GATE ME 2010

## GATE ME

One of the eigen vector of the matrix $$A = \left[ {\matrix{
2 & 2 \cr
1 & 3 \cr
} } \right]$$ is

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The parabolic are $$y = \sqrt x ,1 \le x \le 2$$ is revolved around the $$x$$-axis. The volume of the solid of revolutio

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The function $$y = \left| {2 - 3x} \right|$$

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The infinite series $${\,f\left( x \right) = x - {{{x^3}} \over {3!}} + {{{x^5}} \over {5!}} - {{{x^7}} \over {7!}} + -

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The value of the integral $$\int\limits_{ - a}^a {{{dx} \over {1 + {x^2}}}} $$

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A box contains $$2$$ washers, $$3$$ nuts and $$4$$ bolts. Items are drawn from the box at random one at a time without

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The blasius equation $$\,{{{d^3}f} \over {d{\eta ^3}}} + {f \over 2}\,{{{d^2}f} \over {d{\eta ^2}}} = 0\,\,\,\,$$ is a

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The Laplace transform of $$f\left( t \right)$$ is $${1 \over {{s^2}\left( {s + 1} \right)}}.$$
The function

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A lightly loaded full journal bearing has a journal of $$50mm,$$ bush bore of $$50.50mm$$ and bush length of $$20mm.$$ i

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For the stability of a floating body, under the influence of gravity alone, which of
the following is TRUE?

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Velocity vector of a flow fields is given as $$\overrightarrow V = 2xy\widehat i - {x^2}z\widehat j.$$ The vorticity ve

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A smooth pipe of diameter $$200$$ $$mm$$ carries water. The pressure in the pipe at section
$${S_1}\,\,$$ (elevation :

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Maximum velocity of a one-dimensional incompressible fully developed viscous flow, between two fixed parallel plates, is

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A fin has $$5mm$$ diameter and $$100mm$$ length. The thermal conductivity of fin material is $$400W/m K.$$ One end of t

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Match the following
List-$${\rm I}$$
$$P.$$ Compressible flow
$$Q.$$ Free surface flow
$$R.$$ Boundary layer flow
$$S.$

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Annual demand for window frames is $$10000.$$ Each frame costs Rs. $$200$$ and ordering cost is Rs. $$300$$ per order. I

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The project activities, precedence relationships and durations are described in the table. The critical path of the proj

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The demand and forecast for February are $$12000$$ and $$10275,$$ respectively. Using single exponential smoothening met

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Little’s law is relationship between

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Simplex method of solving linear programming problem uses

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Four jobs are to be processed on a machine as per data listed in the table.
If the Earliest Due Date $$(EDD)$$ rule i

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Four jobs are to be processed on a machine as per data listed in the table.
Using the Shortest Processing Time $$(SPT

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A bracket shown in fig. is rigidly mounted on wall using four rivets. Each rivet is $$6mm$$ in diameter and has an effec

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Tooth interference in an external involute spur gear pair can be reduced by

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A band brake having band-width of $$80mm,$$ drum diameter of $$250mm,$$ coefficient of friction of $$0.25$$ and angle of

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In a gating system, the ratio $$1:2:4$$ represents

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For the case of molding, it is decided to replace a spherical riser of diameter $$100$$ $$mm$$ by a cylindrical riser. D

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Two steel bars each of diameter $$10mm$$ are coaxially friction welded end to end at an axial pressure of $$200MPa$$ and

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For tool $$A,$$ Taylor’s tool life exponent $$(n)$$ is $$0.45$$ and constant $$(K)$$ is $$90.$$ Similarly for tool $$B,$

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In a shear cutting operation, a sheet of $$5mm$$ thickness is cut along a length of $$200mm.$$ The cutting blade is $$40

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In a shear cutting operation, a sheet of $$5mm$$ thickness is cut along a length of $$200mm.$$ The cutting blade is $$40

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A shaft has a dimension $$\phi $$ $${35^{\matrix{
{ - 0.009} \cr
{ - 0.025} \cr
} }}$$. The respective value

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A taper hole is inspected using a $$CMM,$$ with a probe of $$2mm$$ diameter. At a height, $$Z=10mm$$ from the bottom, $$

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In a $$CNC$$ program block, $$N002\,\,\,\,G02\,\,\,\,G91\,\,\,\,X40\,\,\,\,Z40....,\,\,\,\,G02\,\,\,\,\& \,\,\,\,G9

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The state of plane-stress at a point is given by $${\sigma _x}\,\, = 200$$ MPa, $${\sigma _x}\,\, = 100$$ MPa and $${\t

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There are two points P and Q on a planar rigid body. The relative velocity between the two points

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Mobility of a statically indeterminate structure is

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Which of the following statements is INCORRECT

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For the configuration shown, the angular velocity of link AB is $$10$$ rad/s counterclockwise. The magnitude of the rela

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Tooth interference in an external involute spur gear pair can be reduced by

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For the epicyclic gear arrangement shown in the figure, $${{\omega _2} = 100}$$ rad/s clockwise (CW) and $${{\omega _{a

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The natural frequency of a spring-mass system on earth is $${\omega _n}.$$ The natural frequency of this system on the m

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A mass $$m$$ attached to a spring is subjected to a harmonic force as shown in the figure. The amplitude of the forced m

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A mono-atomatic ideal gas $$\left( {\gamma = 1.67,} \right.$$ molecular weight$$=40$$ $$\left. \, \right)$$ is compress

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One kilogram of water at room temperature is brought into contact with a high temperature thermal reservoir. The entropy

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Consider the following two processes;
$$\left( {\rm I} \right)$$ A heat source at $$1200$$ $$K$$ loses $$2500$$ $$kJ$$

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In a steam power plant operating on the Rankine cycle, steam enters the turbine at $$4$$ $$MPa,$$ $${350^ \circ }C$$ and

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In a steam power plant operating on the Rankine cycle, steam enters the turbine at $$4$$ $$MPa,$$ $${350^ \circ }C$$ and

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A hydraulic turbine develops $$1000$$ $$kW$$ power for a head of $$40$$ $$m.$$ If the head is reduced to $$20$$ $$m,$$ t

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A phenomenon is modeled using $$n$$ dimensional variables with $$k$$ primary dimensions. The number of non-dimensional v

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