GATE PI 2007

## GATE PI

In a sand casting process, a sprue of $$10mm$$ base diameter and $$250mm$$ height leads to a runner which fills a cubica

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In a sand casting process, a sprue of $$10mm$$ base diameter and $$250mm$$ height leads to a runner which fills a cubica

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Match the following

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The determinant $$\left| {\matrix{
{1 + b} & b & 1 \cr
b & {1 + b} & 1 \cr
1 & {2b} &am

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If $$A$$ is square symmetric real valued matrix of dimension $$2n$$, then the eigen values of $$A$$ are

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For the function $$\,\,f\left( {x,y} \right) = {x^2} - {y^2}\,\,$$ defined on $${R^2},$$ the point $$(0,0)$$ is

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What is the value of $$\mathop {Lim}\limits_{x \to \pi /4} {{\cos x - \sin x} \over {x - \pi /4}}\,\,$$

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The angle (in degrees) between two planar vectors $$\vec a = {{\sqrt 3 } \over 2}\widehat i + {1 \over 2}\widehat j$$ a

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If $$X$$ is a continuous random variable whose probability density function is given by
$$$\,\,\,f\left( x \right) = \l

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The random variable $$X$$ takes on the values $$1,$$ $$2$$ (or) $$3$$ with probabilities $$\,{{2 + 5P} \over 5},{{1 +

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Two cards are drawn at random in succession with replacement from a deck of $$52$$ well shuffled cards Probability of ge

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If a complex number $$z = {{\sqrt 3 } \over 2} + i{1 \over 2}$$ then z4 is

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Matching exercise choose the correct one out of the alternatives $$A, B, C, D$$
Group $$-$$ $${\rm I}$$
$$P.$$ $${2^{nd

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A long glass cylinder of inner diameter $$=0.03m$$ and outer diameter $$=0.05m$$ carries hot fluid inside. If the therma

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The $$DC$$ power source for arc welding has the characteristic $$3V + 1 = 240,$$ where $$V=$$ Voltage and $${\rm I}\,\,

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In an orthogonal cutting test, the following observations were made
Cutting force $$=1200N ;$$ Thrust force $$=500N$$

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In an orthogonal cutting test, the following observations were made
Cutting force $$=1200N ;$$ Thrust force $$=500N$$

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Reaming is primarily used for achieving

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Which of following gear manufacturing processes is based on generation principle.

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Blind hole $$10mm$$ diameter, $$50mm$$ deep are being drilled in steel block, drilling spindle speed is $$600rpm$$, feed

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Blind hole $$10mm$$ diameter, $$50mm$$ deep are being drilled in steel block, drilling spindle speed is $$600rpm$$, feed

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The interpolator in a $$CNC$$ machine controls

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In a $$CAD$$ package, a point $$P(6, 3, 1)$$ is projected along a vector $$v(-2, 1, -1).$$ The projection of this point

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The geometric transformation specified by
$$\left[ {x'\,\,y'\,\,1} \right] = \left[ {x\,\,y\,\,1} \right]\left[ {\matri

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The maximum possible percentage reduction in area per pass during wire drawing of an ideal plastic material without fric

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Circular blanks of $$35$$ $$mm$$ diameter are punched from a steel sheet of $$2$$ $$mm$$ thickness. If the clearance per

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The geometric tolerance that does not need a datum for its specification is

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Which one of the Instrument is a comparator

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A tool with side cutting edge angle of $$30$$ degrees and end cutting edge angle $$10deg$$ is used for fine turning with

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Tolerance on the dimension $$'x'$$ in the two component assembly shown below is (all dimensions are in $$mm$$)

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