GATE ME 2010
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## GATE ME

One of the eigen vector of the matrix $$A = \left[ {\matrix{ 2 &amp; 2 \cr 1 &amp; 3 \cr } } \right]$$ 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 $${\,f\left( x \right) = x - {{{x^3}} \over {3!}} + {{{x^5}} \over {5!}} - {{{x^7}} \over {7!}} + - View Question The value of the integral$$\int\limits_{ - a}^a {{{dx} \over {1 + {x^2}}}} $$View Question A box contains$$2$$washers,$$3$$nuts and$$4$$bolts. Items are drawn from the box at random one at a time without View Question The blasius equation$$\,{{{d^3}f} \over {d{\eta ^3}}} + {f \over 2}\,{{{d^2}f} \over {d{\eta ^2}}} = 0\,\,\,\,$$is a View Question The Laplace transform of$$f\left( t \right)$$is$${1 \over {{s^2}\left( {s + 1} \right)}}.$$The function View Question A lightly loaded full journal bearing has a journal of$$50mm,$$bush bore of$$50.50mm$$and bush length of$$20mm.$$i View Question For the stability of a floating body, under the influence of gravity alone, which of the following is TRUE? View Question Velocity vector of a flow fields is given as$$\overrightarrow V = 2xy\widehat i - {x^2}z\widehat j.$$The vorticity ve View Question A smooth pipe of diameter$$200mm$$carries water. The pressure in the pipe at section$${S_1}\,\,$$(elevation : View Question Maximum velocity of a one-dimensional incompressible fully developed viscous flow, between two fixed parallel plates, is View Question A fin has$$5mm$$diameter and$$100mm$$length. The thermal conductivity of fin material is$$400W/m K.$$One end of t View Question Match the following List-$${\rm I}P.$$Compressible flow$$Q.$$Free surface flow$$R.$$Boundary layer flow$$S.$View Question Annual demand for window frames is $$10000.$$ Each frame costs Rs. $$200$$ and ordering cost is Rs. $$300$$ per order. I View Question The project activities, precedence relationships and durations are described in the table. The critical path of the proj View Question The demand and forecast for February are $$12000$$ and $$10275,$$ respectively. Using single exponential smoothening met View Question Little’s law is relationship between View Question Simplex method of solving linear programming problem uses View Question Four jobs are to be processed on a machine as per data listed in the table. If the Earliest Due Date $$(EDD)$$ rule i View Question Four jobs are to be processed on a machine as per data listed in the table. Using the Shortest Processing Time $$(SPT View Question A bracket shown in fig. is rigidly mounted on wall using four rivets. Each rivet is$$6mm$$in diameter and has an effec View Question Tooth interference in an external involute spur gear pair can be reduced by View Question A band brake having band-width of$$80mm,$$drum diameter of$$250mm,$$coefficient of friction of$$0.25$$and angle of View Question In a gating system, the ratio$$1:2:4$$represents View Question For the case of molding, it is decided to replace a spherical riser of diameter$$100mm$$by a cylindrical riser. D View Question Two steel bars each of diameter$$10mm$$are coaxially friction welded end to end at an axial pressure of$$200MPa$$and View Question For tool$$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 $$40 View Question In a shear cutting operation, a sheet of$$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, $$View Question In a$$CNC$$program block,$$N002\,\,\,\,G02\,\,\,\,G91\,\,\,\,X40\,\,\,\,Z40....,\,\,\,\,G02\,\,\,\,\&amp; \,\,\,\,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 $${\t View Question Which of the following statements is INCORRECT View Question There are two points P and Q on a planar rigid body. The relative velocity between the two points View Question Mobility of a statically indeterminate structure is View Question For the configuration shown, the angular velocity of link AB is$$10$$rad/s counterclockwise. The magnitude of the rela View Question Tooth interference in an external involute spur gear pair can be reduced by View Question For the epicyclic gear arrangement shown in the figure,$${{\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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