Match the items in the first column to their functions in the second column.

In a metal casting process, molten copper alloy is poured into a sand mould. The level of molten metal in the pouring basin is at a height of $$300$$ $$mm$$ from the runner having diameter of $$10$$ $$mm.$$ If the density and melting temperature of molten copper alloy are $$9000$$ $$kg/{m^3}$$ and $${1000^ \circ }C.$$ respectively then the rate of flow of molten metal into the mould neglecting friction and other losses, in $$c{m^3}/s,$$ is ______________.

In numerical integration using Simpson's rule, the approximating function in the interval is a

The value of $$\mathop {\lim }\limits_{\left( {x,y} \right) \to \left( {0,0} \right)} {{{x^2} - xy} \over {\sqrt x - \sqrt y }}$$ is

The curve $$\,\,y = {x^4}\,\,$$

The function $$f\left( x \right) = {x^2} = x + x + x + ....x$$ times, is defined

A coin is tossed thrice. Let $$X$$ be the event that head occurs in each of the first two tosses. Let $$Y$$ be the event that a tail occurs on the third toss. Let $$Z$$ be the event that two tails occur in three tosses. Based on the above information, which one of the following statements is TRUE?

A product is an assemble of $$5$$ different components. The product can be sequentially assembled in two possible ways. If the $$5$$ components are placed in a box and these are drawn at random from the box, then the probability of getting a correct sequence is

The solution to $$\,6y{y^1} - 25x = 0\,\,$$ represents a

The solution to $$\,\,{x^2}{y^{11}} + x{y^1} - y = 0\,\,$$ is

In a vertical piston-cylinder arrangement the force applied to the piston, pushes water through a nozzle as shown in the figure. The water flows out from the nozzle, and reaches the top of its trajectory. The kinetic and pressure energies at points $$(1), (2)$$ and $$(3),$$ respectively, are

In a $$1$$ $$m$$ thick wall, the temperature distribution at a given instant is
$$T\left( x \right) = {c_0} + {c_1}x + {c_2}{x^2}$$ where $$T$$ is in $${}^ \circ C$$ and $$x$$ is in $$m.$$ The constants are: $${c_0} = {800^ \circ }C,$$ $${c_1} = - {250^ \circ }C/m$$ and $${c_2} = - {40^ \circ }C/{m^2}.$$ The thermal conductivity of the wall is $$50$$ $$W/mK$$ and wall area is $$5\,\,{m^2}.$$ If there is a heat source generating uniform volumetric heating at the rate of $$500$$ $$W/{m^3}$$ inside the wall, then the rate of change of energy storage in the wall, in $$kW,$$ is _____________.

A manufacturing line requires $$7.2$$ minutes to make a product. The line has six workstations arranged as per the required sequence of operations. Total production required is $$300$$ products in $$7.5$$ hours. At steady state, the line efficiency, in $$\% $$, is ______________

Arrival of machines for repair in a maintenance shop follows a Poisson distribution at a rate of one per $$18$$ hours. The time to repair follows an exponential distribution with Mean Time To Repair $$(MTTR)$$ of $$14$$ hours. If the productivity loss is Rs.$$22,500$$ per hour, then the total expected loss of productivity due to machine breakdowns, in Rs., is

A line balancing problem is solved in the context of

Two aluminium alloy plates each $$10$$ $$mm$$ thick and $$1$$ $$m$$ long are welded without crowning by multipass tungsten inert gas butt welding. The joint configuration is $$V$$-type with $${60^ \circ }$$ angle and root gap is maintained at $$5$$ $$mm.$$ If electrode of $$5$$ $$mm$$ diameter with $$500$$ $$mm$$ length is used for welding, then the number of electrodes required is

In Computer Aided Process Planning, determination of process sequence for manufacture of any part design without predefined standard plans is known as

Built-up edge formation decreases under the conditions listed below EXCEPT

The angle of a twist drill that determines its rake angle is

In an orthogonal machining experiment carried out using a cutting tool with zero degree rake angle, the measured cutting force was $$1700$$ $$N.$$ If the friction angle at the rake face-chip interface is $${26^ \circ },$$ then the thrust force value, in $$N$$ is ___________________

During turning of mild steel work material, the maximum temperature is observed at

Which one of the following statements related to grinding process is INCORRECT?

