GATE ME 1994

## GATE ME

Find out the eigen value of the matrix $$A = \left[ {\matrix{
1 & 0 & 0 \cr
2 & 3 & 1 \cr
0

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

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

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

View Question
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

View Question
If $$f(t)$$ is a finite and continuous Function for $$t \ge 0$$ the laplace transformation is given by
$$F = \int\limit

View Question
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

View Question
Streamlines, path lines and streak lines are virtually identical for

View Question
In a flow field, the streamlines and equipotential lines

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

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

View Question
Existence of velocity potential implies that

View Question
Bodies in floatation to be in stable equilibrium the necessary and sufficient condition is that the center of gravity is

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

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

View Question
For a fully developed laminar flow through a pipe, the ratio of the maximum velocity to the average velocity is ________

View Question
Prandtl’s mixing length is turbulent flow signifies

View Question
Fluid is flowing with an average velocity of $$V$$ through a pipe of diameter $$d.$$ over a length of $$L,$$ the “head”

View Question
As the transition from laminar to turbulent flow is induced in a cross flow past a circular cylinder the value of the dr

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

View Question
Two insulting materials of thermal conductivity $$K$$ and $$2K$$ are available for lagging a pipe carrying a hot fluid.

View Question
When the fluid velocity is doubled the thermal time constant of a thermometer used for measuring the fluid temperature r

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

View Question
The shape factors with themselves of two infinitely long black body concentric cylinders with a dia ratio of $$3$$ are .

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

View Question
Two streams of fluid of unit constant specific heats and unit mass flow rate exchange thermal energy in an adiabatic hea

View Question
Two shafts $$A$$ and $$B$$ are made of the same material. The diameter of shaft $$B$$ is twice that of shaft $$A.$$ The

View Question
Only $$4$$ pairs can be matched :

View Question
The process of hot extrusion is used to produce

View Question
Calculate the bite angle when rolling plates $$12mm$$ thick using work rolls $$600mm$$ diameter and reducing the thickne

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

View Question
Generally cylindrical parts produced by powder metallurgy should not have non uniform cross section and a length to diam

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

View Question
A single point cutting tool made of $$HSS$$ has the value of constant $$'C'$$ $$80,$$ and $$n=0.2$$ in the basic tool li

View Question
A mild steel block of width $$40$$ $$mm$$ is being milled using a straight slab cutter $$70mm$$ diameter with $$30$$teet

View Question
To get good surface finish on a turned job, one should use a sharp tool with a ......... Feed rate and ............... S

View Question
A grinding wheel $$A$$ $$27$$ $$K7$$ $$V$$ is specified for finish grinding of a $$HSS$$ cutting tool. What do you under

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

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

View Question
$$CNC$$ machines are more accurate than conventional machines because they have a high resolution encoder and digital re

View Question
Below Fig. shows a rigid bar hinged at A and supported in a horizontal position by two vertical identical steel wires. N

View Question
Two shafts $$A$$ and $$B$$ are made of the same material. The diameter of shaft $$B$$ is twice that of shaft $$A$$. the

View Question
For the case of a slender column of length $$l,$$ and flexural rigidity $$EI$$ built-in at its base and free at the top,

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

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

View Question
Any thermodynamic cycle operating between two temperature limits is reversible if the product of efficiency when operati

View Question
A $$1500$$ $$W$$ electrical heater is used to heat $$20$$ $$kg$$ of water $$\left( {{C_p} = 4186\,\,J/kg\,\,K} \right)$$

View Question
The slopes of constant volume and constant pressure lines in the $$T$$-$$s$$ diagram are ___________ and ___________resp

View Question
For a single stage impulse turbine with rotor diameter of $$2$$ $$m$$ and a speed of $$3000$$ $$rpm$$ when the nozzle an

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

View Question
In terms of speed of rotation of the impeller $$N$$, discharge $$Q$$ and a change in total head $$H$$, through the machi

View Question