GATE 2000 Mechanical Engineering
33 questions across 1 session
In finish machining of an island on a casting with $$CNC$$ milling machine, an end mill with $$10$$ $$mm$$ diameter is employed. The corner points of the island are represented by...
Find the solution of the differential equation $$\,{{{d^2}u} \over {d{t^2}}} + {\lambda ^2}y = \cos \left( {wt + k} \right)$$ with initial conditions $$\,y\left( 0 \right) = 0,\,\,...
A $$1.5$$ $$kW$$ motor is running at $$1440$$ rev/min. It is to be connected to a stirrer running at $$36$$ rev/min. the gearing arrangement suitable for this application is
Two different pairs of sheets of same material are welded by resistance-spot welding. In one pair, the average radius $$(r)$$ of each spherical bridge is $$0.2$$ $$mm$$ and the num...
In computer aided drafting practice, an arc is defined by
A steel wheel of 600 mm diameter rolls on a horizontal steel rail. It carries a load of 500 N. The coefficient of rolling resistance is 0.3 mm. The force in N, necessary to roll th...
Solve the following linear programming problem by simplex method $$\eqalign{ & Maximize\,\,\,\,\,\,4{x_1} + 6{x_2} + {x_3} \cr & Subject\,\,to\,\,\,\,\,\,2{x_1} - {x_2} + 3{x_3}\,...
Two castings, a cube and a slab of the same material solidify under identical conditions. The volumes of the castings are equal but the slab dimensions are in the ratio of $$1:2:4$...
The life of a ball bearing at a load of $$10$$ $$kN$$ is $$8000$$ hours. Its life in hours, if the load is increased to $$20$$ $$kN,$$ keeping all other conditions same, is
In a manufacturing plant, the probability of making a defective bolts is $$0.1$$. The mean and standard deviation of defective bolts in a total of $$900$$ bolts are respectively
Air enters a counter-flow heat exchanger at $${7^ \circ }C$$ and leaves at $${40^ \circ }C$$. Water enters at $${30^ \circ }C$$ and leaves at $${50^ \circ }C$$. The $$LMTD$$ in deg...
A cylindrical billet of $$100$$ $$mm$$ diameter is forged from $$50$$ $$mm$$ height to $$40$$ $$mm$$ at $${1000^0}$$$$C$$. The material has constant flow stress of $$80$$ $$MPa.$$...
The forecasts for a product for the next three months are given as $$750,850$$ and $$1000$$ units. The number of regular time days and overtime days available are $$22,18,$$ $$22$$...
Availability of a system at any given state is
For a compressible fluid, sonic velocity is
Which of the following is a pressure compounded turbine?
A steam turbine receives steam steadily at $$10$$ $$bar$$ with an enthalpy of $$3000$$ $$kJ/kg$$ and discharges at $$1$$ bar with an enthalpy of $$2700$$ $$kJ/kg.$$ The work output...
A simple impulse turbine expands steam frictionlessly from $$12$$ bar, $${250^0}C$$ with an enthalpy of $$2935$$ $$kJ/kg$$ to an enthalpy of $$2584$$ $$kJ/kg$$ at $$0.1$$ bar. Assu...
A certain mass of a pure substance undergoes an irreversible process from state $$1$$ to state $$2,$$ the path of the process being a straight line on the $$T$$-$$s$$ diagram. Calc...
When an ideal gas with constant specific heats is throttled adiabatically, with negligible changes in kinetic and potential energies
In a single server infinite population queuing model, arrivals follow a Poisson distribution with mean $$\lambda = 4$$ per hour. The service times are exponential with mean service...
Cellular manufacturing is suitable for
A company places orders for supply of two items $$A$$ and $$B.$$ The order cost for each of the items is Rs.$$300$$ /order. The inventory carrying cost is $$18\% $$ of the unit pri...
Disposable patterns are made of
Abrasive material used in grinding wheel selected for grinding ferrous alloys is
The abrasive material used in grinding wheel selected for grinding of ferrous alloys is
A built up edge is formed while machining
Navier Stoke's equation represents the conservation of
In a time series forecasting model, the demand for five time periods was $$10, 13,$$ $$15,$$ $$18$$ and $$22.$$ A linear regression fit resulted in an equation $$F = 6.9 + 2.9$$ $$...
A thin metal plate is exposed to solar radiation. The air and the surroundings are at $${30^ \circ }C\,.$$ The heat transfer coefficient by free convection from the upper surface o...
The ratio of tension on the tight side to that on the slack side in a flat belt drive is
Deep hole drilling of small diameter, say $$0.2$$ $$mm$$ is done with $$EDM$$ by selecting the tool material as
A 1.5 kW motor is running at 1440 rev/min. Its is to be connected to a stirrer running at 36 rev/min. The gearing arrangement suitable for this application is