GATE 1998 Mechanical Engineering
24 questions across 1 session
The general solution of the differential equation $${x^2}{{{d^2}y} \over {d{x^2}}} - x{{dy} \over {dx}} + y = 0$$ is
The probability that two friends share the same birth-month is
Which one of the following forecasting techniques is not suited for making forecasts for planning production schedules in the short range?
A strip with sectional area $$150mm\,\, \times \,\,4.5mm$$ is being rolled with $$20\% $$ reduction of area using $$450mm$$ diameter rollers. The angle subtended by the deformation...
Bolts in the flanged end of pressure vessel are usually pre- tensioned. Indicate which of the following statements is not true
One of the following statements about $$PRS$$ (Periodic Reordering System) is not true. Identify.
Two castings of the same metal have the same surface area one casting is in the form of a sphere and the other is a cube. What is the ratio of the solidification time for the spher...
In inventory planning, extra inventory is unnecessarily carried to the end of the planning period when using one of the following lot size decision policies:
Heat transfer coefficients for free convection in gasses, forced convection in gases and vapors, and for boiling water lie, respectively, in the range of
A Curtis stage, Rateau stage and a $$50$$% reaction stage in a steam turbine are examples of
Hot water flows with a velocity of $$0.1$$ $$m/s$$ in a $$100mm$$ long, $$0.1m$$ diameter pipe. Heat lost from the pipe outer wall is uniform and equal to $$420$$ $$W/{m^2}$$. If t...
If $$\,\,{V_N}\,\,$$ and $$\alpha $$ are the nozzle exit velocity and nozzle angle in an impulse turbine, the optimum blade velocity is given by
The isentropic heat drop in the nozzle of an impulse steam turbine with a nozzle efficiency $$0.9,$$ blade velocity ratio $$0.5,$$ and mean blade velocity $$150$$ $$m/s$$ in $$kJ/k...
The basic load rating of a ball bearing is
A gas filled tube has $$2$$ $$mm$$ inside diameter and $$25$$ $$cm$$ length. The gas is heated by an electrical wire of diameter $$50$$ microns ($$0.05$$ $$mm$$) located along the...
Which theory of failure will you use for aluminium components under steady loading is
A cylinder of $$155$$ $$mm$$ is to be reduced $$150$$ $$mm$$ diameter in one turning cut with a feed of $$0.15$$ $$mm$$/ revolution and a cutting speed of $$150$$ $$m/min$$ on a $$...
The voltage-arc length characteristics of a $$DC$$ arc is given by $$V=20+4L.$$ Where $$L$$ is in $$mm$$. During a welding operation arc length is expected to vary between $$4$$ an...
In orthogonal machining operation, the chip thickness and the uncut chip thickness are equal to $$0.45mm$$. If the tool rake angle is $$0$$ deg. The shear plane angle is
A hot fluid at $${200^ \circ }C$$ enters a heat exchanger at a mass flow rate of $${10^4}\,\,kg/hr.$$ Its specific heat is $$2000$$ $$J/kg$$-$$K.$$ It is to be cooled by another fl...
The voltage-arc length characteristics of a $$DC$$ arc is given by $$V=20+4L.$$ Where $$L$$ is in $$mm$$. During a welding operation arc length is expected to vary between $$4$$ an...
The radial displacement in a rotating disc is governed by the differential equation $$\,\,{{{d^2}u} \over {d{x^2}}} + {1 \over x}{{du} \over {dx}} - {u \over {{x^2}}} = 8x.\,\,\,$$...
A car moving with uniform acceleration covers 450 m in a 5 second interval, and covers 700 m in the next 5 second interval. The acceleration of the car is
A flywheel of moment of inertia $$9.8$$ kg m 2 fluctuates by $$30$$ rpm for a fluctuation in energy of $$1936$$ Jouls. The mean speed of the flywheel is (in rpm)