GATE 2010 Mechanical Engineering

A hydraulic turbine develops $$1000$$ $$kW$$ power for a head of $$40$$ $$m.$$ If the head is reduced to $$20$$ $$m,$$ the power developed (in $$kW$$) is

Little’s law is relationship between

The demand and forecast for February are $$12000$$ and $$10275,$$ respectively. Using single exponential smoothening method (smoothening coefficient $$= 0.25$$), forecast for the m...

In a gating system, the ratio $$1:2:4$$ represents

For tool $$A,$$ Taylor’s tool life exponent $$(n)$$ is $$0.45$$ and constant $$(K)$$ is $$90.$$ Similarly for tool $$B,$$ $$n=0.3$$ and $$K=60.$$ The cutting speed (in $$m/min$$) a...

The blasius equation $$\,{{{d^3}f} \over {d{\eta ^3}}} + {f \over 2}\,{{{d^2}f} \over {d{\eta ^2}}} = 0\,\,\,\,$$ is a

Velocity vector of a flow fields is given as $$\overrightarrow V = 2xy\widehat i - {x^2}z\widehat j.$$ The vorticity vector at $$(1,1,1)$$ is

The Laplace transform of $$f\left( t \right)$$ is $${1 \over {{s^2}\left( {s + 1} \right)}}.$$ The function

The function $$y = \left| {2 - 3x} \right|$$

Simplex method of solving linear programming problem uses

A shaft has a dimension $$\phi $$ $${35^{\matrix{ { - 0.009} \cr { - 0.025} \cr } }}$$. The respective values of fundamental deviation and tolerance are

For the stability of a floating body, under the influence of gravity alone, which of the following is TRUE?

Match the following List-$${\rm I}$$ $$P.$$ Compressible flow $$Q.$$ Free surface flow $$R.$$ Boundary layer flow $$S.$$ Pipe flow $$T.$$ Heat convection List-$${\rm II}$$ $$U.$$ R...

For the case of molding, it is decided to replace a spherical riser of diameter $$100$$ $$mm$$ by a cylindrical riser. Determine size of the cylindrical riser that will have the id...

Two steel bars each of diameter $$10mm$$ are coaxially friction welded end to end at an axial pressure of $$200MPa$$ and rotational speed of $$400rpm$$. The coefficient of friction...

The parabolic are $$y = \sqrt x ,1 \le x \le 2$$ is revolved around the $$x$$-axis. The volume of the solid of revolution is

In a $$CNC$$ program block, $$N002\,\,\,\,G02\,\,\,\,G91\,\,\,\,X40\,\,\,\,Z40....,\,\,\,\,G02\,\,\,\,\& \,\,\,\,G91$$ refer to

A phenomenon is modeled using $$n$$ dimensional variables with $$k$$ primary dimensions. The number of non-dimensional variables is

Tooth interference in an external involute spur gear pair can be reduced by

A band brake having band-width of $$80mm,$$ drum diameter of $$250mm,$$ coefficient of friction of $$0.25$$ and angle of wrap of $$270$$ degrees is required to exert a friction tor...

Annual demand for window frames is $$10000.$$ Each frame costs Rs. $$200$$ and ordering cost is Rs. $$300$$ per order. Inventory holding cost is Rs. $$40$$ per frame per year. The...

The infinite series $${\,f\left( x \right) = x - {{{x^3}} \over {3!}} + {{{x^5}} \over {5!}} - {{{x^7}} \over {7!}} + - - - \,\,}$$ Converges to

Consider the following two processes; $$\left( {\rm I} \right)$$ A heat source at $$1200$$ $$K$$ loses $$2500$$ $$kJ$$ of heat to a sink at $$800$$ $$K$$ $$\left( {\rm II} \right)$...

One kilogram of water at room temperature is brought into contact with a high temperature thermal reservoir. The entropy change of the universe is

A mono-atomatic ideal gas $$\left( {\gamma = 1.67,} \right.$$ molecular weight$$=40$$ $$\left. \, \right)$$ is compressed adiabatically from $$0.1$$ $$MPa,$$ $$300K$$ to $$0.2$$ $$...

A fin has $$5mm$$ diameter and $$100mm$$ length. The thermal conductivity of fin material is $$400W/m K.$$ One end of the fin is maintained at $${130^ \circ }C$$ and its remaining...

Tooth interference in an external involute spur gear pair can be reduced by

A smooth pipe of diameter $$200$$ $$mm$$ carries water. The pressure in the pipe at section $${S_1}\,\,$$ (elevation : $$10$$ $$m$$ ) is the $$50$$ $$kPa.$$ At section $${S_2}\,\,$...

A lightly loaded full journal bearing has a journal of $$50mm,$$ bush bore of $$50.50mm$$ and bush length of $$20mm.$$ if rotational speed of journal is $$1200rpm$$ and average vis...

The value of the integral $$\int\limits_{ - a}^a {{{dx} \over {1 + {x^2}}}} $$

One of the eigen vector of the matrix $$A = \left[ {\matrix{ 2 & 2 \cr 1 & 3 \cr } } \right]$$ is

Maximum velocity of a one-dimensional incompressible fully developed viscous flow, between two fixed parallel plates, is $$6\,\,m{s^{ - 1}}.$$ Then mean velocity (in $$m{s^{ - 1}}$...

A box contains $$2$$ washers, $$3$$ nuts and $$4$$ bolts. Items are drawn from the box at random one at a time without replacement. The probability of drawing $$2$$ washers first f...

Mobility of a statically indeterminate structure is

The state of plane-stress at a point is given by $${\sigma _x}\,\, = 200$$ MPa, $${\sigma _x}\,\, = 100$$ MPa and $${\tau _{xy}} = 100$$ MPa. The maximum shear stress (in MPa) is

Which of the following statements is INCORRECT

The natural frequency of a spring-mass system on earth is $${\omega _n}.$$ The natural frequency of this system on the moon (g moon = g earth /6) is

There are two points P and Q on a planar rigid body. The relative velocity between the two points