GATE PI 2014

## GATE PI

Chills are used in casting moulds to

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For a given volume of a riser, if the solidification time of the molten metal in riser needs to be quadrupled, the surfa

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The system of equations, given below, has
$$$x+2y+4z=2$$$
$$$4x+3y+z=5$$$
$$$3x+2y+3z=1$$$

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Directional derivative of $$\phi = 2xz - {y^2}$$ at the point $$(1, 3, 2)$$ becomes maximum in the direction of

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If $$\,\phi = 2{x^3}{y^2}{z^4}$$ then $${\nabla ^2}\phi $$ is

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In a given day in the rainy season, it may rain$$70$$% of the time . If it rains, chance that a village fair will make a

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A simple random sample of $$100$$ observations was taken form a large population. The sample mean and the standard devi

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Marks obtained by $$100$$ students in an examination are given in the table
What would be the mean, median, and mode

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Using the Simpson's $$1/{3^{rd}}$$ rule, the value of $$\,\int {ydx} \,\,$$ computed, for the data given below, is

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If the equation $$sin(x)$$ $$\, = {x^2}$$ is solved by Newton Raphson's method with the initial guess of $$x=1,$$ then t

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Brazing and soldering are

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In an arc welding operation carried out with a power source maintained at $$40$$ volts and $$400$$ amperes, the consumab

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A spindle speed of $$300$$ $$rpm$$ and a feed $$0.3mm/revolution$$ are chosen for longitudinal turning operation on an e

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Match the following:

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Reaming is a process used for

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An $$HSS$$ drill of $$20mm$$ diameter with $$5mm$$ cone height is used to drill a through hole in a steel work-piece of

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In an open loop, point-to-point controlled $$CN$$ drilling machine, a stepper motor, producing $$200$$ angular steps per

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Each axis of $$NC$$ machine is driven by a stepper motor drive with a lead screw. The pitch of lead screw is $$p$$ $$mm.

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A $$CNC$$ instruction $$G91\,\,\,G01\,\,\,X30\,\,\,Y40\,\,\,F100$$ commands the movement of tool along the path at a fee

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A moving mandrel is used in

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In an open die forging, a circular disc is gradually compressed between two flat plates. The exponential decay of normal

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A $$80$$ $$mm$$ thick steel plate with $$400$$ $$mm$$ width is rolled to $$40mm$$ thickness in $$4$$ passes with equal r

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The alignment test ''Spindle square with base plate'' is applied to the radial drilling machine. A dial indicator is fix

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