GATE 1993 Mechanical Engineering

An electric hot plate is maintained at a temperature of $${350^ \circ }C,$$ and is used to keep a solution boiling at $${95^ \circ }C.$$ The solution is contained in cast iron vess...

A milling cutter having $$8$$ teeth is rotating at $$150$$ $$rpm.$$ If the feed per tooth is $$0.1$$ $$mm,$$ the speed in $$mm$$ per minute is

A shaft of diameter $${20^{\matrix{ { + 0.05} \cr { - 0.15} \cr } }}\,\,mm$$ and a hole of diameter $${20^{\matrix{ { + 0.20} \cr { + 0.10} \cr } }}\,\,mm$$ when assembled would yi...

The differential $$\,\,\,{{{d^2}y} \over {d{x^2}}} + {{dy} \over {dx}} + \sin y = 0\,\,$$ is

Cavitation in a hydraulic reaction turbine is most likely to occur at the turbine

In $$DC$$ welding, the straight polarity (electrode negative) results in

The radiative heat transfer rate per unit area $$\left( {W/{m^2}} \right)$$ between two plane parallel gray surfaces (emissivity $$=0.9$$) maintained at $$400K$$ and $$300K$$ is ($...

The differential equation $${y^{11}} + y = 0\,$$ is subjected to the conditions $$y(0) = 0,$$ $$\,\,\,y\left( \lambda \right) = 0.\,\,$$ In order that the equation has non-trivial...

Centrifugally casted products have

A velocity field is given as $$$\overrightarrow V = 3{x^2}y\widehat i - 6xyz\widehat k$$$ Where $$x,y,z$$ are in $$m$$ and $$V$$ $$m/s.$$ Determine if (i) It represents an incompre...

The function $$f\left( {x,y} \right) = {x^2}y - 3xy + 2y + x$$ has

Round the clock cooling of an apartment having a load of $$300$$ $$MJ/day$$ requires and air-conditioning plant of capacity about

In the vicinity of the triple point, the vapour pressures of liquid and solid ammonia are respectively given by $$\eqalign{ & \ln \,\,P = 15.16 - 3063/T \cr & \,\,\,\,\,\,\,\,\,\,\...

At the point of a pure substance, the number of degrees of freedom is :

A body of weight $$100$$ $$N$$ falls freely a vertical distance of $$50m$$.The atmospheric drag force is $$0.5N.$$ For the body, the work interaction is

When a system executes an irreversible cycle:

A rigid insulated cylinder has two compartments separated by a thin membrane. While one compartment contains one kmol nitrogen at a certain pressure and temperature, the other cont...

An insulated rigid vessel contains a mixture of fuel and air. The mixture is ignited by a minute spark. The contents of the vessel experience.

A vessel of volume $$\,\,1.0\,\,{m^3}$$ contains a mixture of liquid water and steam in equilibrium at $$1.0$$ bar.Given that $$90\% $$ of the volume is occupied by the steam, find...

The relationship $$\,{\left( {\partial T/{\partial _p}} \right)_h} = 0$$ holds good for :

Which among the following relations is/are valid ONLY for reversible process undergone by a pure substance?

The first law of thermodynamics takes the form $$W = - \Delta \,H$$ when applied to :

A reversible heat transfer demands:

The equivalent evaporation $$(kg/hr)$$ of a boiler producing $$2000$$ $$kg/hr$$ of steam with enthalpy content of $$2426$$ $$kJ/kg$$ from feed water at temperature $${40^ \circ }C$...

In a single stage single row impulse turbine, the steam is entering at a velocity of $$1200$$ $$m/s$$ with a nozzle angle of $${20^ \circ }$$ and leaving the blade in the axial dir...

During the phase change of a pure substance:

Given the differential equation $${y^1} = x - y$$ with initial condition $$y(0)=0.$$ The value of $$y(0.1)$$ calculated numerically upto the third place of decimal by the $${2^{nd}...

$$\mathop {Lim}\limits_{x \to 0} {{x\left( {{e^x} - 1} \right) + 2\left( {\cos x - 1} \right)} \over {x\left( {1 - \cos x} \right)}} = \_\_\_\_\_\_.$$

An aluminium cube of $$10$$ $$cm$$ side has to be cast along with a cylindrical riser of height equal to its diameter. The riser is not insulated on any surface. If the volume shri...

Simpson's rule for integration gives exact result when $$f(x)$$ is a polynomial function of degree less than or equal to ________.

The yield strength of a steel shaft is twice its endurance limit. Which of the following torque fluctuations represent the most critical situation according to Soderberg criterion?

The outside diameter of a hollow shaft is twice its inside diameter. The ratio of its torque carrying capacity to that of a solid shaft of the same material and the same outside di...

With reference to $$NC$$ machines, which of the following statements is wrong?

A concentrated load $$P$$ acts on a simply supported beam of span $$L$$ at a distance $${L \over 3}$$ from the left support. The bending moment at the point of application of the l...