If $$f(t)$$ is a finite and continuous Function for $$t \ge 0$$ the laplace transformation is given by
$$F = \int\limits_0^\infty {{e^{ - st}}\,\,f\left( t \right)dt,} $$ then for $$f(t)=cos$$ $$h$$ $$mt,$$ the laplace transformation is ___________.

Find out the eigen value of the matrix $$A = \left[ {\matrix{ 1 & 0 & 0 \cr 2 & 3 & 1 \cr 0 & 2 & 4 \cr } } \right]$$ for any one of the eigen values, find out the corresponding eigen vector?

The value of $$\int\limits_0^\infty {{e^{ - {y^3}}}.{y^{1/2}}} $$ dy is _________.

If $$H(x, y)$$ is homogeneous function of degree $$n$$ then $$x{{\partial H} \over {\partial x}} + y{{\partial H} \over {\partial y}} = nH$$

For the differential equation $$\,\,{{dy} \over {dt}} + 5y = 0\,\,$$ with $$y(0)=1,$$ the general solution is

Solve for $$y$$ if $${{{d^2}y} \over {d{t^2}}} + 2{{dy} \over {dt}} + y = 0$$ with $$y(0)=1$$ and $${y^1}\left( 0 \right) = 2$$

A stone of mass m at the end of a string of length l is whirled in a vertical circle at a constant speed. The tension in the string will be maximum when the stone is

For a fluid element in a two dimensional flow field ($$x-y$$ plane), it will undergo

Streamlines, path lines and streak lines are virtually identical for

In a flow field, the streamlines and equipotential lines

Circulation is defined as line integral of tangential component of velocity about a _________ (fill in the blank)

Existence of velocity potential implies that

Bodies in floatation to be in stable equilibrium the necessary and sufficient condition is that the center of gravity is located below the _____________

Bernoulli’s equation can be applied between any two points on a stream line for a rotational flow field.

In a venturimeter, the angle of the diverging section is more than that of converging section.

For a fully developed laminar flow through a pipe, the ratio of the maximum velocity to the average velocity is ___________ (fill in the blank)

Prandtl’s mixing length is turbulent flow signifies

Fluid is flowing with an average velocity of $$V$$ through a pipe of diameter $$d.$$ over a length of $$L,$$ the “head” loss is given by $${{fL{V^2}} \over {2gD}}.$$ The friction factor, $$f,$$ for laminar flow in terms of Reynolds number ($$Re$$) is ______________ (fill the blank)

The necessary and sufficient condition which brings about separation of boundary layer is
$${{dP} \over {dx}} > 0$$

As the transition from laminar to turbulent flow is induced in a cross flow past a circular cylinder the value of the drag coefficient drops.

When the fluid velocity is doubled the thermal time constant of a thermometer used for measuring the fluid temperature reduces by a factor of $$2$$

For air near atmospheric condition flowing over a flat plate the laminar thermal boundary layer is thicker than hydrodynamic boundary layer

The shape factors with themselves of two infinitely long black body concentric cylinders with a dia ratio of $$3$$ are ....... For the inner and ..... for the outer

The practice to use steam on the shell side and cooling water on the tube side in condensers of steam power plant is because

Two streams of fluid of unit constant specific heats and unit mass flow rate exchange thermal energy in an adiabatic heat exchanger. The inlet temps of hot and cold streams are $${300^ \circ }C$$ and $${30^ \circ }C$$ respectively. Calculate the $$LMTD$$ and effectiveness of the heat exchanger if the hot fluid is cooled to zero entropy condition.

Two insulting materials of thermal conductivity $$K$$ and $$2K$$ are available for lagging a pipe carrying a hot fluid. If the radial thickness of each material is same

Two shafts $$A$$ and $$B$$ are made of the same material. The diameter of shaft $$B$$ is twice that of shaft $$A.$$ The ratio of power which can be transmitted by shaft $$A$$ to that of shaft $$B$$ is

Only $$4$$ pairs can be matched :

The process of hot extrusion is used to produce

Calculate the bite angle when rolling plates $$12mm$$ thick using work rolls $$600mm$$ diameter and reducing the thickness by $$3mm$$

The electrodes used in $$arc$$ welding are coated. This coating is not expected to

The ratio of acetylene to oxygen is approximately ................ for neutral flame used in gas welding

Generally cylindrical parts produced by powder metallurgy should not have non uniform cross section and a length to diameter ratio exceeding . . . . . . . . . . . . . . .

A single point cutting tool made of $$HSS$$ has the value of constant $$'C'$$ $$80,$$ and $$n=0.2$$ in the basic tool life equation. If the tool cost per regrind is Rs $$2$$ and the vmachine hour rate is Rs. $$30,$$ determine the most economical cutting speed (tool cost includes the cost of time spent on changing.

A mild steel block of width $$40$$ $$mm$$ is being milled using a straight slab cutter $$70mm$$ diameter with $$30$$teeth. If the cutter rotates at $$40$$$$rpm$$ and the depth of cut is $$2mm,$$ determine the value of maximum uncut chip thickness when the table feed is $$20mm/min$$

To get good surface finish on a turned job, one should use a sharp tool with a ......... Feed rate and ............... Speed of rotation of the job.

A grinding wheel $$A$$ $$27$$ $$K7$$ $$V$$ is specified for finish grinding of a $$HSS$$ cutting tool. What do you understand about the wheel from the above code. Is this an appropriate choice?

In deep drawing of sheets, the values of limiting draw ratio depends on

$$CNC$$ machines are more economical to use even for simple turning jobs.

$$CNC$$ machines are more accurate than conventional machines because they have a high resolution encoder and digital readouts for positioning

Below Fig. shows a rigid bar hinged at A and supported in a horizontal position by two vertical identical steel wires. Neglect the weight of the beam. The tension $${T_1}$$ and $${T_2}$$ induced in these wires by a vertical load P applied as shown are

Two shafts $$A$$ and $$B$$ are made of the same material. The diameter of shaft $$B$$ is twice that of shaft $$A$$. the ratio of power which can be transmitted by shaft $$A$$ to that of shaft $$B$$ is

For the case of a slender column of length $$l,$$ and flexural rigidity $$EI$$ built-in at its base and free at the top, the Euler’s critical buckling load is

In spur gears having involute teeth, the product of circular pitch and diametral pitch is _________

The definition of 1 K as per the internationally accepted temperature scale is

Any thermodynamic cycle operating between two temperature limits is reversible if the product of efficiency when operating as a heat engine and the coefficient of performance when operating as a refrigeration is equal to $$1.$$

A $$1500$$ $$W$$ electrical heater is used to heat $$20$$ $$kg$$ of water $$\left( {{C_p} = 4186\,\,J/kg\,\,K} \right)$$ in an insulated bucket, from a temperature of $${30^{^0}}C$$ to $${80^{^0}}C$$. If the heater temperature is only infinitesimally larger than the water temperature during the process, the change in entropy for the heater is ________$$J/K$$ and for water _______$$J/K.$$

The slopes of constant volume and constant pressure lines in the $$T$$-$$s$$ diagram are ___________ and ___________respectively.

For a given set of operating pressure limits of a Rankine cycle, the highest efficiency occurs for

For a single stage impulse turbine with rotor diameter of $$2$$ $$m$$ and a speed of $$3000$$ $$rpm$$ when the nozzle angle is $${20^0},$$ the optimum velocity of steam in $$m/s$$

In terms of speed of rotation of the impeller $$N$$, discharge $$Q$$ and a change in total head $$H$$, through the machine,the Specific Speed for a pump is ________________ (fill the blank)