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## GATE ME 2017 Set 1

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

The product of eigenvalues of the matrix $$P$$ is $$P = \left[ {\matrix{ 2 &a... The value of$$\mathop {\lim }\limits_{x \to 0} \left( {{{{x^3} - \sin \left( x ...
A parametric curve defined by $$x = \cos \left( {{{\pi u} \over 2}} \right),y = ... For the vector$$\overrightarrow V = 2yz\widehat i + 3xz\widehat j + 4xy\wideha...
A six-face fair dice is rolled a large number of times. The mean value of the ou...
The differential equation $$\,{{{d^2}y} \over {d{x^2}}} + 16y = 0$$ for $$y(x)$$...
Consider the following partial differential equation for $$u(x,y)$$ with the con...
$$\,\,P\,\,\,\left( {0,3} \right),\,\,Q\,\,\,\left( {0.5,4} \right),\,\,$$ and ...
A Particle of unit mass is moving on a plane. Its trajectory, in polar coordinat...
The following figure shows the velocity- time plot for a particle traveling alon...
Two disks A and B with identical mass (m) and radius (R) are initially at rest. ...
Consider the two-dimensional velocity field given by <br>$$\overrightarrow V =... For a steady flow, the velocity field is$$\overrightarrow V = \left( { - {x^2}...
For steady flow of a viscous incompressible fluid through a circular pipe of con...
Consider steady flow of an incompressible fluid through two long and straight pi...
The velocity profile inside the boundary layer for flow over a flat plate is giv...
Heat is generated uniformly in a long solid cylindrical rod ( diameter $$= 10\,... Two black surfaces,$$AB$$and$$BC,$$of lengths$$5m$$and$$6m,$$respectivel... Saturated steam at$${100^ \circ }C$$condenses on the outside of a tube. Cold f... Two models,$$P$$and$$Q,$$of a product earn profits of Rs.$$100$$and Rs.$$...
Following data refers to the jobs $$(P, Q, R, S)$$ which have arrived at a machi...
Consider the schematic of a riveted lap joint subjected to tensile load $$F,$$ a...
A machine element has an ultimate strength $$\left( {{\sigma _u}} \right)$$ of $... A sprue in a sand mould has a top diameter of $$20mm$$ and height of $$200mm.$$ ... In a metal forming operation when the material has just started yielding, the pr... In an arc welding process, welding speed is doubled. Assuming all other process ... Two cutting tools with tool life equations given below are being compared: <br>... Metric thread of $$0.8$$ $$mm$$ pitch is to be cut on a lathe. Pitch of the lead... A block of length $$200$$ $$mm$$ is machined by a slab milling cutter $$34$$ $$m... A$$10mm$$deep cylindrical cup with diameter of$$15mm$$is drawn fro... Cylindrical pins of diameter$${15^{ \pm 0.020}}\,\,mm$$are being produced on a... Assume that the surface roughness profile is triangular as shown schematically i... Circular arc on a part profile is being machined on a vertical$$CNC$$milling m... In the engineering stress-strain curve for mild steel, the Ultimate Tensile Stre... The Poisson's ratio for a perfectly incompressible linear elastic material is A horizontal bar, fixed at one end (x = 0), has a length of 1 m, and cross-secti... A point mass of$$100$$kg is dropped onto a massless elastic bar (cross-section... A rectangular region in a solid is in a state of plane strain. The$$(x,y)$$coo... Consider a beam with circular cross-section of diameter$$d.$$The ratio of the ... A motor driving a solid circular steel shaft transmits$$40kW$$of power at... An initially stress-free massless elastic beam of length$$L$$and circular cros... For an inline slider-crank mechanism, the lengths of the crank and connecting ro... In an epicyclic gear train, shown in the figure, the outer ring gear is fixed, w... The damping ratio for a viscously damped spring mass system, governed by the rel... A thin uniform rigid bar of length$$L$$and mass$$M$$is hinged at point$$O,$...
The molar specific heat at constant volume of an ideal gas is equal to $$2.5$$ t...
Water (density $$= 1000$$ $$kg/{m^3}$$) at ambient temperature flows through a ...
One $$kg$$ of an ideal gas (gas constant, $$R = 400$$ $$J/kg.K;$$ specific heat ...
A heat pump absorbs $$10$$ $$kW$$ of heat from outside environment at $$250$$ ...
Which one of the following is NOT a rotating machine?

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