GATE ME 1993
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## GATE ME

$$\mathop {Lim}\limits_{x \to 0} {{x\left( {{e^x} - 1} \right) + 2\left( {\cos x - 1} \right)} \over {x\left( {1 - \cos View Question The function$$f\left( {x,y} \right) = {x^2}y - 3xy + 2y + x$$has View Question The differential equation$${y^{11}} + y = 0\,$$is subjected to the conditions$$y(0) = 0,\,\,\,y\left( \lambda \
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The differential $$\,\,\,{{{d^2}y} \over {d{x^2}}} + {{dy} \over {dx}} + \sin y = 0\,\,$$ is
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Given the differential equation $${y^1} = x - y$$ with initial condition $$y(0)=0.$$ The value of $$y(0.1)$$ calculated
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Simpson's rule for integration gives exact result when $$f(x)$$ is a polynomial function of degree less than or equal to
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The laplace transform of the periodic function $$f(t)$$ described by the curve below $$i.e.\,\,f\left( t \right) = \lef View Question The cylinder shown below rolls without slipping. In which direction does the friction force act? Towards which of the f View Question A velocity field is given as$$$\overrightarrow V = 3{x^2}y\widehat i - 6xyz\widehat k$$Where$$x,y,z$$are in$$m$$View Question Shown below are three pipe sections through which water flows as shown. Option$$(a)$$to$$(d)$$below pertain to the d View Question Shown below are three cylindrical gates which restrain water in$$2$$-$$D$$channel. Which gate experiences the maximum View Question Shown below are three tanks, tank$$1$$without an orifice tube and tanks$$2$$and$$3$$with orifice tubes as shown. N View Question The velocity profile across a boundary layer on a flat plate may be approximated as linear$$${V_x}\left( {x,y} \right)
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An electric hot plate is maintained at a temperature of $${350^ \circ }C,$$ and is used to keep a solution boiling at $$View Question The radiative heat transfer rate per unit area$$\left( {W/{m^2}} \right)$$between two plane parallel gray surfaces (em View Question For a small project with five jobs, the following data is given (i) Draw the project network in activity on arc mode View Question The outside diameter of a hollow shaft is twice its inside diameter. The ratio of its torque carrying capacity to that o View Question The yield strength of a steel shaft is twice its endurance limit. Which of the following torque fluctuations represent t View Question Centrifugally casted products have View Question An aluminium cube of$$10cm$$side has to be cast along with a cylindrical riser of height equal to its diameter. T View Question In$$DC$$welding, the straight polarity (electrode negative) results in View Question A milling cutter having$$8$$teeth is rotating at$$150rpm.$$If the feed per tooth is$$0.1mm,$$the speed View Question A shaft of diameter$${20^{\matrix{ { + 0.05} \cr { - 0.15} \cr } }}\,\,mm$$and a hole of diameter$${20^{\
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With reference to $$NC$$ machines, which of the following statements is wrong?
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Determine the temperature rise necessary to induce buckling in a 1 m long circular rod of diameter 40 mm shown in the fi
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At a point in a stressed body the state of stress on two planes $$45$$0 apart is as shown below. Determine the two princ
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A concentrated load $$P$$ acts on a simply supported beam of span $$L$$ at a distance $${L \over 3}$$ from the left supp
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The compound shaft shown is built-in at the two ends. It is subjected to a twisting moment $$T$$ at the middle. What is
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A circular rod of diameter $$d$$ and length $$3d$$ is subjected to a compressive force $$F$$ acting at the top point as
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The number of degrees of freedom of a five link plane mechanism with five revolute pairs as shown in the figure is:
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During the phase change of a pure substance:
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The relationship $$\,{\left( {\partial T/{\partial _p}} \right)_h} = 0$$ holds good for :
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At the point of a pure substance, the number of degrees of freedom is :
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A vessel of volume $$\,\,1.0\,\,{m^3}$$ contains a mixture of liquid water and steam in equilibrium at $$1.0$$ bar.Given
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In the vicinity of the triple point, the vapour pressures of liquid and solid ammonia are respectively given by $$\eqal View Question An insulated rigid vessel contains a mixture of fuel and air. The mixture is ignited by a minute spark. The contents of View Question A body of weight$$100N$$falls freely a vertical distance of$$50m$$.The atmospheric drag force is$$0.5N.$$For t View Question The first law of thermodynamics takes the form$$W = - \Delta \,H$$when applied to : View Question A rigid insulated cylinder has two compartments separated by a thin membrane. While one compartment contains one kmol ni View Question A vertical cylinder with a freely floating piston contains$$0.1kg$$air at$$1.2$$bar and a small electrical res View Question A reversible heat transfer demands: View Question Round the clock cooling of an apartment having a load of$$300MJ/day$$requires and air-conditioning plant of capac View Question When a system executes an irreversible cycle: View Question Which among the following relations is/are valid ONLY for reversible process undergone by a pure substance? View Question Figure below shows a reversible heat engine$${E_R}$$having heat interactions with three constant temperature systems. View Question The equivalent evaporation$$(kg/hr)$$of a boiler producing$$2000kg/hr$$of steam with enthalpy content of$$2426
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In a single stage single row impulse turbine, the steam is entering at a velocity of $$1200$$ $$m/s$$ with a nozzle angl
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Cavitation in a hydraulic reaction turbine is most likely to occur at the turbine
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Specific speed of a Kaplan turbine ranges between
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