GATE ME 2013
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## 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 $$F = xi + yj View Question Let$$X$$be a normal random variable with mean$$1$$and variance$$4.$$The probability$$P\left\{ {X &lt; 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 $$\,\,{{\partial u} \over {\partial t}} + u{{\partial u} \over {\partial x}} = {{{\par View Question Match the CORRECT pairs. View Question The function$$f(t)$$satisfies the differential equation$${{{d^2}f} \over {d{t^2}}} + f = 0$$and the auxiliary condit View Question A pin jointed uniform rigid rod of weight W and length is supported horizontally by an external force F as shown in the View Question A hinged gate of length$$5m,$$inclined at$${30^ \circ }$$with the horizontal and with water mass on its left, i View Question Water is coming out from a tap and falls vertically downwards. At the tap opening, the stream diameter is$$20mm$$View Question For steady, fully developed flow inside a straight pipe of diameter$$D,$$neglecting gravity effects, the pressure drop View Question Consider one-dimensional steady state heat conduction, without heat generation, in a plane wall; with boundary condition View Question Consider one-dimensional steady state heat conduction along x-axis$$\left( {0 \le x \le L} \right),$$through a planewa View Question A steel ball of diameter$$60mm$$is initially in thermal equilibrium at$${1030^ \circ }C$$in a furnace. It is su View Question Two large diffuse gray parallel plates, separated by a small distance, have surface temperatures of$$400K$$and$$
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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 $${20 View Question Water (specific heat,$${c_p} = 4.18\,\,kJ/kgK$$) enters a pipe at a rate of$$0.01kg/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{ &amp; Maximize\,\,\,\,3x + 7y \cr &amp; Subject\,\,to\,\ View Question A bar is subjected to fluctuating tensile load from20kN$$to$$100kN.$$The material has yield strength of View Question A single riveted lap joint of two similar plates as shown in the figure below has the following geometrical and material View Question A single riveted lap joint of two similar plates as shown in the figure below has the following geometrical and material View Question A cube shaped casting solidifies in$$5$$min. The solidification time in min for a cube of the same material, which is View Question In a rolling process, the state of stress of the material undergoing deformation is View Question Two cutting tools are being compared for a machining operation. The tool life equations are:$$\eqalign{ &amp; \,\,\,\
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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 $$4$$ $$m View Question In orthogonal turning of a bar of$$100mm$$diameter with a feed of$$0.25min/rev,$$depth of cut of$$4m
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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 $$\sin \left( {3\pi x/L} \right)N{m^{ View Question A long thin walled cylindrical shell, closed at both the ends, is subjected to an internal pressure. The ratio of the ho View Question For a ductile material, toughness is a measure of View Question Two threaded bolts A and B of same material and length are subjected to identical tensile load. If the elastic strain en View Question A link OB is rotating with a constant angular velocity of 2 rad/s in counter clockwise direction and a block is sliding View Question A planar closed kinematic chain is formed with rigid links$$PQ = 2.0 m, QR = 3.0 m, RS = 2.5 m$$and$$SP = 2.7 m$$wit View Question A compound gear train with gears P, Q, R and S has number of teeth 20, 40, 15 and 20, respectively. Gears Q and R are mo View Question A flywheel connected to a punching machine has to supply energy of$$400$$Nm while running at a mean angular speed of View Question If two nodes are observed at a frequency of$$1800$$rpm during whirling of a simply supported long slender rotating sha View Question A single degree of freedom system having mass$$1kg$$and stiffness$$10kN/m$$initially at rest is subjected View Question Specific enthalpy and velocity of steam at inlet and exit of a steam turbine, running under steady state, are as given b View Question A cylinder contains$$5\,\,{m^3}$$of an ideal gas at a pressure of$$1$$bar. This gas is compressed in a reversible is View Question The pressure, temperature and velocity of air flowing in a pipe are$$5bar,500K$$and$$50m/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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