GATE ME 2024
Paper was held on Sat, Feb 3, 2024 9:00 AM
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## GATE ME

In order to numerically solve the ordinary differential equation dy/dt = -y for t > 0, with an initial condition y(0) =
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The value of the surface integralwhere S is the external surface of the sphere x2 + y2 + z2 = R2 is
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Let f(z) be an analytic function, where z = x + iy . If the real part of f(z) is cosh x cos y , and the imaginary
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Consider the system of linear equationsx + 2y + z = 52x + ay + 4z = 122x + 4y + 6z = bThe values of a and b such that th
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Let $f(.)$ be a twice differentiable function from $\mathbb{R}^{2} \rightarrow \mathbb{R}$. If $P, \mathbf{x}_{0} \in \ View Question The matrix$\begin{bmatrix} 1 & a \\ 8 & 3 \end{bmatrix}$(where$a > 0$) has a negative eigenvalue if$a$is greater th View Question If the value of the double integral$\int_{x=3}^{4} \int_{y=1}^{2} \frac{dydx}{(x + y)^2}$is$\log_e(\frac{a}{24})$, then View Question If$x(t)$satisfies the differential equation$t \frac{dx}{dt} + (t - x) = 0$subject to the condition$x(1) = 0$, then th View Question Let$X$be a continuous random variable defined on$[0, 1]$such that its probability density function$f(x) = 1$for$0
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A ram in the form of a rectangular body of size $l = 9 \text{ m}$ and $b = 2 \text{ m}$ is suspended by two parallel rop
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A rigid massless tetrahedron is placed such that vertex O is at the origin and the other three vertices A, B, and C lie
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A three-hinge arch ABC in the form of a semi-circle is shown in the figure. The arch is in static equilibrium under vert
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The velocity field of a two-dimensional, incompressible flow is given by $\overrightarrow{V} = \ 2sin{h}\,x\,\hat{i} + View Question In the pipe network shown in the figure, all pipes have the same cross-section and can be assumed to have the same frict View Question Steady, compressible flow of air takes place through an adiabatic converging-diverging nozzle, as shown in the figure. F View Question A liquid fills a horizontal capillary tube whose one end is dipped in a large pool of the liquid. Experiments show that View Question A plane, solid slab of thickness L, shown in the figure, has thermal conductivity k that varies with the spatial coordin View Question Consider incompressible laminar flow over a flat plate with freestream velocity of$u_{\infty}$. The Nusselt number corr View Question Consider a hydrodynamically fully developed laminar flow through a circular pipe with the flow along the axis (i.e., z d View Question Consider a slab of 20 mm thickness. There is a uniform heat generation of$ \dot{q} = 100 \text{ MW/m}^3 $inside the sl View Question A condenser is used as a heat exchanger in a large steam power plant in which steam is condensed to liquid water. The co View Question Consider a hemispherical furnace of diameter$ D = 6 \text{ m} $with a flat base. The dome of the furnace has an emissi View Question A set of jobs$U, V, W, X, Y, Z$arrive at time$t = 0$to a production line consisting of two workstations in series. E View Question A queueing system has one single server workstation that admits an infinitely long queue. The rate of arrival of jobs to View Question A company orders gears in conditions identical to those considered in the economic order quantity (EOQ) model in invento View Question At the current basic feasible solution (bfs)$v_0 (v_0 \in \mathbb{R}^5)$, the simplex method yields the following form View Question In a supplier-retailer supply chain, the demand of each retailer, the capacity of each supplier, and the unit cost in ru View Question For a ball bearing, the fatigue life in millions of revolutions is given by$L = \left(\frac{C}{P}\right)^n$, where$P$View Question Which one of the following failure theories is the most conservative design approach against fatigue failure? View Question A solid massless cylindrical member of 50 mm diameter is rigidly attached at one end, and is subjected to an axial force View Question A band brake shown in the figure has a coefficient of friction of 0.3. The band can take a maximum force of 1.5 kN. The View Question The "Earing" phenomenon in metal forming is associated with View Question The grinding wheel used to provide the best surface finish is View Question The allowance provided to a pattern for easy withdrawal from a sand mold is View Question The most suitable electrode material used for joining low alloy steels using Gas Metal Arc Welding (GMAW) process is View Question The preparatory functions in Computer Numerical Controlled (CNC) machine programming are denoted by the alphabet View Question A cutting tool provides a tool life of 60 minutes while machining with the cutting speed of 60 m/min. When the same tool View Question Aluminium is casted in a cube-shaped mold having dimensions as 20 mm × 20 mm × 20 mm. Another mold of the same mold mate View Question A blanking operation is performed on C20 steel sheet to obtain a circular disc having a diameter of 20 mm and a thicknes View Question In an arc welding process, the voltage and current are 30 V and 200 A, respectively. The cross-sectional area of the joi View Question A flat surface of a C60 steel having dimensions of 100 mm (length) × 200 mm (width) is produced by a HSS slab mill cutte View Question The phases present in pearlite are View Question Which of the following beam(s) is/are statically indeterminate? View Question A horizontal beam of length 1200 mm is pinned at the left end and is resting on a roller at the other end as shown in th View Question The figure shows a thin cylindrical pressure vessel constructed by welding plates together along a line that makes an an View Question The change in kinetic energy$\Delta E$of an engine is$300$J, and minimum and maximum shaft speeds are$\omega_{min}
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A linear spring-mass-dashpot system with a mass of 2 kg is set in motion with viscous damping. If the natural frequency
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The Levi type-A train illustrated in the figure has gears with module $m = 8 \text{ mm/tooth}$. Gears 2 and 3 have 19 an
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At the instant when OP is vertical and AP is horizontal, the link OD is rotating counter clockwise at a constant rate ω
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A vibratory system consists of mass $m$, a vertical spring of stiffness $2k$ and a horizontal spring of stiffness $k$. T
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A furnace can supply heat steadily at 1200 K at a rate of 24000 kJ/min. The maximum amount of power (in kW) that can be
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Which one of the following statements regarding a Rankine cycle is FALSE?
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A piston-cylinder arrangement shown in the figure has a stop located 2 m above the base. The cylinder initially contains
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A heat pump (H.P.) is driven by the work output of a heat engine (H.E.) as shown in the figure. The heat engine extracts
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Consider an air-standard Brayton cycle with adiabatic compressor and turbine, and a regenerator, as shown in the figure.
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## General Aptitude

If &lsquo;&rarr;&rsquo; denotes increasing order of intensity, then the meaning of the words [smile &rarr; giggle &rarr;
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Find the odd one out in the set: {19, 37, 21, 17, 23, 29, 31, 11}
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In the following series, identify the number that needs to be changed to form the Fibonacci series.1, 1, 2, 3, 6, 8, 13,
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The real variables $x, y, z$, and the real constants $p, q, r$ satisfy\$\frac{x}{pq - r^2} = \frac{y}{qr - p^2} = \frac{z
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Take two long dice (rectangular parallelepiped), each having four rectangular faces labelled as 2, 3, 5, and 7. If throw
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In the given text, the blanks are numbered (i)–(iv). Select the best match for all the blanks.Prof. P __(i)__ merely a m
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How many combinations of non-null sets A, B, C are possible from the subsets of {2, 3, 5} satisfying the conditions: (i)
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The bar chart gives the batting averages of VK and RS for 11 calendar years from 2012 to 2022. Considering that 2015 and
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A planar rectangular paper has two V-shaped pieces attached as shown below.This piece of paper is folded to make the fol
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Four equilateral triangles are used to form a regular closed three-dimensional object by joining along the edges. The an
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