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## GATE ME 2013

Exam Held on Thu Jan 01 1970 00:00:00 GMT+0000 (Coordinated Universal Time)
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## GATE ME

The eigen values of a symmetric matrix are all
Choose the CORRECT set of functions, which are linearly dependent.
The value of the definite integral $$\int_1^e {\sqrt x \ln \left( x \right)dx} ... The following surface integral is to be evaluated over a sphere for the given st... Let$$X$$be a normal random variable with mean$$1$$and variance$$4.$$The pr... The probability that a student knows the correct answer to a multiple choice que... The solution to the differential equation$$\,{{{d^2}u} \over {d{x^2}}} - k{{du}...
The partial differential equation $$\,\,{{\partial u} \over {\partial t}} + u{{\... Match the CORRECT pairs. <img class="question-image" src="https://imagex.cdn.exa... The function$$f(t)$$satisfies the differential equation$${{{d^2}f} \over {d{t...
A pin jointed uniform rigid rod of weight W and length is supported horizontally...
A hinged gate of length $$5$$ $$m,$$ inclined at $${30^ \circ }$$ with the horiz...
Water is coming out from a tap and falls vertically downwards. At the tap openin...
For steady, fully developed flow inside a straight pipe of diameter $$D,$$ negle...
Consider one-dimensional steady state heat conduction, without heat generation, ...
Consider one-dimensional steady state heat conduction along x-axis $$\left( {0 \... A steel ball of diameter$$60mm$$is initially in thermal equilibrium at$$...
Two large diffuse gray parallel plates, separated by a small distance, have surf...
Water (specific heat, $${c_p} = 4.18\,\,kJ/kgK$$ ) enters a pipe at a rate of $$... Water (specific heat,$${c_p} = 4.18\,\,kJ/kgK$$) enters a pipe at a rate of$$...
In simple exponential smoothing forecasting, to give higher weightage to recent ...
Customers arrive at a ticket counter at a rate of $$50$$ per hr and tickets are ...
A linear programming problem is shown below. <br>\eqalign{ &amp; Maximize\,... A bar is subjected to fluctuating tensile load from20kN$$to$$100k...
A single riveted lap joint of two similar plates as shown in the figure below ha...
A single riveted lap joint of two similar plates as shown in the figure below ha...
A cube shaped casting solidifies in $$5$$ min. The solidification time in min fo...
In a rolling process, the state of stress of the material undergoing deformation...
Two cutting tools are being compared for a machining operation. The tool life eq...
In orthogonal turning of a bar of $$100$$ $$mm$$ diameter with a feed of $$0.25... In orthogonal turning of a bar of$$100mm$$diameter with a feed of$$0.25\$...
A steel bar $$200$$ $$mm$$ in diameter is turned at a feed of $$0.25$$ $$mm/rev... A metric thread of pitch$$2mm$$and thread angle 60° is inspected for its ... Cylindrical pins of$${25^{\matrix{ { + 0.020} \cr { + 0.010} \cr }...
In a $$CAD$$ package, mirror image of a $$2D$$ points $$P(5, 10)$$ is to be obta...
A rod of length $$L$$ having uniform cross-sectional area $$A$$ is subjected to ...
A simply supported beam of length $$L$$ is subjected to a varying distributed lo...
A long thin walled cylindrical shell, closed at both the ends, is subjected to a...
For a ductile material, toughness is a measure of
Two threaded bolts A and B of same material and length are subjected to identica...
A link OB is rotating with a constant angular velocity of 2 rad/s in counter clo...
A planar closed kinematic chain is formed with rigid links $$PQ = 2.0 m, QR = 3.... A compound gear train with gears P, Q, R and S has number of teeth 20, 40, 15 an... A flywheel connected to a punching machine has to supply energy of$$400$$Nm w... If two nodes are observed at a frequency of$$1800$$rpm during whirling of a si... A single degree of freedom system having mass$$1kg$$and stiffness$$10$$... Specific enthalpy and velocity of steam at inlet and exit of a steam turbine, ru... A cylinder contains$$5\,\,{m^3}$$of an ideal gas at a pressure of$$1$$bar. T... The pressure, temperature and velocity of air flowing in a pipe are$$5bar,...
In order to have maximum power from a Pelton turbine, the bucket speed must be

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