A cast steel slab of dimension $$30 \times 20 \times 5\,\,cm$$ is poured horizontally using a side riser. The riser is cylindrical in shape with diameter and height, both equal to $$D.$$ The freezing ratio of the moulds is

An expandable pattern is used in

The shape factor for a casting in the form of an annular cylinder of outside diameter $$30$$ $$cm,$$ inside diameter $$20$$ $$cm$$ and height $$30$$ $$cm$$ (correction factor $$k=1.0$$) will be

Which one of the following is Not associated with vector calculus?

Two dice are thrown simultaneously. The probability that the sum of numbers on both exceeds $$8$$ is

The life of a bulb (in hours) is a random variable with an exponential distribution $$\,\,f\left( t \right) = \alpha {e^{ - \alpha t}},0 \le t \le \infty .\,\,\,$$ The probability that its value lies $$b/w$$ $$100$$ and $$200$$ hours is

The differential equation $${\left[ {1 + {{\left( {{{d\,y} \over {d\,x}}} \right)}^2}} \right]^3} = {C^2}{\left[ {{{{d^2}\,y} \over {d\,{x^2}}}} \right]^2}$$ is of

The function $$$w = u + iv = {1 \over 2}\log \left( {{x^2} + {y^2}} \right) + i{\tan ^{ - 1}}\left( {{y \over x}} \right)$$$ is not analytic at the point.

For solving algebraic and transcendental equation which one of the following is used?

The real root of the equation $$x{e^x} = 2$$ is evaluated using Newton $$-$$ Raphson's method. If the first approximation of the value of $$x$$ is $$0.8679,$$ the $${2^{nd}}$$ approximation of the value of $$x$$ correct to three decimal places is

Newton $$-$$ Raphson formula to find the roots of an equation $$f(x)=0$$ is given by

The eigen values of the matrix $$M$$ given are $$15, 3, $$ and $$0.$$
$$M = \left[ {\matrix{ 8 & { - 6} & 2 \cr { - 6} & 7 & { - 4} \cr 2 & { - 4} & 3 \cr } } \right],$$ the value of the determinant of a matrix is

A well machined steel plate of thickness $$L$$ is kept such that the wall temperature are $${T_h}$$ and $${T_c}$$ as shown in the figure below. A smooth copper plate of the same thickness $$L$$ is now attached to the steel plate without any gap as indicated in the figure below. The temperature at the interface is $${T_i},$$ The temperature of the outer walls are still the same at $${T_h},$$ and $${T_c}.$$ The heat transfer rates are $${q_1}$$ and $${q_2}$$ per unit area in the two cases respectively in the direction shown. Which of the following statements is correct?

In a fabrication shop, a $$T$$-joint is to be made between two plates using a chain intermittent, double fillet weld of $$6$$ $$mm$$ leg length. The intermittent welds are $$40$$ $$mm$$ long and spaced $$80$$ $$mm$$ apart, edge to edge.

The welding symbol of the joint is

Two $$8$$ $$mm$$ thick steel plates are placed $$5$$ $$mm$$ apart and welded by a butt joint. Welding is carried out at $$20$$ $$V$$ and speed of $$5$$ $$mm/sec.$$ Heat transfer efficiency is $$0.80.$$ If the heat required to melt steel is $$10$$ $$J/m{m^3}$$ and melting efficiency is $$0.625.$$ The weld current (in Amperes) will be

Match List - I (welding problems) with List - II (Causes) and select the correct answer using the codes given below the lists:

Consider the following statements:

The size of the heat affected zone (HAZ) will increase with
$$1.$$ increased starting temperature
$$2.$$ increased welding speed
$$3.$$ increased thermal conductivity of the base metal
$$4.$$ increase in base metal thickness

Which of the statements given above are correct?

Consider the following statements :

The magnitude of residual stresses in welding depends upon
$$1.$$ Metal melted / deposited
$$2.$$ Design of weldment
$$3.$$ Support and clamping of components
$$4.$$ Welding process used

Which of the statements given above are correct?