In a slab milling operation, a cutter of $$75$$ $$mm$$ diameter with sufficient width is used to remove $$5$$ $$mm$$ thick material from a $$200$$ $$mm$$ long part in a single pass. The minimum length of travel, in $$mm,$$ for the cutter to engage and completely cut the part surface is ______________.

In drilling operation, a twist-drill of $$30$$ $$mm$$ diameter with point angle of $$118$$ degrees is used. If the $$CNC$$ command issued to execute the drilling operation is $$G90$$ $$G01$$ $$Z??$$ $$F20.$$ The datum is defined on the top surface of the work material and the approach distance is $$3$$ $$mm.$$ Then, to achieve a cylindrical hole depth of $$40$$ $$mm,$$ the $$Z$$ coordinate to be provided in the $$CNC$$ command, in $$mm,$$ is ______________.

Match the linear transformation matrices listed in the first column to their interpretations in the second column.

In a Flexible manufacturing system, the Automated Guided Vehicles $$(AGV)$$ move at a speed of $$50$$ $$m/min,$$ cover an average distance of $$150$$ $$m$$ to deliver and $$100$$ $$m$$ for return. If the time required for pick-up and drop is $$30$$ $$s$$ each, neglecting idle times, then the number of $$AGV$$$$s$$ required to meet the demand of $$50$$ delivers per hour is ____________.

Open die forging of a cylinder made of a rigid perfectly plastic material with yield strength of $$200$$ $$MPa$$ having a height of $$25$$ $$mm$$ and diameter of $$25$$ $$mm$$ is being carried out. The cylinder is subjected to a true compressive strain of $$3.6$$ during the process. Assuming frictionless and homogeneous deformation, the energy expended, in $$kJ$$ is __________________.

The maximum reduction per pass during wire drawing of an aluminium alloy ignoring friction and redundant work is $$77\% $$. The strain hardening exponent of the material is ______________.

In rolling of a flat strip, the relative velocity of strip with respect to the roller is

The true stress at fracture of a tensile tested specimen, having an initial diameter of specimen at fracture is $$10$$ $$mm,$$ then the engineering stress, in $$MPa,$$ at fracture is ____________

A surface is prepared specially for an application with the profile as shown in the figure.

The theoretical $${R_a}$$ value for this surface, in $$\mu m,$$ is _______________.

During the measurement of internal taper of a part using standard balls of diameter $$15$$ $$mm$$ and $$20$$ $$mm$$, the large ball is found to protrude by $$5$$ $$mm$$ $$\left( {{h_1}} \right)$$ and the top of small ball is found to be $$35$$ $$mm$$ $$\left( {{h_2}} \right)$$ below the top face of the gauge. The taper angle, in degree, is ________________.

The room-temperature stress $$\left( \sigma \right)$$ - strain $$\left( \varepsilon \right)$$ curves of four materials $$P, Q, R$$ and $$S$$ are shown in the figure below. The material that behaves as a rigid perfectly plastic material is

A beam is loaded as shown in the figure

The bending moment, in $$Nm$$, at point $$R$$ is _______.

A metallic bar of uniform cross-section with specific weight of $$100$$ kN/m³ is hung vertically down. The length and Young's modulus of the bar are $$100$$ m and $$200$$ GPa, respectively. The elongation of the bar, in mm, due to its own weight is __________ .

If the principal stress values are $$120$$ MPa, $$-50$$ MPa and $$10$$ MPa in a given state of stress, then maximum shear stress in the material, in MPa, is _______.

In an off-set slider crank mechanism, shown in figure, the crank is rotated at a constant speed of $$150$$ rpm. The value of the angle $$\theta $$ shown in the figure is $${20^ \circ }$$ . What is the ratio of forward to return stroke time? Can this mechanism be used in an application involving quick return?

An ideal gas of mass $$m$$ is contained in a rigid tank of volume $$V$$ at a pressure $$P.$$ During a reversible process its pressure reduces to $${P_1}.$$ Following statements are made regarding the process.
$$(P)$$ Heat is transferred from the gas.
$$(Q)$$ Work done by the gas is zero.
$$(R)$$ Entropy of the gas remains constant.
$$(S)$$ Entropy of the gas decreases.

Among the above statements, the correct ones are