GATE ME 2013

## GATE ME

The eigen values of a symmetric matrix are all

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Choose the CORRECT set of functions, which are linearly dependent.

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The value of the definite integral $$\int_1^e {\sqrt x \ln \left( x \right)dx} $$ is

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The following surface integral is to be evaluated over a sphere for the given steady velocity vector field $$F = xi + yj

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Let $$X$$ be a normal random variable with mean $$1$$ and variance $$4.$$ The probability $$P\left\{ {X < 0} \right\}

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The probability that a student knows the correct answer to a multiple choice question is $${2 \over 3}$$. If the studen

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The solution to the differential equation $$\,{{{d^2}u} \over {d{x^2}}} - k{{du} \over {dx}} = 0\,\,\,$$ where $$'k'$$

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The partial differential equation $$\,\,{{\partial u} \over {\partial t}} + u{{\partial u} \over {\partial x}} = {{{\par

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Match the CORRECT pairs.

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The function $$f(t)$$ satisfies the differential equation $${{{d^2}f} \over {d{t^2}}} + f = 0$$ and the auxiliary condit

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A pin jointed uniform rigid rod of weight W and length is supported horizontally by an external force F as shown in the

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A hinged gate of length $$5$$ $$m,$$ inclined at $${30^ \circ }$$ with the horizontal and with water mass on its left, i

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Water is coming out from a tap and falls vertically downwards. At the tap opening, the stream diameter is $$20$$ $$mm$$

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For steady, fully developed flow inside a straight pipe of diameter $$D,$$ neglecting gravity effects, the pressure drop

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Consider one-dimensional steady state heat conduction, without heat generation, in a plane wall; with boundary condition

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Consider one-dimensional steady state heat conduction along x-axis $$\left( {0 \le x \le L} \right),$$ through a planewa

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A steel ball of diameter $$60$$ $$mm$$ is initially in thermal equilibrium at $${1030^ \circ }C$$ in a furnace. It is su

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Two large diffuse gray parallel plates, separated by a small distance, have surface temperatures of $$400$$ $$K$$ and $$

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Water (specific heat, $${c_p} = 4.18\,\,kJ/kgK$$ ) enters a pipe at a rate of $$0.01$$ $$kg/s$$ and temperature of $${20

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Water (specific heat, $${c_p} = 4.18\,\,kJ/kgK$$ ) enters a pipe at a rate of $$0.01$$ $$kg/s$$ and temperature of $${20

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In simple exponential smoothing forecasting, to give higher weightage to recent demand information, the smoothing consta

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Customers arrive at a ticket counter at a rate of $$50$$ per hr and tickets are issued in the order of their arrival. Th

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A linear programming problem is shown below.
$$\eqalign{
& Maximize\,\,\,\,3x + 7y \cr
& Subject\,\,to\,\

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A bar is subjected to fluctuating tensile load from $$20$$ $$kN$$ to $$100$$ $$kN.$$ The material has yield strength of

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A single riveted lap joint of two similar plates as shown in the figure below has the following geometrical and material

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A single riveted lap joint of two similar plates as shown in the figure below has the following geometrical and material

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A cube shaped casting solidifies in $$5$$ min. The solidification time in min for a cube of the same material, which is

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In a rolling process, the state of stress of the material undergoing deformation is

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Two cutting tools are being compared for a machining operation. The tool life equations are:
$$\eqalign{
& \,\,\,\

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In orthogonal turning of a bar of $$100$$ $$mm$$ diameter with a feed of $$0.25$$ $$min/rev,$$ depth of cut of $$4$$ $$m

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In orthogonal turning of a bar of $$100$$ $$mm$$ diameter with a feed of $$0.25$$ $$min/rev,$$ depth of cut of $$4$$ $$m

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A steel bar $$200$$ $$mm$$ in diameter is turned at a feed of $$0.25$$ $$mm/rev$$ with a depth of cut of $$4$$ $$mm.$$ T

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A metric thread of pitch $$2$$ $$mm$$ and thread angle 60° is inspected for its pitch diameter using 3-wire method. The

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Cylindrical pins of $${25^{\matrix{
{ + 0.020} \cr
{ + 0.010} \cr
} }}\,\,mm$$ diameter are electroplated i

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In a $$CAD$$ package, mirror image of a $$2D$$ points $$P(5, 10)$$ is to be obtained about a line which passes through t

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A rod of length $$L$$ having uniform cross-sectional area $$A$$ is subjected to a tensile force $$P$$ as shown in the fi

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A simply supported beam of length $$L$$ is subjected to a varying distributed load $$\sin \left( {3\pi x/L} \right)N{m^{

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A long thin walled cylindrical shell, closed at both the ends, is subjected to an internal pressure. The ratio of the ho

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For a ductile material, toughness is a measure of

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Two threaded bolts A and B of same material and length are subjected to identical tensile load. If the elastic strain en

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A link OB is rotating with a constant angular velocity of 2 rad/s in counter clockwise direction and a block is sliding

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A planar closed kinematic chain is formed with rigid links $$PQ = 2.0 m, QR = 3.0 m, RS = 2.5 m$$ and $$SP = 2.7 m$$ wit

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A compound gear train with gears P, Q, R and S has number of teeth 20, 40, 15 and 20, respectively. Gears Q and R are mo

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A flywheel connected to a punching machine has to supply energy of $$400$$ Nm while running at a mean angular speed of

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If two nodes are observed at a frequency of $$1800$$ rpm during whirling of a simply supported long slender rotating sha

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A single degree of freedom system having mass $$1$$ $$kg$$ and stiffness $$10$$ $$kN/m$$ initially at rest is subjected

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Specific enthalpy and velocity of steam at inlet and exit of a steam turbine, running under steady state, are as given b

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A cylinder contains $$5\,\,{m^3}$$ of an ideal gas at a pressure of $$1$$ bar. This gas is compressed in a reversible is

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The pressure, temperature and velocity of air flowing in a pipe are $$5$$ $$bar,$$ $$500$$ $$K$$ and $$50$$ $$m/s,$$ res

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In order to have maximum power from a Pelton turbine, the bucket speed must be

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