GATE ME 2022 Set 1
Paper was held on Sun, Feb 13, 2022 3:30 AM
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## GATE ME

The limit $\rm p = \displaystyle\lim_{x \rightarrow \pi} \left( \frac{x^2 + α x + 2 \pi^2}{x - \pi + 2 \sin x} \right)$
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Solution of ∇2T = 0 in a square domain (0 &lt; x &lt; 1 and 0 &lt; y &lt; 1) with boundary conditions: T(x, 0) = x; T(0
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Given a function $\rm ϕ = \frac{1}{2} (x^2 + y^2 + z^2)$&nbsp;in three-dimensional Cartesian space, the value of the su
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The Fourier series expansion of x3&nbsp;in the interval −1 ≤ x &lt; 1 with periodic continuation has
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If A =&nbsp;$\begin{bmatrix} 10 &amp; 2k + 5 \\\ 3k - 3 &amp; k + 5 \end{bmatrix}$&nbsp;is a symmetric matrix, the valu
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The value of the integral $\rm \oint \left( \frac{6z}{2z^4 - 3z^3 + 7 z^2 - 3z + 5} \right) dz$ evaluated over a count
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The system of linear equations in real (x, y) given by $\rm \begin{pmatrix} \rm x &amp; \rm y \end{pmatrix} \begin{bmat View Question Let a random variable X follow Poisson distribution such that Prob(X&nbsp;= 1) = Prob(X&nbsp;= 2). The value of Prob(X View Question Consider two vectors$\rm \vec a = 5 i + 7 j + 2 k \rm \vec b = 3i - j + 6k$Magnitude of the component of&nbsp;$\
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The plane of the figure represents a horizontal plane. A thin rigid rod at rest is&nbsp;pivoted without friction about a
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A structure, along with the loads applied on it, is shown in the figure. Self-weight of all the members is negligible an
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Two rigid massless rods PR and RQ are joined at frictionless pin-joint R and are resting on ground at P and Q, respectiv
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A cylindrical disc of mass m = 1 kg and radius r = 0.15 m was spinning at&nbsp;𝜔 = 5 rad/s when it was placed on a flat
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A tiny temperature probe is fully immersed in a flowing fluid and is moving with zero relative velocity with respect to
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In the following two-dimensional momentum equation for natural convection over a surface immersed in a quiescent fluid a
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The figure shows a purely convergent nozzle with a steady, inviscid compressible flow of an ideal gas with constant ther
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A solid spherical bead of lead (uniform density = 11000 kg/m3) of diameter d = 0.1 mm sinks with a constant velocity V i
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Consider steady, one-dimensional compressible flow of a gas in a pipe of diameter 1 m. At one location in the pipe, the
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A steady two-dimensional flow field is specified by the stream function ψ = kx3y, where x&nbsp;and y&nbsp;are in meter
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A flat plate made of cast iron is exposed to a solar flux of 600 W/m2 at an ambient temperature of 25 °C. Assume that th
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Consider a rod of uniform thermal conductivity whose one end (x = 0) is insulated and the other end (x = L) is exposed t
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Consider a solid slab (thermal conductivity, k = 10 W∙m-1∙K-1) with thickness 0.2 m and of infinite extent in the other
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During open-heart surgery, a patient’s blood is cooled down to 25 °C from 37 °C using a concentric tube counter-flow hea
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In a linear programming problem, if a resource is not fully utilized, the shadow price of that resource is
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Which one of the following is NOT a form of inventory?
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Activities A to K are required to complete a project. The time estimates and the immediate predecessors of these activit
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An assignment problem is solved to minimize the total processing time of four jobs (1, 2, 3 and 4) on four different mac
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The product structure diagram shows the number of different components required at each level to produce one unit of the
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A square threaded screw is used to lift a load W by applying a force F. Efficiency of square threaded screw is expressed
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A CNC worktable is driven in a linear direction by a lead screw connected directly to a stepper motor. The pitch of the
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The type of fit between a mating shaft of diameter&nbsp;$25.0^{\begin{matrix} +0.010 \\\ -0.010 \end{matrix}}$&nbsp;mm a
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Which of the following methods can improve the fatigue strength of a circular mild steel (MS) shaft?
