Solidification time of a metallic alloy casting is

During the filling process of a given sand mould cavity by metal through a horizontal runner of circular $$C.S,$$ the frictional head loss of the molten metal in the runner will increase with the

The value of $$q$$ for which the following set of linear equations $$2x+3y=0, 6x+qy=0$$ can have non-trivial solution is

The following algorithm computes the integral $$\,J = \int\limits_a^b {f\left( x \right)dx\,\,\,} $$ from the given values $${f_j} = f\left( {{x_j}} \right)$$ at equidistant points $$\,\,{x_0} = a,\,\,{x_1} = {x_0} + h,\,\,$$ $$\,{x_2} = {x_0} + 2h,...\,{x_{2m}} = {x_0} + 2mh = b\,\,$$ compute
$${S_0} = {f_0} + {f_{2m}}$$
$${S_1} = {f_1} + {f_3} + .... + {f_{2m - 1}}$$
$${S_2} = {f_2} + {f_4} + .... + {f_{2m - 2}}$$

$$J = {h \over 3}\left[ {{S_0} + 4\left( {{S_1}} \right) + 2\left( {{S_2}} \right)} \right]$$

The rule of numerical integration, which uses the above algorithm is

The solution of the differential equation $${{dy} \over {dx}} - {y^2} = 1$$ satisfying the condition $$y(0)=1$$ is

Which one of the following differential equations has a solution given by the function $$y = 5\sin \left( {3x + {\pi \over 3}} \right)$$

Two white and two black balls, kept in two bins, are arranged in four ways as shown below. In each arrangement, a bin has to be chosen randomly and only one ball needs to be picked randomly from the chosen bin. Which one of the following arrangements has the highest probability for getting a while ball picked?

If a random variable $$X$$ satisfies the poission's distribution with a mean value of $$2,$$ then the probability that $$X > 2$$ is

The integral $$\,\,{1 \over {\sqrt {2\pi } }}\int\limits_{ - \infty }^\infty {{e^{{{ - {x^2}} \over 2}}}} dx\,\,$$ is equal to

If $$f\left( x \right) = \sin \left| x \right|\,\,$$ then the value of $${{df} \over {dx}}\,\,$$ at $$\,\,x = {{ - \pi } \over 4}\,\,$$ is

If $$(1, 0, -1)$$$${}^T$$ is an eigen vector of the following matrix $$\left[ {\matrix{ 1 & { - 1} & 0 \cr { - 1} & 2 & { - 1} \cr 0 & { - 1} & 1 \cr } } \right]$$ then the corresponding eigen value is

An industrial gas $$\left( {{C_p} = 1kJ/kgK} \right)$$ enters a parallel flow heat exchanger at $${250^ \circ }C$$ with a flow rate of $$2$$ $$kg/s$$ to heat a water stream.
The water stream $$\left( {{C_p} = 4kJ/kgK} \right)$$ enters the heat exchanger at $${50^ \circ }C$$ with a flow rate of $$1kg/s.$$ The heat exchanger has an effectiveness of $$0.75.$$ The gas stream exit temperature will be

During a steady gas metal arc welding with direct current electrode positive polarity, the welding current, voltage and weld speed are $$150A,$$ $$30V$$ and $$6m/min$$ respectively. A metallic wire electrode of diameter $$1.2mm$$ is being fed at a constant rate of $$12m/min.$$ The density, specific heat and melting temp of the wire electrode are $$7000$$ $$kg/{m^3},$$ $$500$$ $$J/kg$$ and $${1530^ \circ }C$$ respectively. Assume the ambient temp to be $${30^ \circ }C$$ and neglect the latent heat of melting. Further consider that $$2/{3^{rd}}$$ of the total electrical power is available for melting of the wire electrode. The melting efficiency (in percentage) of the wire electrode is

For a $$3$$-axes $$CNC$$ table, the slide along the vertical axis of the table driven by a $$DC$$ servo motor via lead screw nut mechanism. The lead screw has a pitch of $$5mm.$$ This lead screw is fitted with a relative (incremental) circular encoder. The basic length unit $$(BLU)$$ of the slide along the vertical axis of the table is $$0.005mm.$$ When the table moves along the vertical axis by $$9mm.$$ The corresponding number of pulses generated by the encounter is

Which of the following powder production methods produces spongy and porous particles?

During turning of a low carbon steel bar with TiN coated carbide insert, one needs to improve surface finish without sacrificing material removal rate. To achieve improved surface finish one should

During open die forging process using two flat and parallel dies, a solid steel disc of initial radius $$({R_{IN}})\,\,200mm$$ and Initial height $$({H_{IN}})\,\,50mm$$ attains a height $$({H_{FN}})$$ of $$30mm$$ and radius of $${R_{FN}}$$. Along the die-disc interfaces

(i) The coefficient of friction $$\left( \mu \right)$$ is :
$$\,\,\,\,\,\,\,\mu = 0.35\left[ {1 + {e^{ - {R_{IN}}/{R_{FN}}}}} \right]$$

(ii) In the region $${R_{SS}}\,\, \le \,\,r\,\, \le \,\,{R_{FN}},$$ sliding friction prevails and
$$\,\,\,\,\,\,P = \sqrt 3 .K.{e^{2\mu \left( {{R_{IN}} - r} \right)/{H_{FN}}}}$$ and $$\tau = \mu \,p$$

Where $$p$$ and $$\tau $$ are the normal and the shear stress respectively; $$K$$ is the shear yield strength of steel and $$r$$ is the radial distance of any point
(i) In the region $$0\, \le \,r\, \le \,{R_{IN}}.$$ sticking condition prevails

The value of $$RSS$$ (in $$mm$$ ), where sticking condition changes to sliding friction is

In a rolling process, the roll separating force can be decreased by

Hot die steel, used for large solid dies in drop forging, should necessarily have

Cold shut (lap) may occur in products obtained by:

A small bore is designated as $$25H7.$$ The lower (minimum) and upper (maximum) limits of the bore are $$25.000mm$$ and $$25.021$$ respectively. When the bore is designated as $$25H8,$$ then the upper limit is $$25.033mm.$$ When the bore is designated as $$25H6,$$ then the upper limit of the bore in $$mm$$ is