In a sand casting process, a sphere and a cylinder of equal volumes are separately cast from the same molten metal under identical conditions. The height and diameter of the cylinder are equal. The ratio of the solidification time of the sphere to that of the cylinder is

Which of the following casting processes uses expandable pattern and expandable mold

In sand casting fluidity of the molten metal increases with

The eigen values of the following matrix $$\left[ {\matrix{ {10} & { - 4} \cr {18} & { - 12} \cr } } \right]$$ are

The solution of the differential equation $$\,\,\,{{{d^2}y} \over {d{x^2}}} + 6{{dy} \over {dx}} + 9y = 9x + 6\,\,\,\,$$ with $${C_1}$$ and $${C_2}$$ as constants is

It is estimated that the average number of events during a year is three. What is the probability of occurrence of not more than two events over a two-year duration? Assume that the number of events follow a poisson distribution.

If $$T(x, y, z)$$ $$ = {x^2} + {y^2} + 2{z^2}$$ defines the temperature at any location $$(x, y, z)$$ then the magnitude of the temperature gradient at point $$P(1,1,1)$$ is _________.

If $$A$$ $$(0,4,3),$$ $$B(0,0,0)$$ and $$C(3,0,4)$$ are there points defined in $$x, y, z$$ coordinate system, then which one of the following vectors is perpendicular to both the vectors $$\overrightarrow {AB} $$ and $$\overrightarrow {BC} $$.

The line integral $$\int\limits_{{P_1}}^{{P_2}} {\left( {ydx + xdy} \right)} $$ from $${P_1}\left( {{x_1},{y_1}} \right)$$ to $${P_2}\left( {{x_2},{y_2}} \right)$$ along the semi-circle $${P_1}$$ $${P_2}$$ shown in the figure is

If a matrix $$A = \left[ {\matrix{ 2 & 4 \cr 1 & 3 \cr } } \right]$$ and matrix $$B = \left[ {\matrix{ 4 & 6 \cr 5 & 9 \cr } } \right]$$ the transpose of product of these two matrices i.e., $${\left( {AB} \right)^T}$$ is equal to

Water is flowing through a horizontal pipe of constant diameter and the flow is laminar. If the diameter of the pipe is increased by $$50\% $$ keeping the volume flow rate constant, then the pressure drop in the pipe due to friction will decrease by

Cold water flowing at $$0.1$$ $$kg/s$$ is heated from $${20^ \circ }C$$ to $${70^ \circ }C$$ in a counter-flow type heat exchanger by a hot water stream flowing at $$0.1$$ $$kg/s$$ and entering at $${90^ \circ }C$$. The specific heat of water is $$4200$$ $$J$$($$kg$$ $$K$$) and density is $$1000$$ $$kg/{m^3}.$$ If the overall heat transfer coefficient $$U$$ for the heat exchanger is $$2000$$ $$W/\,\,\left( {{m^2}\,\,K} \right),$$ the required heat exchange area (in $${{m^2}}$$) is

In resistance seam welding, the electrode is in the form of a

Which of the following welding process results in the smallest heat affected zone

During orthogonal machining of a mild steel specimen with a cutting tool of zero rake angle, the following data is obtained:
Uncut chip thickness $$=0.25$$ $$mm$$
Chip thickness $$=0.75$$ $$mm$$
Width of cut $$=2.5$$ $$mm$$
Normal force $$=950$$ $$N$$
Thrust force $$=475$$ $$N$$

The ultimate shear stress (in $$N/m{m^2}$$) of the work material is

During orthogonal machining of a mild steel specimen with a cutting tool of zero rake angle, the following data is obtained:
Uncut chip thickness $$=0.25$$ $$mm$$
Chip thickness $$=0.75$$ $$mm$$
Width of cut $$=2.5$$ $$mm$$
Normal force $$=950$$ $$N$$
Thrust force $$=475$$ $$N$$

The shear angle and shear force, respectively, are

Match the following materials with their most appropriate application:

The number of defective produced by a six sigma process (in Parts per million) is

Grinding ratio is defined as

The binding material used in cemented carbide cutting tools is

The thickness of a plate is reduced from $$30$$ $$mm$$ to $$10$$ $$mm$$ by successive cold rolling passes using identical rolls of diameter $$600$$ $$mm.$$ Assume that there is no change in width. If the coefficient of friction between the rolls and the work piece is $$0.1,$$ the minimum number of passes required is

In multi-pass operation, a round bar of $$10$$ $$mm$$ diameter and $$100$$ $$mm$$ length is reduced in cross-section by drawing it successively through a series of seven dies of decreasing exit diameter. During each of theses drawing operations, the reduction in cross-sectional area is $$35\% $$. The yield strength of the material is $$200$$ $$MPa.$$ Ignore strain hardening.

The total true strain applied and the final length (in $$mm$$), respectively, are

In multi-pass operation, a round bar of $$10$$ $$mm$$ diameter and $$100$$ $$mm$$ length is reduced in cross-section by drawing it successively through a series of seven dies of decreasing exit diameter. During each of theses drawing operations, the reduction in cross-sectional area is $$35\% $$. The yield strength of the material is $$200$$ $$MPa.$$ Ignore strain hardening.

Neglecting friction and redundant work, the force (in $$kN$$) required for drawing the bar through the first die, is

To measure the effective diameter of an external metric thread (included angle is $$60$$ degrees) of $$3.5$$ $$mm$$ pitch, a cylindrical standard of $$30.5$$ $$mm$$ diameter and two wires of $$2$$ $$mm$$ diameter each are used. The micrometer reading over the standard and over the wires are $$16.532$$ $$mm$$ and $$15.398$$ $$mm$$ respectively. The effective diameter (in $$mm$$) of the thread is

Observation of a slip gauge on a flatness interferometer produced fringe counts numbering $$10$$ and $$14$$ for two readings. The second reading is taken by rotating the setup by $${180^ \circ }$$ Assume that both faces of the slip gauge are flat and the wavelength of the radiation is $$0.5086$$ $$\mu m.$$ The parallelism error (in $$\mu m.$$) between the two faces of the slip gauge is