diameter 100 mm is made of a linear elastic material with a shear m
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A cuboidal part has to be accurately positioned first, arresting six degrees of freedom and then clamped in a fixture, t
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Two meshing spur gears 1 and 2 with diametral pitch of 8 teeth per mm and an angular velocity ratio |Ο2&nbsp;|/|Ο1&nbsp;
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The figure shows a block of mass m = 20 kg attached to a pair of identical linear springs, each having a spring constant
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The figure shows a wheel rolling without slipping on a horizontal plane with angular velocity π1. A rigid bar PQ is pin
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A heat engine extracts heat (πH) from a thermal reservoir at a temperature of 1000 K and rejects heat (πL) to a therma
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Which one of the following statements is FALSE?
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Consider a fully adiabatic piston-cylinder arrangement as shown in the figure. The piston is massless and cross-sectiona
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Consider a mixture of two ideal gases, X and Y, with molar masses MΜX = 10 kg/kmol and MΜY = 20 kg/kmol, respectively, i
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## General Aptitude

He did not manage to fix the car himself, so he _______ in the garage.
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Planting : Seed :: Raising : _____ (By word meaning)&nbsp;
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A certain country has 504 universities and 25951 colleges. These are categorised into Grades I, II, and III as shown in
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The minute-hand and second-hand of a clock cross each other _______ times between 09:15:00 AM and 09:45:00 AM on a day.&
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The symbols O$, *, \Delta$, and $\square$ are to be filled, one in each box, as shown below. The rules for filling in t
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In a recently held parent-teacher meeting, the teachers had very few complaints about Ravi. After all, Ravi was a hardwo
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Consider the following inequalities π2 β 4π &lt; 4 3π + 2π &lt; 6 where π and π are positive integers. The val
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Which one of the sentence sequences in the given options creates a coherent narrative? (i) I could not bring myself to
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How many pairs of sets (S,T) are possible among the subsets of {1, 2, 3, 4, 5, 6} that satisfy the condition that S is a
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An opaque pyramid (shown below), with a square base and isosceles faces, is suspended in the path of a parallel beam of
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