The following data relate to an orthogonal turning process:
$$\,\,\,\,\,\,\,\,\,\,\,$$Back rake angle $$=15deg,$$
$$\,\,\,\,\,\,\,\,\,\,\,$$Width of cut $$=2mm,$$
$$\,\,\,\,\,\,\,\,\,\,\,$$Chip thickness $$=0.4mm,$$
$$\,\,\,\,\,\,\,\,\,\,\,$$Feed rate $$=0.2mm/rev.$$

The shear angle is

The effects of setting a boring tool above center height leads to a/an.

If each abrasive grain is viewed as a cutting tool, then which of the following represents the cutting parameters in common grinding operations?

In a machining operation chip thickness ratio is $$0.3$$ and the back rake angle of the tool is $${10^ \circ }.$$ What is the value of the shear strain?

Consider the following statements
During the third stage of tool-wear, rapid deterioration of tool edge takes place because
$$1.$$ Flank wear is only marginal.
$$2.$$ Flank wear is large.
$$3.$$ Temperature of the tool increases gradually.
$$4.$$ Temperature of the tool increases drastically.

Which of the statements given above are correct?

The rake angle of a cutting tool is $${15^ \circ }$$, shear angle $${45^ \circ }$$ and cutting velocity $$35$$ $$m/min$$. What is the velocity of chip along the tool face?

Match List - $${\rm I}$$ with List - $${\rm I}$$$${\rm I}$$ and select the correct answer using the codes given below:

Consider the following statements
$$1.$$ $$\,\,\,\,\,\,\,\,\,\,\,\,$$ As the cutting speed increases, the cost of production initially reduces, then
$$\,\,\,\,\,\,\,\,\,\,\,\,$$after an optimum cutting speed it increases.
$$2.$$ $$\,\,\,\,\,\,\,\,\,\,\,\,$$ As the cutting speed increases the cost of production also increases and
$$\,\,\,\,\,\,\,\,\,\,\,\,$$after a critical value to it reduces.
$$3.$$ $$\,\,\,\,\,\,\,\,\,\,\,\,$$ Higher feed rate for the same cutting speed reduces cost of production.
$$4.$$ $$\,\,\,\,\,\,\,\,\,\,\,\,$$ Higher feed rate for the same cutting speed increases the cost of production

Which of the statements given above are correct?

Match List - $${\rm I}$$ (Cutting tool materials) with List - $${\rm I}$$$${\rm I}$$ (Manufacturing methods) and select the correct answer using the codes given below the lists:

A batch of $$500$$ jobs of diameter $$50$$ $$mm$$ and length $$100$$ $$mm$$ is to be turned at $$200$$ $$rev/min$$ and feed $$0.2$$ $$mm/rev.$$

Applying Taylor's equation $$V{T^{0.25}} = 160,$$ the tool life in minutes is

A batch of $$500$$ jobs of diameter $$50$$ $$mm$$ and length $$100$$ $$mm$$ is to be turned at $$200$$ $$rev/min$$ and feed $$0.2$$ $$mm/rev.$$

The number of components per tool life

A $$\phi $$ $$40$$ $$mm$$ job is subjected to orthogonal turning by a $$ + {10^ \circ }$$ rake angle tool at $$500$$ $$rev/min.$$ By direct measurement during the cutting operation, the shear angle was found equal to $${25^ \circ }.$$

If the friction angle at the tool-chip interface is $${58^ \circ }$$ $$10'$$ and the cutting force components measured by a dynamometer are $$600$$ $$N$$ and $$200$$ $$N$$, the power loss due to friction (in $$kNm/min$$) is approximately

A $$\phi $$ $$40$$ $$mm$$ job is subjected to orthogonal turning by a $$ + {10^ \circ }$$ rake angle tool at $$500$$ $$rev/min.$$ By direct measurement during the cutting operation, the shear angle was found equal to $${25^ \circ }.$$

