GATE PI 2010

## GATE PI

Solidification time of a metallic alloy casting is

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During the filling process of a given sand mould cavity by metal through a horizontal runner of circular $$C.S,$$ the fr

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The value of $$q$$ for which the following set of linear equations $$2x+3y=0, 6x+qy=0$$ can have non-trivial solution is

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If $$(1, 0, -1)$$$${}^T$$ is an eigen vector of the following matrix $$\left[ {\matrix{
1 & { - 1} & 0 \cr

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If $$f\left( x \right) = \sin \left| x \right|\,\,$$ then the value of $${{df} \over {dx}}\,\,$$ at $$\,\,x = {{ - \pi }

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The integral $$\,\,{1 \over {\sqrt {2\pi } }}\int\limits_{ - \infty }^\infty {{e^{{{ - {x^2}} \over 2}}}} dx\,\,$$ is e

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If a random variable $$X$$ satisfies the poission's distribution with a mean value of $$2,$$ then the probability that

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Two white and two black balls, kept in two bins, are arranged in four ways as shown below. In each arrangement, a bin ha

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The solution of the differential equation $${{dy} \over {dx}} - {y^2} = 1$$ satisfying the condition $$y(0)=1$$ is

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Which one of the following differential equations has a solution given by the function $$y = 5\sin \left( {3x + {\pi \o

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The following algorithm computes the integral $$\,J = \int\limits_a^b {f\left( x \right)dx\,\,\,} $$ from the given valu

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An industrial gas $$\left( {{C_p} = 1kJ/kgK} \right)$$ enters a parallel flow heat exchanger at $${250^ \circ }C$$ with

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During a steady gas metal arc welding with direct current electrode positive polarity, the welding current, voltage and

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During turning of a low carbon steel bar with TiN coated carbide insert, one needs to improve surface finish without sac

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Which of the following powder production methods produces spongy and porous particles?

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For a $$3$$-axes $$CNC$$ table, the slide along the vertical axis of the table driven by a $$DC$$ servo motor via lead s

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Cold shut (lap) may occur in products obtained by:

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Hot die steel, used for large solid dies in drop forging, should necessarily have

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During open die forging process using two flat and parallel dies, a solid steel disc of initial radius $$({R_{IN}})\,\,2

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In a rolling process, the roll separating force can be decreased by

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A small bore is designated as $$25H7.$$ The lower (minimum) and upper (maximum) limits of the bore are $$25.000mm$$ and

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