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

View Question 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

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

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

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

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

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

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

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

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

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

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

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

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

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

View Question Biot number signifies the ratio of

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

View Question 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

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

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

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

View Question The flatness of a machine bed can be measured using

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

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

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

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

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

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

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

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

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

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

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

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