The velocity (in $$m/min$$) with which the chip flows on the tool face is

The following data relate to an orthogonal turning process:
$$\,\,\,\,\,\,\,\,\,\,\,$$Back rake angle $$=15deg,$$
$$\,\,\,\,\,\,\,\,\,\,\,$$Width of cut $$=2mm,$$
$$\,\,\,\,\,\,\,\,\,\,\,$$Chip thickness $$=0.4mm,$$
$$\,\,\,\,\,\,\,\,\,\,\,$$Feed rate $$=0.2mm/rev.$$

If the cutting force and the thrust force are $$900N$$ and $$810N,$$ the mean strength in $$Mpa$$

Tool life in the case of a grinding wheel is the time

In a shaper machine, the mechanism for tool feed is

One brand of milling machine has the following two index plates supplied along with the indexing head:
Plate 1: $$15, 16, 17, 18, 19, 20$$ hole circles.
Plate 2: $$21, 23, 27, 29, 31, 33$$ hole circles.

It is proposed to mill a spur gear of $$28$$ teeth using simple indexing method. Which one of the following combinations of index plate and number of revolutions is correct?

Match List - $${\rm I}$$ (Milling problem) with List - $${\rm I}$$$${\rm I}$$ (Probable causes) and select the correct answer using the codes given below the lists:

Match List - $${\rm I}$$ (Cutting tools) with List - $${\rm I}$$$${\rm I}$$ (Features) and select the correct answer using the codes given below the lists:

$$NC$$ contouring is an example of

Consider the following characteristics:

$$1.$$ Single machine tool.
$$2.$$ Manual materials handling system
$$3.$$ Computer control.
$$4.$$ Random sequencing of part to machines.

Which of the above characteristics are associated with flexible manufacturing system?

A $$\phi \,\,25$$ $$mm$$ hole is pierced in a $$t=2.5mm$$ thick steel sheet having shear strength $$\tau = 350\,\,MPa.$$ If the diametral clearance is given by the expression $$C=0.0064$$ $$t$$ $$\sqrt \tau ,$$ the die diameter (in $$mm$$), punch diameter (in $$mm$$) and punch force in $$(kN)$$ respectively are

Flash and gutter are provided in drop forging dies at the following stage:

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

A level having $${90^0}$$ bend is to be produced by drop forging using mild steel bar as raw material. The various operations to be performed on it during forging are:
$$P$$ - Cutting;
$$Q$$ - Bending;
$$R$$ - Fullering;
$$S$$ - Blocking cum finishing;
$$T$$ - Edgering

The correct sequence for performing the operations is:

A round billet made of brass is to be extruded (extrusion constant $$=250$$ $$MPa$$ ) at $${700^ \circ }C.$$ The billet diameter is $$100$$ $$mm$$ and the diameter of the extrusion is $$50$$ $$mm.$$ The extrusion force required (in $$MN$$) is

The true stress-true strain curve is given by $$\sigma = 1400\,{\varepsilon ^{0.33}},$$ where the stress $$\sigma $$ is in $$MPa.$$ The true stress at maximum load (in $$MPa$$) is

Assertion (A) : Cold working of metals result in increase of strength and hardness.
Reason (R) : Cold working reduces the total number of dislocations per unit volume of the material.

Consider the following statements:
In comparison to hot working, in cold working,
$$1.$$ Higher forces are required
$$2.$$ No heating is required
$$3.$$ Less ductility is required
$$4.$$ Better surface finish is obtained.

Which of the statements given above are correct?

Ring gage is used to measure

A cylindrical pin of diameter $${1.996^{\matrix{ { + 0.0015} \cr { - 0.0015} \cr } }}\,\,mm$$ is assembled into a hole of diameter $${2.000^{\matrix{ { + 0.0015} \cr { - 0.0015} \cr } }}\,\,mm.$$ The allowance (in $$mm$$) provided for this assembly is