GATE 2007 Production & Industrial

Circular blanks of $$35$$ $$mm$$ diameter are punched from a steel sheet of $$2$$ $$mm$$ thickness. If the clearance per side between the punch and die is to be kept as $$40$$ micr...

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

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

If a complex number $$z = {{\sqrt 3 } \over 2} + i{1 \over 2}$$ then z 4 is

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

The determinant $$\left| {\matrix{ {1 + b} & b & 1 \cr b & {1 + b} & 1 \cr 1 & {2b} & 1 \cr } } \right|$$ equals to

Matching exercise choose the correct one out of the alternatives $$A, B, C, D$$ Group $$-$$ $${\rm I}$$ $$P.$$ $${2^{nd}}$$ order differential equations $$Q.$$ Non-linear algebraic...

Two cards are drawn at random in succession with replacement from a deck of $$52$$ well shuffled cards Probability of getting both 'Aces' is

If $$X$$ is a continuous random variable whose probability density function is given by $$$\,\,\,f\left( x \right) = \left\{ {\matrix{ {k\left( {5x - 2{x^2}} \right),} & {0 \le x \...

The random variable $$X$$ takes on the values $$1,$$ $$2$$ (or) $$3$$ with probabilities $$\,{{2 + 5P} \over 5},{{1 + 3P} \over 5}\,\,$$ and $$\,\,{{1.5 + 2P} \over 5}\,\,$$ respec...

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

A long glass cylinder of inner diameter $$=0.03m$$ and outer diameter $$=0.05m$$ carries hot fluid inside. If the thermal conductivity of glass $$=1.05$$ $$W/mK,$$ the thermal resi...

The maximum possible percentage reduction in area per pass during wire drawing of an ideal plastic material without friction is of the order of

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

In a sand casting process, a sprue of $$10mm$$ base diameter and $$250mm$$ height leads to a runner which fills a cubical mold cavity of $$100mm$$ size. The mold filling time in se...

The $$DC$$ power source for arc welding has the characteristic $$3V + 1 = 240,$$ where $$V=$$ Voltage and $${\rm I}\,\, = $$ current in amp. For maximum arc power at the electrode,...

A tool with side cutting edge angle of $$30$$ degrees and end cutting edge angle $$10deg$$ is used for fine turning with a feed of $$1mm/rev$$. Neglecting nose radius of the tool,...

The interpolator in a $$CNC$$ machine controls

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

The geometric transformation specified by $$\left[ {x'\,\,y'\,\,1} \right] = \left[ {x\,\,y\,\,1} \right]\left[ {\matrix{ {0.5} & 0 & 0 \cr 0 & {0.25} & 0 \cr 1 & 2 & 1 \cr } } \ri...

Reaming is primarily used for achieving

Blind hole $$10mm$$ diameter, $$50mm$$ deep are being drilled in steel block, drilling spindle speed is $$600rpm$$, feed $$0.2$$$$mm/rev,$$ point angle of drill is $$120.$$ During...

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

Blind hole $$10mm$$ diameter, $$50mm$$ deep are being drilled in steel block, drilling spindle speed is $$600rpm$$, feed $$0.2$$$$mm/rev,$$ point angle of drill is $$120.$$ Machini...

In an orthogonal cutting test, the following observations were made Cutting force $$=1200N ;$$ Thrust force $$=500N$$ Tool rake angle $$=zero ;$$ Cutting speed $$=1$$ $$m/s,$$ Dept...

In an orthogonal cutting test, the following observations were made Cutting force $$=1200N ;$$ Thrust force $$=500N$$ Tool rake angle $$=zero ;$$ Cutting speed $$=1$$ $$m/s,$$ Dept...

In a sand casting process, a sprue of $$10mm$$ base diameter and $$250mm$$ height leads to a runner which fills a cubical mold cavity of $$100mm$$ size. The volume flow rate (in $$...