GATE ME 1994
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## GATE ME

Find out the eigen value of the matrix $$A = \left[ {\matrix{ 1 &amp; 0 &amp; 0 \cr 2 &amp; 3 &amp; 1 \cr 0 View Question The value of$$\int\limits_0^\infty {{e^{ - {y^3}}}.{y^{1/2}}} $$dy is _________. View Question If$$H(x, y)$$is homogeneous function of degree$$n$$then$$x{{\partial H} \over {\partial x}} + y{{\partial H} \over
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For the differential equation $$\,\,{{dy} \over {dt}} + 5y = 0\,\,$$ with $$y(0)=1,$$ the general solution is
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Solve for $$y$$ if $${{{d^2}y} \over {d{t^2}}} + 2{{dy} \over {dt}} + y = 0$$ with $$y(0)=1$$ and $${y^1}\left( 0 \right View Question If$$f(t)$$is a finite and continuous Function for$$t \ge 0$$the laplace transformation is given by$$F = \int\limit
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A stone of mass m at the end of a string of length l is whirled in a vertical circle at a constant speed. The tension in
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Streamlines, path lines and streak lines are virtually identical for
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In a flow field, the streamlines and equipotential lines
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For a fluid element in a two dimensional flow field ($$x-y$$ plane), it will undergo
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Circulation is defined as line integral of tangential component of velocity about a _________ (fill in the blank)
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Existence of velocity potential implies that
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Bodies in floatation to be in stable equilibrium the necessary and sufficient condition is that the center of gravity is
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Bernoulli’s equation can be applied between any two points on a stream line for a rotational flow field.
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In a venturimeter, the angle of the diverging section is more than that of converging section.
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For a fully developed laminar flow through a pipe, the ratio of the maximum velocity to the average velocity is ________
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Prandtl’s mixing length is turbulent flow signifies
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Fluid is flowing with an average velocity of $$V$$ through a pipe of diameter $$d.$$ over a length of $$L,$$ the “head”
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As the transition from laminar to turbulent flow is induced in a cross flow past a circular cylinder the value of the dr
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The necessary and sufficient condition which brings about separation of boundary layer is $${{dP} \over {dx}} &gt; 0$$
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Two insulting materials of thermal conductivity $$K$$ and $$2K$$ are available for lagging a pipe carrying a hot fluid.
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When the fluid velocity is doubled the thermal time constant of a thermometer used for measuring the fluid temperature r
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For air near atmospheric condition flowing over a flat plate the laminar thermal boundary layer is thicker than hydrodyn
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The shape factors with themselves of two infinitely long black body concentric cylinders with a dia ratio of $$3$$ are .
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The practice to use steam on the shell side and cooling water on the tube side in condensers of steam power plant is bec
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Two streams of fluid of unit constant specific heats and unit mass flow rate exchange thermal energy in an adiabatic hea
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Two shafts $$A$$ and $$B$$ are made of the same material. The diameter of shaft $$B$$ is twice that of shaft $$A.$$ The
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Only $$4$$ pairs can be matched :
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The process of hot extrusion is used to produce
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Calculate the bite angle when rolling plates $$12mm$$ thick using work rolls $$600mm$$ diameter and reducing the thickne
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The electrodes used in $$arc$$ welding are coated. This coating is not expected to
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Generally cylindrical parts produced by powder metallurgy should not have non uniform cross section and a length to diam
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The ratio of acetylene to oxygen is approximately ................ for neutral flame used in gas welding
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A single point cutting tool made of $$HSS$$ has the value of constant $$'C'$$ $$80,$$ and $$n=0.2$$ in the basic tool li
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A mild steel block of width $$40$$ $$mm$$ is being milled using a straight slab cutter $$70mm$$ diameter with $$30$$teet
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To get good surface finish on a turned job, one should use a sharp tool with a ......... Feed rate and ............... S
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A grinding wheel $$A$$ $$27$$ $$K7$$ $$V$$ is specified for finish grinding of a $$HSS$$ cutting tool. What do you under
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In deep drawing of sheets, the values of limiting draw ratio depends on
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$$CNC$$ machines are more economical to use even for simple turning jobs.
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$$CNC$$ machines are more accurate than conventional machines because they have a high resolution encoder and digital re
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Below Fig. shows a rigid bar hinged at A and supported in a horizontal position by two vertical identical steel wires. N
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Two shafts $$A$$ and $$B$$ are made of the same material. The diameter of shaft $$B$$ is twice that of shaft $$A$$. the
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For the case of a slender column of length $$l,$$ and flexural rigidity $$EI$$ built-in at its base and free at the top,
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In spur gears having involute teeth, the product of circular pitch and diametral pitch is _________
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The definition of 1 K as per the internationally accepted temperature scale is
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Any thermodynamic cycle operating between two temperature limits is reversible if the product of efficiency when operati
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A $$1500$$ $$W$$ electrical heater is used to heat $$20$$ $$kg$$ of water $$\left( {{C_p} = 4186\,\,J/kg\,\,K} \right)$$
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The slopes of constant volume and constant pressure lines in the $$T$$-$$s$$ diagram are ___________ and ___________resp
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For a single stage impulse turbine with rotor diameter of $$2$$ $$m$$ and a speed of $$3000$$ $$rpm$$ when the nozzle an
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For a given set of operating pressure limits of a Rankine cycle, the highest efficiency occurs for
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In terms of speed of rotation of the impeller $$N$$, discharge $$Q$$ and a change in total head $$H$$, through the machi
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