GATE ME 2012
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## GATE ME

For the matrix $$A = \left[ {\matrix{ 5 &amp; 3 \cr 1 &amp; 3 \cr } } \right],$$ ONE of the normalized eigen
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$$x+2y+z=4, 2x+y+2z=5, x-y+z=1$$ The system of algebraic equations given above has
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Consider the function $$f\left( x \right) = \left| x \right|$$ in the interval $$\,\, - 1 \le x \le 1.\,\,\,$$ At the po
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The area enclosed between the straight line $$y=x$$ and the parabola $$y = {x^2}$$ in the $$x-y$$ plane is
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$$\,\mathop {Lim}\limits_{x \to 0} \left( {{{1 - \cos x} \over {{x^2}}}} \right)$$ is
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At $$x=0,$$ the function $$f\left( x \right) = {x^3} + 1$$ has
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A political party orders an arch for the entrance to the ground in which the annual convention is being held. The profil
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For the spherical surface $${x^2} + {y^2} + {z^2} = 1,$$ the unit outward normal vector at the point $$\left( {{1 \ove View Question A box contains$$4$$red balls and$$6$$black balls. Three balls are selected randomly from the box one after another, View Question An automobile plant contracted to buy shock absorbers from two suppliers$$X$$and$$Y$$.$$X$$supplies$$60$$% and  View Question Consider the differential equation$$\,\,{x^2}{{{d^2}y} \over {d{x^2}}} + x{{dy} \over {dx}} - 4y = 0\,\,\,$$with the b View Question The inverse Laplace transform of the function$$F\left( s \right) = {1 \over {s\left( {s + 1} \right)}}$$is given by View Question Two steel truss members, AC and BC, each having cross sectional area of 100 mm2, are subjected to a horizontal force F a View Question Two steel truss members, AC and BC, each having cross sectional area of 100 mm2, are subjected to a horizontal force F a View Question A large tank with a nozzle attached contains three immiscible, inviscid fluids as shown. Assuming that the changes in$$
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An incompressible fluid flows over a flat plate with zero pressure gradient. The boundary layer thickness is $$1mm$$ at
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Which one of the following configurations has the highest fin effectiveness?
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For an opaque surface, the absorptivity $$\left( \alpha \right),$$ transmissivity $$\left( \tau \right)$$ and reflecti
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Consider two infinitely long thin concentric tubes of circular cross section as shown in the figure. If $${D_1}$$ and $$View Question Water$$\left( {{C_p} = 4.18\,kJ/kg.K} \right)$$at$${80^ \circ }C$$enters a counter flow heat exchanger with a mass View Question For a particular project, eight activities are to be carried out. Their relationships with other activities and expected View Question For a particular project, eight activities are to be carried out. Their relationships with other activities and expected View Question Which one of the following is NOT a decision taken during the aggregate production planning stage? View Question A solid circular shaft needs to be designed to transmit a torque of$$50N.m.$$If the allowable shear stress of the View Question The homogeneous state of stress for a metal part undergoing plastic deformation is$$$T = \left( {\matrix{ {10} &amp View Question A fillet welded joint is subjected to transverse loading F as shown in the figure. Both legs of the fillets are of $$10 View Question A force of$$400N$$is applied to the brake drum of$$0.5m$$diameter in a band-brake system as shown in the f View Question A solid cylinder of diameter$$100mm$$and height$$50mm$$is forged between two frictionless flat dies to a h View Question In a single pass rolling process using$$410mm$$diameter steel rollers, a strip of width$$140mm$$and thickness$$8mm$
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In a $$DC$$ $$arc$$ welding operating, the length characteristic was obtained as $${V_{arc}} = 20 + 5l$$ where the $$arc View Question In a single pass drilling operation, a through hole of$$15mm$$diameter is to be drilled in a steel plate of$$50$View Question Match the following metal forming processes with their associated stresses in the Work-piece View Question Calculate the punch size in $$mm,$$ for a circular blanking operation for which details are given below. Size of the bla View Question In an interchangeable assembly, shafts of size $${25.000^{\matrix{ { + 0.040} \cr { - 0.010} \cr } }}\,\,mm View Question A$$CNC$$vertical milling machine has to cut a straight slot of$$10mm$$width and$$2mm$$depth by a cutter View Question A solid steel cube constrained on all six faces is heated so that the temperature rises uniformly by$$\Delta T.$$If th View Question A$$200$$mm long, stress free rod at room temperature is held between two immovable rigid walls. The temperature of the View Question The state of stress at a point under plane stress condition is$${\sigma _{xx}} = 40\,$$MPa,$${\sigma _{yy}} = 100\,$
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A solid circular shaft needs to be designed to transmit a torque of 50N.m. If the allowable shear stress of the material
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A cantilever beam of length $$L$$ is subjected to a moment $$M$$ at the free end. The moment of inertia of the beam cros
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For a long slender column of uniform cross section, the ratio of critical buckling load for the case with both ends clam
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A thin walled spherical shell is subjected to an internal pressure. If the radius of the shell is increased by 1% and th
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A solid disc of radius $$r$$ rolls without slipping on a horizontal floor with angular velocity $$\omega$$ and angular
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In the mechanism given below, if the angular velocity of the eccentric circular disc is $$1$$ rad/s, the angular velocit
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The following are the data for two crossed helical gears used for speed reduction: Gear $$I:$$ Pitch circle diameter in
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A circular solid disc of uniform thickness $$20mm,$$ radius $$200mm$$ and $$mass$$ $$20kg,$$ is used as a fly wheel. If
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A concentrated mass $$m$$ is attached at the centre of a rod of length $$2L$$ as shown in the figure. The rod is kept in
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Air enters an adiabatic nozzle at $$300$$ $$kPa,$$ $$500$$ $$K$$ with a velocity of $$10$$ $$m/s.$$ It leaves the nozzle
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Steam enters an adiabatic turbine operating at steady state with an enthalpy of $$3251.0kJ/kg$$ and leaves as a saturate
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Air enters an adiabatic nozzle at $$300$$ $$kPa,$$ $$500$$ $$K$$ with a velocity of $$10$$ $$m/s.$$ It leaves the nozzle
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An ideal gas of mass $$m$$ and temperature $${T_1}$$ undergoes a reversible isothermal process from an initial pressure
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