GATE ME 2014 Set 2

## GATE ME

$$\mathop {Lt}\limits_{x \to 0} \left( {{{{e^{2x}} - 1} \over {\sin \left( {4x} \right)}}} \right)\,\,$$ is equal to

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Curl of vector $$\,\,\overrightarrow F = {x^2}{z^2}\widehat i - 2x{y^2}z\widehat j + 2{y^2}{z^3}\widehat k\,\,$$ is

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A box contains $$25$$ parts of which $$10$$ are defective. Two parts are being drawn simultaneously in a random manner f

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Consider an unbiased cubic die with opposite faces coloured identically and each face coloured red, blue or green such t

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The general solution of the differential equation $$\,\,{{dy} \over {dx}} = \cos \left( {x + y} \right),\,\,$$ with $$c$

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The value of $$\int\limits_{2.5}^4 {\ln \left( x \right)} $$ calculated using the Trapezoidal rule with five sub-interv

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An analytic function of a complex variable $$z=x+iy,$$ where $$i = \sqrt { - 1} $$ is expressed as
$$f\left( z \right)

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A two member truss ABC is shown in the figure. The force (in kN) transmitted in member AB is ________

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A truck accelerates up a 10° incline with a crate of 100 kg. Value of static coefficient of friction between the crate a

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The difference in pressure (in $$N/{m^2}$$) across an air bubble of diameter $$0.001$$ $$m$$ immersed in water (surface

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For an incompressible flow field , $$\overrightarrow {V,} $$ which one of the following conditions must be satisfied?

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A spherical balloon with a diameter of $$10m,$$ shown in the figure below is used for advertisements. The balloon is fil

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Water flows through a $$10$$ $$mm$$ diameter and $$250$$ $$m$$ long smooth pipe at an average velocity of $$0.1$$ $$m/s.

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Consider laminar flow of water over a flat plate of length $$1$$ $$m.$$ If the boundary layer thickness at a distance of

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A material $$P$$ of thickness $$1$$ $$mm$$ is sandwiched between two steel slabs, as shown in the figure below. $$A$$ he

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Biot number signifies the ratio of

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Consider a two-dimensional laminar flow over a long cylinder as shown in the figure below.
The free stream velocity is

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For laminar forced convection over a flat plate, if the free stream velocity increases by a factor of $$2,$$ the average

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A hemispherical furnace of $$1$$ $$m$$ radius has the inner surface (emissivity, $$\varepsilon = 1$$) of its roof maint

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Water flows through a tube of diameter $$25mm$$ at an average velocity of $$1.0m/s.$$ The properties of water are $$\rho

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In a heat exchanger, it is observed that $$\Delta {T_1} = \Delta {T_2},$$ where $$\Delta {T_1}$$ is the temperature diff

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In a concentric counter flow heat exchanger, water flows through the inner tube at $${25^ \circ }C$$ and leaves at $${4

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Consider the following data with reference to elementary deterministic economic order quantity model
The total number

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A project has four activities $$P,Q, R$$ and $$S$$ as shown below.
The normal cost of the project is Rs. $$10,000/-$$

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If there are $$m$$ sources and $$n$$ destinations in a transportation matrix, the total number of basic variables in a b

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A component can be produced by any of the four processes $${\rm I},$$ $${\rm II},$$ $${\rm III},$$ and $${\rm IV}$$. The

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Consider the two states of stress as shown in configurations $${\rm I}$$ and $${\rm II}$$ in the figure below. From the

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In a structure subjected to fatigue loading, the minimum and maximum stresses developed in a cycle are $$200$$$$MPa$$ an

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For the three bolt system shown in the figure, the bolt material has shear yield strength of $$200$$ $$MPa.$$ For a fact

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A spur pinion of pitch diameter $$50$$ $$mm$$ rotates at $$200$$ $$rad/s$$ and transmits $$3$$ $$kW$$ power. The pressur

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A disc clutch with a single friction surface has coefficient of friction equal to $$0.3.$$ The maximum pressure which ca

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With respect to metal working, match Group A with Group B:

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The relationship between true strain $$\left( {{\varepsilon _T}} \right)$$ and engineering strain $$\left( {{\varepsilon

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A mild steel plate has to be rolled in one pass such that the final plate thickness is $$2/{3^{rd}}$$ of the initial thi

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Match the Machine Tools (Group A) with the probable Operations (Group B)

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A hole of $$20$$ $$mm$$ diameter is to be drilled in a steel block of $$40$$ $$mm$$ thickness. The drilling is performed

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A rectangular hole of size $$100\,\,mm \times 50\,\,mm$$ is to be made on a $$5$$ $$mm$$ thick sheet of steel having ult

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The flatness of a machine bed can be measured using

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A robot arm $$PQ$$ with end coordinates $$P(0,0)$$ and $$Q(2,5)$$ rotates counter clockwise about $$P$$ in the $$XY$$ pl

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For the $$CNC$$ part programming, match Group A with Group B:

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A steel cube, with all faces free to deform, has Young’s modulus, $$E,$$ Poisson’s ratio, $$ν,$$ and coefficient of ther

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A thin plate of uniform thickness is subject to pressure as shown in the figure below
Under the assumption of plane s

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A cantilever beam of length, $$L,$$ with uniform cross-section and flexural rigidity $$ EI,$$ is loaded uniformly by a v

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The flexural rigidity $$(EI)$$ of a cantilever beam is assumed to be constant over the length of the beam as shown in fi

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Maximum fluctuation of kinetic energy in an engine has been calculated to be $$2600$$ J. Assuming that the engine runs a

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Consider a flywheel whose mass $$M$$ is distributed almost equally between a heavy, ring-like rim of radius $$R$$ and a

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What is the natural frequency of the spring mass system shown below? The contact between the block and the inclined plan

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A pure substance at $$8$$ $$MPa$$ and $${400^ \circ }C$$ is having a specific internal energy of $$2864$$ $$kJ/kg$$ and

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Steam at a velocity of $$10$$ $$m/s$$ enters the impulse turbine stage with symmetrical blading having blade angle $${30

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