GATE ME 2012

## GATE ME

For the matrix $$A = \left[ {\matrix{
5 & 3 \cr
1 & 3 \cr
} } \right],$$ 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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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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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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$$\,\mathop {Lim}\limits_{x \to 0} \left( {{{1 - \cos x} \over {{x^2}}}} \right)$$ 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

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An automobile plant contracted to buy shock absorbers from two suppliers $$X$$ and $$Y$$. $$X$$ supplies $$60$$% and $

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A box contains $$4$$ red balls and $$6$$ black balls. Three balls are selected randomly from the box one after another,

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Consider the differential equation $$\,\,{x^2}{{{d^2}y} \over {d{x^2}}} + x{{dy} \over {dx}} - 4y = 0\,\,\,$$ with the b

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The inverse Laplace transform of the function $$F\left( s \right) = {1 \over {s\left( {s + 1} \right)}}$$ is given by

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Two steel truss members, AC and BC, each having cross sectional area of 100 mm2, are subjected to a horizontal force F a

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Two steel truss members, AC and BC, each having cross sectional area of 100 mm2, are subjected to a horizontal force F a

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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 $$

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Water $$\left( {{C_p} = 4.18\,kJ/kg.K} \right)$$ at $${80^ \circ }C$$ enters a counter flow heat exchanger with a mass

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For a particular project, eight activities are to be carried out. Their relationships with other activities and expected

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For a particular project, eight activities are to be carried out. Their relationships with other activities and expected

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Which one of the following is NOT a decision taken during the aggregate production planning stage?

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A solid circular shaft needs to be designed to transmit a torque of $$50$$ $$N.m.$$ If the allowable shear stress of the

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The homogeneous state of stress for a metal part undergoing plastic deformation is
$$$T = \left( {\matrix{
{10} &

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A fillet welded joint is subjected to transverse loading F as shown in the figure. Both legs of the fillets are of $$10$

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A force of $$400$$ $$N$$ is applied to the brake drum of $$0.5$$ $$m$$ diameter in a band-brake system as shown in the f

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A solid cylinder of diameter $$100$$ $$mm$$ and height $$50$$ $$mm$$ is forged between two frictionless flat dies to a h

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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

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In a single pass drilling operation, a through hole of $$15$$ $$mm$$ diameter is to be drilled in a steel plate of $$50$

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Match the following metal forming processes with their associated stresses in the Work-piece

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Calculate the punch size in $$mm,$$ for a circular blanking operation for which details are given below.
Size of the bla

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In an interchangeable assembly, shafts of size $${25.000^{\matrix{
{ + 0.040} \cr
{ - 0.010} \cr
} }}\,\,mm$

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A $$CNC$$ vertical milling machine has to cut a straight slot of $$10$$ $$mm$$ width and $$2$$ $$mm$$ depth by a cutter

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A solid steel cube constrained on all six faces is heated so that the temperature rises uniformly by $$\Delta T.$$ If th

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A $$200$$ mm long, stress free rod at room temperature is held between two immovable rigid walls. The temperature of the

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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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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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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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