Match the following

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 $$m{m^3}/s$$) 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 seconds is

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 equations
$$R.$$ Linear algebraic equations
$$S.$$ Numerical integration

Group $$-$$ $${\rm II}$$
$$(1)$$ Runge $$-$$ Kutta method
$$(2)$$ Newton $$-$$ Raphson method
$$(3)$$ Gauss Elimination
$$(4)$$ Simpson's Rule

If a complex number $$z = {{\sqrt 3 } \over 2} + i{1 \over 2}$$ then z⁴ is

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

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

If $$X$$ is a continuous random variable whose probability density function is given by $$$\,\,\,f\left( x \right) = \left\{ {\matrix{ {k\left( {5x - 2{x^2}} \right),} & {0 \le x \le 2} \cr {0,} & {Otherwise} \cr } } \right.\,\,\,\,$$$
Then $$P\left( {x > 1} \right)$$ is

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

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

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 resistance $$(K/W)$$ per unit length of the cylinder is

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, voltage should be set at

The geometric transformation specified by

$$\left[ {x'\,\,y'\,\,1} \right] = \left[ {x\,\,y\,\,1} \right]\left[ {\matrix{ {0.5} & 0 & 0 \cr 0 & {0.25} & 0 \cr 1 & 2 & 1 \cr } } \right]$$ in a $$2D.$$
In a $$2D$$ $$CAD$$ system represents................

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 interpolator in a $$CNC$$ machine controls

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 the above operation, the drill wears out after producing $$200$$ holes. Taylor's tool life equation is of the form $$V{T^{0.3}} = C,$$ where $$V=$$ cutting speed in $$m/min$$ and $$T=$$ tool life in $$min.$$ Taylor's constant $$C$$ will be

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 $$120.$$

Machining time (in min) per hole will be

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

Reaming is primarily used for achieving

In an orthogonal cutting test, the following observations were made
Cutting force $$=1200N ;$$ Thrust force $$=500N$$
Tool rake angle $$=zero ;$$ Cutting speed $$=1$$ $$m/s,$$
Depth of cut $$=0.8mm;$$
Chip thickness $$=1.5$$ $$mm$$

Chip speed along the tool rake face will be

In an orthogonal cutting test, the following observations were made
Cutting force $$=1200N ;$$ Thrust force $$=500N$$
Tool rake angle $$=zero ;$$ Cutting speed $$=1$$ $$m/s,$$
Depth of cut $$=0.8mm;$$
Chip thickness $$=1.5$$ $$mm$$

Friction angle during machining will be

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 $$40$$ microns, the sizes of punch and die should respectively be.

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

Tolerance on the dimension $$'x'$$ in the two component assembly shown below is (all dimensions are in $$mm$$)

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 maximum (peak to valley) height of the surface roughness produced will be

Which one of the Instrument is a comparator

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