For a given volume of a riser, if the solidification time of the molten metal in riser needs to be quadrupled, the surface area of the riser should be made

Chills are used in casting moulds to

The system of equations, given below, has $$$x+2y+4z=2$$$ $$$4x+3y+z=5$$$ $$$3x+2y+3z=1$$$

If the equation $$sin(x)$$ $$\, = {x^2}$$ is solved by Newton Raphson's method with the initial guess of $$x=1,$$ then the value of $$x$$ after $$2$$ iterations would be _________.

Using the Simpson's $$1/{3^{rd}}$$ rule, the value of $$\,\int {ydx} \,\,$$ computed, for the data given below, is

Marks obtained by $$100$$ students in an examination are given in the table

What would be the mean, median, and mode of the marks obtained by the students?

A simple random sample of $$100$$ observations was taken form a large population. The sample mean and the standard deviation were determined to be $$80$$ and $$12,$$ respectively. The standard error of mean is ______.

In a given day in the rainy season, it may rain$$70$$% of the time . If it rains, chance that a village fair will make a loss on that day is $$80$$%. However, if it does not rain, chance that the fair will make a loss on that day is only $$10$$%. If the fair has not made a loss on a given day in the rainy season, what is the probability that it has not rained on that day?

If $$\,\phi = 2{x^3}{y^2}{z^4}$$ then $${\nabla ^2}\phi $$ is

Directional derivative of $$\phi = 2xz - {y^2}$$ at the point $$(1, 3, 2)$$ becomes maximum in the direction of

In an arc welding operation carried out with a power source maintained at $$40$$ volts and $$400$$ amperes, the consumable electrode melts and just fills the gap between the metal plates to be butt-welded. The heat transfer efficiency for the process is $$0.8,$$ melting efficiency is $$0.3$$ and the heat required to melt the electrode is $$20$$ $$J/m{m^3}$$. If the travel speed of the electrode is $$4$$ $$mm/s$$, the cross-sectional area, in $$m{m^2}$$, of the weld joint is ________________.

Brazing and soldering are

A $$CNC$$ instruction $$G91\,\,\,G01\,\,\,X30\,\,\,Y40\,\,\,F100$$ commands the movement of tool along the path at a feed rate of $$100mm/min$$ $$(G91$$-incremental format and $$G01$$-linear interpolation). The feed rate of the tool (in $$mm/min)$$ along the $$X$$ axis will be _______________

Each axis of $$NC$$ machine is driven by a stepper motor drive with a lead screw. The pitch of lead screw is $$p$$ $$mm.$$ The step angle of stepper motor per pulse input is $$\alpha $$ degrees/pulse. The ratio of gear drive in stepper motor drive is $$g$$(number of turns of the motor for each single turn of the lead screw). The number of pulses required to achieve a linear movement of $$x$$ $$mm$$ is

In an open loop, point-to-point controlled $$CN$$ drilling machine, a stepper motor, producing $$200$$ angular steps per revolution drives the table of a drilling machine by one angular step per each pulse generated by a pulse generator (shown in figure). Each angular step moves the table by one Basic Length Unit $$(BLU)$$ along $$X$$ axis with a lead screw having a pitch of $$4mm.$$ If the frequency of pulse generator is doubled, the $$BLU$$ will

An $$HSS$$ drill of $$20mm$$ diameter with $$5mm$$ cone height is used to drill a through hole in a steel work-piece of $$50mm$$ thickness. Cutting speed of $$10m/min$$ and feed rate of $$0.3mm/rev$$ are used. The drilling time, in seconds, neglecting the approach and over travel, is ______________

Reaming is a process used for

Match the following:

A spindle speed of $$300$$ $$rpm$$ and a feed $$0.3mm/revolution$$ are chosen for longitudinal turning operation on an engine lathe. In finishing pass, roughness on the work surface can be reduced by

In an open die forging, a circular disc is gradually compressed between two flat plates. The exponential decay of normal stress on the flat face of the disc, from the center of the disc towards its periphery, indicates that

A $$80$$ $$mm$$ thick steel plate with $$400$$ $$mm$$ width is rolled to $$40mm$$ thickness in $$4$$ passes with equal reduction in each pass, by using rolls of $$800mm$$ diameter. Assuming the plane-strain deformation, what is the minimum coefficient of friction required for unaided rolling to be possible?

A moving mandrel is used in

The alignment test ''Spindle square with base plate'' is applied to the radial drilling machine. A dial indicator is fixed to the cylindrical spindle and the spindle is rotated to make the indicator touch the base plate at different points. The test inspects whether the