GATE PI 2008
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## GATE PI

In hollow cylindrical parts made by centrifugal casting, the density of the part is
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In sand casting of hallow part of lead, a cylindrical core of diameter $$120mm$$ and height $$180mm$$ is placed inside t
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The eigen vector pair of the matrix $$\left[ {\matrix{ 3 &amp; 4 \cr 4 &amp; { - 3} \cr } } \right]$$ is
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The inverse of matrix $$\left[ {\matrix{ 0 &amp; 1 &amp; 0 \cr 1 &amp; 0 &amp; 0 \cr 0 &amp; 0 &amp; 1 \cr View Question The value of the integral$$\,\,\int\limits_{ - \pi /2}^{\pi /2} {\left( {x\,\cos \,x} \right)dx\,\,} $$is View Question The value of the expansion$$\mathop {Lim}\limits_{x \to 0} \left[ {{{\sin \left( x \right)} \over {{e^x}X}}} \right]\,\
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If $$\overrightarrow r$$ is the position vector of any point on a closed surface $$S$$ that encloses the volume $$V$$
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In a game, two players $$X$$ and $$Y$$ toss a coin alternately. Whoever gets a 'head' first, wins the game and the game
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For a random variable $$\,x\left( { - \infty &lt; x &lt; \infty } \right)\,\,$$ following normal distribution, the mean
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The solutions of the differential equation $${{{d^2}y} \over {d{x^2}}} + 2{{dy} \over {dx}} + 2y = 0\,\,$$ are
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The value of the expression $${{ - 5 + 10i} \over {3 + 4i}}$$ is
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Laplace transform of $$8$$ $${t^3}$$ is
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Laplace transform of $$sin$$ $$ht$$ is
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Two pipes of uniform section but different diameters carry water at the same volumetric flow rate. Water properties are
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Oil is being pumped through a straight pipe, the pipe length, diameter and volumetric flow rate are all doubled in a new
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Two pipes of inner diameter $$100mm$$ and outer diameter $$110mm$$ each are joined by flash butt welding using $$30V$$ p
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Aluminium strips of $$2mm$$ thickness are joined together by resistance spot welding process by applying an electric cur
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Which of the following powders should be fed for effective oxy-fuel cutting of stainless steel
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Which pair among the following solid state welding processes uses heat from an external source $$P$$- Diffusion welding
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Diamond cutting tools are not recommended for machining of ferrous metals to
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In an orthogonal cutting experiment, an $$HSS$$ tool having the following tool signature in the orthogonal reference sys
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In an orthogonal cutting experiment, an $$HSS$$ tool having the following tool signature in the orthogonal reference sys
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Brittle materials are machined with tools having zero or negative rake angles because it
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During machining, the wear land $$(h)$$ has been plotted against machining time $$(T)$$ as given in the following figure
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The quick return mechanism used in shaper has rocker arm drive of length $$200mm.$$ If the crank radius is $$50mm$$ and
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A stepper motor has $$150$$ steps. The output shaft of the motor is directly coupled to a lead screw of pitch $$4mm,$$ w
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Suppose point $$P1$$ in $$APT$$ (Automatically programmed Tool) programming is coded by statement $$P1 = POINT/XSMALL,\ View Question In a$$CNC$$feed drive, a stepper motor with step angle of$$1.8deg$$drives a lead screw with pitch of$$2mm.$$The ba View Question In a rolling process, thickness of a strip is reduced from$$4mm$$to$$3mm$$using$$300mm$$diameter rolls rotating at View Question A$$10mm$$diameter annealed steel wire is drawn through a die at a speed of$$0.5/sec$$to reduce the diameter by$$20\
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By application of tensile force, the cross sectional area of bar $$' P '$$ is first reduced by $$30\%$$ and then by an
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A $$10mm$$ diameter annealed steel wire is drawn through a die at a speed of $$0.5/sec$$ to reduce the diameter by $$20\ View Question Match the following View Question A blank of$$50mm$$diameter is to be sheared from a sheet of$$2.5mm$$thickness. The required radial clearan View Question The following data are given for calculating limits of dimensions and tolerances for a hole: Tolerance unit$$'i' (mic
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An experimental setup is planned to determine the taper of work piece as shown in the figure. If the two precision rolle
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