GATE 2012 Production & Industrial

Calculate the punch size in $$mm,$$ for a circular blanking operation for which details are given below. Size of the blank $$25$$ $$mm$$ Thickness of the sheet $$2$$ $$mm$$ Radial...

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

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

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

A political party orders an arch for the entrance to the ground in which the annual convention is being held. The profile of the arch follows the equation $$y = 2x\,\,\, - 0.1{x^2}...

Consider the function $$f\left( x \right) = \left| x \right|$$ in the interval $$\,\, - 1 \le x \le 1.\,\,\,$$ At the point $$x=0, f(x)$$ is

Consider the differential equation $$\,\,{x^2}{{{d^2}y} \over {d{x^2}}} + x{{dy} \over {dx}} - 4y = 0\,\,\,$$ with the boundary conditions of $$\,\,y\left( 0 \right) = 0\,\,\,$$ an...

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

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

A box contains $$4$$ red balls and $$6$$ black balls. Three balls are selected randomly from the box one after another, without replacement. The probability that the selected set c...

An automobile plant contracted to buy shock absorbers from two suppliers $$X$$ and $$Y$$. $$X$$ supplies $$60$$% and $$Y$$ supplies $$40$$% of the shock absorbers. All shock absorb...

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

For the spherical surface $${x^2} + {y^2} + {z^2} = 1,$$ the unit outward normal vector at the point $$\left( {{1 \over {\sqrt 2 }},{1 \over {\sqrt 2 }},0} \right)$$ is given by

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

For an opaque surface, the absorptivity $$\left( \alpha \right),$$ transmissivity $$\left( \tau \right)$$ and reflectivity $$\left( \rho \right)$$ are related by the equation:

A solid cylinder of diameter $$100$$ $$mm$$ and height $$50$$ $$mm$$ is forged between two frictionless flat dies to a height of $$25$$ $$mm.$$ The percentage change in diameter is

In a single pass rolling process using $$410mm$$ diameter steel rollers, a strip of width $$140mm$$ and thickness $$8mm$$ undergoes $$10\% $$ reduction of thickness. The angle of b...

In a $$DC$$ $$arc$$ welding operating, the length characteristic was obtained as $${V_{arc}} = 20 + 5l$$ where the $$arc$$ length $$l$$ was varied between $$5mm$$ and $$7mm.$$ Here...

A $$CNC$$ vertical milling machine has to cut a straight slot of $$10$$ $$mm$$ width and $$2$$ $$mm$$ depth by a cutter of $$10$$ $$mm$$ diameter between points $$(0, 0)$$ and $$(1...

In a single pass drilling operation, a through hole of $$15$$ $$mm$$ diameter is to be drilled in a steel plate of $$50mm$$ thickness. Drill spindle speed is $$500epm,$$ feed is $$...

In a shaping process, the number of double strokes per minute is $$30$$ and the quick return ratio is $$0.6,$$ If the length of the stroke is $$250mm,$$ the average cutting velocit...

In an interchangeable assembly, shafts of size $${25.000^{\matrix{ { + 0.040} \cr { - 0.010} \cr } }}\,\,mm$$ mate with holes of size $${25.000^{\matrix{ { + 0.030} \cr { + 0.020}...

A Sine bar has a length of $$250mm.$$ Each roller has a diameter of $$20mm.$$ During taper angle measurement of a component, the height from the surface plate to the center of a ro...

A mold having dimensions $$100 \times 90 \times 20$$ (all in $$mm$$) is filled with molten metal througgh a gate with height $$'h'$$ and $$C.S$$ area $$A,$$ the mould filling time...