GATE ME 2017 Set 1
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## GATE ME

The product of eigenvalues of the matrix $$P$$ is $$P = \left[ {\matrix{ 2 &amp; 0 &amp; 1 \cr 4 &amp; { - 3} &a View Question The value of$$\mathop {\lim }\limits_{x \to 0} \left( {{{{x^3} - \sin \left( x \right)} \over x}} \right)$$is View Question A parametric curve defined by$$x = \cos \left( {{{\pi u} \over 2}} \right),y = \sin \left( {{{\pi u} \over 2}} \right)\
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For the vector $$\overrightarrow V = 2yz\widehat i + 3xz\widehat j + 4xy\widehat k,$$ the value of $$\,\nabla .\left( { View Question A six-face fair dice is rolled a large number of times. The mean value of the outcomes is _________. View Question The differential equation$$\,{{{d^2}y} \over {d{x^2}}} + 16y = 0$$for$$y(x)$$with the two boundary conditions$${\le
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Consider the following partial differential equation for $$u(x,y)$$ with the constant $$c&gt;1:$$ $$\,{{\partial u} \ove View Question$$\,\,P\,\,\,\left( {0,3} \right),\,\,Q\,\,\,\left( {0.5,4} \right),\,\,$$and$$\,\,R\,\,\,\left( {1,5} \right)\,\,\,$View Question A Particle of unit mass is moving on a plane. Its trajectory, in polar coordinates, is given by $$r\left( t \right) = {t View Question The following figure shows the velocity- time plot for a particle traveling along a straight line. The distance covered View Question Two disks A and B with identical mass (m) and radius (R) are initially at rest. They roll down from the top of identical View Question Consider the two-dimensional velocity field given by$$\overrightarrow V = \left( {5 + {a_1}x + {b_1}y} \right)\wideha View Question For a steady flow, the velocity field is $$\overrightarrow V = \left( { - {x^2} + 3y} \right)\widehat i + \left( {2xy} View Question For steady flow of a viscous incompressible fluid through a circular pipe of constant diameter, the average velocity in View Question Consider steady flow of an incompressible fluid through two long and straight pipes of diameters$${d_1}$$and$${d_2}$$View Question The velocity profile inside the boundary layer for flow over a flat plate is given as$${u \over {{U_\infty }}} = \sin \ View Question Heat is generated uniformly in a long solid cylindrical rod ( diameter $$= 10\,\,mm$$) at the rate of $$4 \times {10^7} View Question Two black surfaces,$$AB$$and$$BC,$$of lengths$$5m$$and$$6m,$$respectively, are oriented as shown. Both surfaces View Question Saturated steam at$${100^ \circ }C$$condenses on the outside of a tube. Cold fluid enters the tube at$${20^ \circ }C$
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Two models, $$P$$ and $$Q,$$ of a product earn profits of Rs. $$100$$ and Rs. $$80$$ per piece, respectively. Production
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Following data refers to the jobs $$(P, Q, R, S)$$ which have arrived at a machine for scheduling. The shortest possible
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Consider the schematic of a riveted lap joint subjected to tensile load $$F,$$ as shown below. Let $$d$$ be the diameter
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A machine element has an ultimate strength $$\left( {{\sigma _u}} \right)$$ of $$600\,\,N/m{m^2},$$ and endurance limit
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A sprue in a sand mould has a top diameter of $$20mm$$ and height of $$200mm.$$ The velocity of the molten metal at the
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In a metal forming operation when the material has just started yielding, the principal stresses are $${\sigma _1} = \,\ View Question In an arc welding process, welding speed is doubled. Assuming all other process parameters to be constant, the cross sec View Question Two cutting tools with tool life equations given below are being compared:$$\eqalign{ &amp; Tool\,\,1:\,\,\,\,\,\,\,
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Metric thread of $$0.8$$ $$mm$$ pitch is to be cut on a lathe. Pitch of the lead screw is $$1.5$$ $$mm.$$ If the spindle
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A block of length $$200$$ $$mm$$ is machined by a slab milling cutter $$34$$ $$mm$$ in diameter. The depth of cut and ta
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A $$10$$ $$mm$$ deep cylindrical cup with diameter of $$15$$ $$mm$$ is drawn from a circular blank. Neglecting the varia
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Cylindrical pins of diameter $${15^{ \pm 0.020}}\,\,mm$$ are being produced on a machine. Statistical quality control te
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Assume that the surface roughness profile is triangular as shown schematically in the figure. If the peak to valley heig
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Circular arc on a part profile is being machined on a vertical $$CNC$$ milling machine. $$CNC$$ part program using metri
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In the engineering stress-strain curve for mild steel, the Ultimate Tensile Strength $$(UTS)$$ refers to
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The Poisson's ratio for a perfectly incompressible linear elastic material is
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A point mass of $$100$$ kg is dropped onto a massless elastic bar (cross-sectional area = $$100$$ $$mm$$2 ,length = $$1 View Question A horizontal bar, fixed at one end (x = 0), has a length of 1 m, and cross-sectional area of 100 mm2. Its elastic modulu View Question A rectangular region in a solid is in a state of plane strain. The$$(x,y)$$coordinates of the corners of the undeforme View Question Consider a beam with circular cross-section of diameter$$d.$$The ratio of the second moment of area about the neutral View Question A motor driving a solid circular steel shaft transmits$$40kW$$of power at$$500rpm$$. If the diameter of the View Question An initially stress-free massless elastic beam of length$$L$$and circular cross-section with diameter$$d (d &lt; &lt;
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For an inline slider-crank mechanism, the lengths of the crank and connecting rod are 3 m and 4 m respectively. At the i
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In an epicyclic gear train, shown in the figure, the outer ring gear is fixed, while the sun gear rotates counterclockwi
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The damping ratio for a viscously damped spring mass system, governed by the relationship $$\,m{{{d^2}x} \over {d{t^2}}} View Question A thin uniform rigid bar of length$$L$$and mass$$M$$is hinged at point$$O,$$located at a distance of$${L \over 3}
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The molar specific heat at constant volume of an ideal gas is equal to $$2.5$$ times the universal gas constant ($$8.314 View Question Water (density$$ = 1000kg/{m^3}$$) at ambient temperature flows through a horizontal pipe of uniform cross section View Question One$$kg$$of an ideal gas (gas constant,$$R = 400J/kg.K;$$specific heat at constant volume,$${c_v} = 1000\,J/kg
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A heat pump absorbs $$10$$ $$kW$$ of heat from outside environment at $$250$$ $$K$$ while absorbing $$15$$ $$kW$$ of wor
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Which one of the following is NOT a rotating machine?
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