GATE PI 2012

## GATE PI

A mold having dimensions $$100 \times 90 \times 20$$ (all in $$mm$$) is filled with molten metal througgh a gate with he

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For the matrix $$A = \left[ {\matrix{
5 & 3 \cr
1 & 3 \cr
} } \right],$$ ONE of the normalized eigen

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$$x+2y+z=4, 2x+y+2z=5, x-y+z=1$$
The system of algebraic equations given above has

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Consider the function $$f\left( x \right) = \left| x \right|$$ in the interval $$\,\, - 1 \le x \le 1.\,\,\,$$ At the po

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The area enclosed between the straight line $$y=x$$ and the parabola $$y = {x^2}$$ in the $$x-y$$ plane is

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$$\,\mathop {Lim}\limits_{x \to 0} \left( {{{1 - \cos x} \over {{x^2}}}} \right)$$ is

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At $$x=0,$$ the function $$f\left( x \right) = {x^3} + 1$$ has

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A political party orders an arch for the entrance to the ground in which the annual convention is being held. The profil

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For the spherical surface $${x^2} + {y^2} + {z^2} = 1,$$ the unit outward normal vector at the point $$\left( {{1 \ove

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A box contains $$4$$ red balls and $$6$$ black balls. Three balls are selected randomly from the box one after another,

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An automobile plant contracted to buy shock absorbers from two suppliers $$X$$ and $$Y$$. $$X$$ supplies $$60$$% and $

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Consider the differential equation $$\,\,{x^2}{{{d^2}y} \over {d{x^2}}} + x{{dy} \over {dx}} - 4y = 0\,\,\,$$ with the b

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The inverse Laplace transform of the function $$F\left( s \right) = {1 \over {s\left( {s + 1} \right)}}$$ is given by

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Which one of the following configurations has the highest fin effectiveness?

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For an opaque surface, the absorptivity $$\left( \alpha \right),$$ transmissivity $$\left( \tau \right)$$ and reflecti

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Consider two infinitely long thin concentric tubes of circular cross section as shown in the figure. If $${D_1}$$ and $$

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In a $$DC$$ $$arc$$ welding operating, the length characteristic was obtained as $${V_{arc}} = 20 + 5l$$ where the $$arc

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In a shaping process, the number of double strokes per minute is $$30$$ and the quick return ratio is $$0.6,$$ If the le

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In a single pass drilling operation, a through hole of $$15$$ $$mm$$ diameter is to be drilled in a steel plate of $$50m

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A $$CNC$$ vertical milling machine has to cut a straight slot of $$10$$ $$mm$$ width and $$2$$ $$mm$$ depth by a cutter

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A solid cylinder of diameter $$100$$ $$mm$$ and height $$50$$ $$mm$$ is forged between two frictionless flat dies to a h

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In a single pass rolling process using $$410mm$$ diameter steel rollers, a strip of width $$140mm$$ and thickness $$8mm$

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Match the following metal forming processes with their associated stresses in the Work-piece

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Calculate the punch size in $$mm,$$ for a circular blanking operation for which details are given below.
Size of the bla

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In an interchangeable assembly, shafts of size $${25.000^{\matrix{
{ + 0.040} \cr
{ - 0.010} \cr
} }}\,\,mm$

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A Sine bar has a length of $$250mm.$$ Each roller has a diameter of $$20mm.$$ During taper angle measurement of a compon

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