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A bracket is attached to a vertical column by means of two identical rivets U and V separated by a distance of 2a = 100
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Which of the following heat treatment processes is/are used for surface hardening of steels?
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Which of the following additive manufacturing technique(s) can use a wire as a feedstock material?
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Electrochemical machining operations are performed with tungsten as the tool, and&nbsp;copper and aluminum as two differ
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Under orthogonal cutting condition, a turning operation is carried out on a metallic workpiece at a cutting speed of 4 m
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A 1 mm thick cylindrical tube, 100 mm in diameter, is orthogonally turned such that the entire wall thickness of the tub
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A 4 mm thick aluminum sheet of width w = 100 mm is rolled in a two-roll mill of roll diameter 200 mm each. The workpiece
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Two mild steel plates of similar thickness, in butt-joint configuration, are welded&nbsp;by gas tungsten arc welding pro
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A uniform light slender beam AB of section modulus EI is pinned by a frictionless joint A to the ground and supported by
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Assuming the material considered in each statement is homogeneous, isotropic, linear elastic, and the deformations are i
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An L-shaped elastic member ABC with slender arms AB and BC of uniform crosssection&nbsp;is clamped at end A and connecte
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A thin-walled cylindrical pressure vessel has mean wall thickness of t and nominal radius of r. The Poisson’s ratio of t
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The figure shows a schematic of a simple Watt governor mechanism with the spindle O1O2 rotating at an angular velocity&n
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A rigid uniform annular disc is pivoted on a knife edge A in a uniform gravitational field as shown, such that it can ex
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A planar four-bar linkage mechanism with 3 revolute kinematic pairs and 1 prismatic kinematic pair is shown in the figur
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Consider a forced single degree-of-freedom system governed by&nbsp;\$\rm \ddot x(t) + 2 ζ ω_n \dot x (t) + ω_n^2 x(t) = ω
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A schematic of an epicyclic gear train is shown in the figure. The sun (gear 1) and&nbsp;planet (gear 2) are external, a
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The Clausius inequality holds good for
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A polytropic process is carried out from an initial pressure of 110 kPa and volume of 5 m3 to a final volume of 2.5 m3.
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In Fe-Fe3C phase diagram, the eutectoid composition is 0.8 weight % of carbon at 725 ºC. The maximum solubility of carbo
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Consider a one-dimensional steady heat conduction process through a solid slab of thickness 0.1 m. The higher temperatur
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In a steam power plant based on Rankine cycle, steam is initially expanded in a high-pressure turbine. The steam is then
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An engine running on an air standard Otto cycle has a displacement volume 250 cm3 and a clearance volume 35.7 cm3. The p
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## General Aptitude

After playing _________ hours of tennis, I am feeling _________ tired to walk back.
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The average of the monthly salaries of M, N and S is ₹ 4000. The average of the monthly salaries of N, S and P is ₹ 5000
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A person travelled 80 km in 6 hours. If the person travelled the first part with a uniform speed of 10 kmph and the rema
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Four girls P, Q, R and S are studying languages in a University. P is learning French and Dutch. Q is learning Chinese a
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A block with a trapezoidal cross-section is placed over a block with rectangular cross section as shown above. Which o
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Humans are naturally compassionate and honest. In a study using strategically placed wallets that appear “lost”, it was
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A rhombus is formed by joining the midpoints of the sides of a unit square. What is the diameter of the largest circle
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An equilateral triangle, a square and a circle have equal areas. What is the ratio of the perimeters of the equilateral
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Given below are three conclusions drawn based on the following three statements. Statement 1 : All teachers are profess
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In a 12-hour clock that runs correctly, how many times do the second, minute, and hour hands of the clock coincide, in a
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