Schematic diagram of pouring basin and sprue of a gating system is shown in the Figure. Depth of molten metal in the pouring basin is $$100$$ $$mm$$ and the height of the sprue is $$1,500$$ $$mm.$$

Considering the cross-section of the sprue is circular, the ratio $${d_1}:{d_2}$$ to avoid aspiration is

In carbon dioxide molding process, the binder used is

A manometer is used for the pressure measurement in a closed tank. The three fluids $$f1,f2$$ and $$f3$$ have specific weights $$\gamma ,$$ $$2\gamma ,$$ and $$0.5\gamma ,$$, respectively. The schematic arrangement with manometric readings and other dimensions are shown in the Figure. In order to ensure zero gauge pressure in the tank at the mid-height level $$(h/2),$$ the height of the tank $$h$$ (in $$m$$) is _________________.

A pipeline with variable cross-section contains water with specific weight
$${10^4}\,\,N/{m^3}.$$ The flow conditions at two points $$1$$ and $$2$$ on the axis of the pipe are:
$$\eqalign{ & {P_1} = 3\,\,bar,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{V_1} = 10\,\,m/s \cr & {P_2} = 1\,\,bar,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{V_2} = 20\,\,m/s \cr} $$

Consider frictional losses to be negligible. For no-flow condition between points $$1$$ and $$2$$ (as shown in Figure), if the height $${z_1}$$ from the datum is $$1$$ $$m,$$ then the height $${z_2}$$ (in $$m$$) is _____________ $$\left( {g = 9.81\,\,m/{s^2}} \right)$$

A metallic cylindrical casing of an exhaust pipe has inner radius $$50$$ $$mm$$ and wall thickness $$7$$ $$mm.$$ If the thermal conductivity of the material of the casing is $$50$$ $$W/m$$-$$K,$$ then the thermal resistance of the casing in $$K/kW$$ is ________________ (up to three decimal places).

In a calendar year, the demand forecast of motorbikes for the month of june is $$200.$$ The actual demand of motorbikes for the month of June and July are $$300$$ and $$350,$$ respectively. If single exponential smoothing method with smoothing constant $$0.7$$ is used, then the demand forecast for the month of August is ___________.

An electrical appliances showroom sells $$2,400$$ ceiling fans in one year ($$52$$ weeks). The holding cost is $$10\% $$ of the cost of the ceiling fan. The most of one ceiling fan is Rs. $$600$$. The cost incurred for placing an order is Rs. $$201.$$ There is a lead time of $$5$$ weeks. The economic order quantity $$(EOQ)$$ and the reorder level, respectively (rounded to the next higher integer) are

The potential production alternatives for manufacturing a product along with their unit cost and monthly capacity are given in the Table.

The inventory at the end of july is $$100$$ units. If the demand for the month of August is $$620,$$ then the minimum total cost (in Rs.) to meet the demand is ______________

In a project, tasks $$A, B, C, D, E, F, G, H, I$$ and $$J$$ are to be performed. The precedence relationships and the time required (in days) to complete the tasks are given in the Table.

The time required (in days) to complete the project along the critical path is ______________

In gas tungsten arc welding process, the material coated on pure tungsten electrode to enhance its current carrying capacity is

A pair of spur gears with $${20^ \circ }$$ full-depth involute teeth is used to transmit $$3.5$$ $$kW$$ of power. The pinion rotates at $$700$$ $$rpm$$ and has pitch circle diameter of $$100$$ $$mm.$$ Assuming a single pair of teeth in contact, the total force acting on a gear tooth (in $$kN$$) is

A solid circular shaft is subjected to a bending moment $$M$$ and torque $$T$$ simultaneously. Neglecting the effects of stress concentration, the equivalent bending moment is expressed as

In a numerical control $$(NC)$$ machine positioning system, the measures of precision are expressed by considering a single axis as shown in the Figure.

If $$\sigma $$ is standard deviation of the error distribution, the $$L$$, $$M$$ and $$N$$ are

The preparatory and miscellaneous codes used in $$CNC$$ part programming and the functions are given in the Table

The correct combination of code and the respective function is

A schematic diagram of peripheral milling is shown in the Figure.

If $$t$$ is the depth of cut and $$d$$ is the diameter of the milling cutter, then the length of approach $$\left( {la} \right)$$ is expressed as

In a machining operation with turning tool, the tool life $$(T)$$ is related to cutting speed $$v$$ $$(m/s),$$ feed $$f(mm)$$ and depth of cut $$d(mm)$$ as $$$T = C\,v{\,^{ - 2.5}}\,{f^{ - 0.9}}\,{d^{ - 0.15}}$$$
where, $$C$$ is a constant. The suggested values for the cutting parameters are: $$V=1.5$$ $$m/s,$$ $$f=0.25$$ $$mm$$ and $$d=3$$ $$mm$$ for normal rough turning. If the operation is performed at twice the cutting speed and the other parameters remain unchanged, the corresponding percentage change in tool life is ______________.

Turning, drilling, boring and milling are commonly used machining operations. Among these, the operation (s) performed by a single point cutting tool is (are)

The Merchant circle diagram showing various forces associated with a cutting process using a wedge shaped tool is given in the Figure

The coefficient of friction can be estimated from the ratio

A metallic strip having a thickness of $$12$$ $$mm$$ is to be rolled using two steel rolls, each of $$800$$ $$mm$$ diameter. It is assumed that there is no change in width of the strip during rolling. In order to achieve $$10\% $$ reduction in cross-sectional area of the strip after rolling, the angle subtended (in degrees) by the deformation zone at the center of the roll is

A steel wire of $$2$$ $$mm$$ diameter is to be drawn from a wire of $$5mm$$ diameter. The value of true strain developed is _____________ (up to three decimal places)

Accuracy of a measuring instrument is expressed as

A machined surface with standard symbols indicating the surface texture is shown in the Figure. (ALL dimensions in the Figure are in micrometer).

The waviness height (in micrometer) of the surface is

For a two dimensional state-of-stress defined as $${\sigma _{xx}} = {\sigma _{yy}} = {\tau _{xy}} = S,$$ the Mohr's circle of stress has

The simply-supported beam shown in the Figure is loaded symmetrically using two equal point loads $$P.$$ The radius of curvature of the deflection-curve is $$15$$ m for the portion of the beam that is subjected to pure bending. The vertical deflection (in mm) at point $$M,$$ equidistant from both the supports is _______ (up to two decimal places).

The inside and outside radii of a thick- walled cylindrical pressure vessel are denoted by $$a$$ and $$b,$$ respectively. If the vessel is subjected to an internal pressure $$P,$$ then the magnitude of the radial stress $${\sigma _{rr}}$$ is

If $$E$$ is the modulus of elasticity in $$GPa$$, $$G$$ is the shear modulus in $$GPa$$ and $$v$$ is the Poisson's ratio of a linear elastic and isotropic material, the three terms are related as

A reversible heat engine $$(E)$$ operating in a cycle interacts with three reservoirs $$1,$$ $$2$$ and $$3$$ maintained at temperature $${T_1} = 500K,$$ $${T_2} = 400K,$$ and $${T_3} = 300K,$$ respectively. The engine receives $$10$$ $$kJ$$ of heat from reservoir $$1$$ and rejects $$3$$ $$kJ$$ to reservoir $$3.$$ The net work output, $${W_{net}}$$ (in $$kJ$$) from the engine is