GATE 2006 Mechanical Engineering
46 questions across 1 session
A $$4$$ $$mm$$ thick sheet is rolled with $$300$$ $$mm$$ diameter rolls to reduce thickness without any change in its width. The friction coefficient at the work-roll interface is...
In a wire drawing operation, diameter of a steel wire is reduced from $$10$$ $$mm$$ to $$8$$ $$mm.$$ the mean flow stress of the material is $$400$$ $$MPa.$$ The ideal force requir...
$$NC$$ contouring is an example of
A $$100$$ $$W$$ electric bulb was switched on in a $$2.5 \times 3 \times 3m$$ size thermally insulated room having temperature of $${20^0}C.$$ Room temp at the end of $$24$$ hours...
Multiplication of matrices $$E$$ and $$F$$ is $$G.$$ Matrices $$E$$ and $$G$$ are $$E = \left[ {\matrix{ {\cos \theta } & { - sin\theta } & 0 \cr {sin\theta } & {\cos \theta } & 0...
In a two-dimensional velocity field with velocities $$u$$ and $$v$$ along $$x$$ and $$y$$ directions respectively, the convective acceleration along the $$x$$-direction is given by
A $$60mm$$ long and $$6mm$$ thick fillet weld carries a steady load of $$15kN$$ along the weld. The shear strength of the weld material is equal to $$200MPa.$$ The factor of safety...
In an orthogonal machining operation: $$\,\,\,\,\,\,\,\,\,\,$$Uncut thickness $$\,\,\,\,\,$$ $$= 0.5$$ $$mm$$ $$\,\,\,\,\,\,\,\,\,\,$$Cutting speed $$\,\,\,\,\,\,\,\,\,\,$$ $$= 20$...
For a Newtonian fluid:
With an increase in the thickness of insulation around a circular pipe, heat loss to surroundings due to
For $$\,\,\,{{{d^2}y} \over {d{x^2}}} + 4{{dy} \over {dx}} + 3y = 3{e^{2x}},\,\,$$ the particular integral is
An expendable pattern is used in
If each abrasive grain is viewed as a cutting tool, then which of the following represents the cutting parameters in common grinding operations?
The number of customers arriving at a railway reservation counter is Poisson distributed with an arrival rate of eight customers per hour. The reservation clerk at this counter tak...
Twenty degree full depth involute profiled $$19$$-tooth pinion and $$37$$-tooth gear are in mesh. If the module is $$5mm,$$ the center distance between the gear pair will be
Ring gage is used to measure
A disk clutch is required to transmit $$5$$ $$kW$$ at $$2000$$ $$rpm$$ the disk has a friction lining with Coefficient of friction equal to $$0.25.$$ Bore radius of friction lining...
A two-dimensional flow field has velocities along the $$x$$ and $$y$$ directions given by $$u = {x^2}t$$ and $$v = - 2xyt$$ respectively, where $$t$$ is time. The equation of strea...
A $$100$$ $$W$$ electric bulb was switched on in a $$2.5\,m \times 3m \times 3m$$ size thermally insulated room having a temperature of $${20^ \circ }C$$. The room temperature at t...
A football was inflated to a gauge pressure of $$1$$ bar when the ambient temperature was $${15^ \circ }C$$. When the game started next day, the air temperature at the stadium was...
Assertion (A): Condenser is an essential equipment in a steam power plant. Reason(R): For the same mass flow rate and the same pressure rise, a water pump requires substantially le...
In a Pelton wheel, the bucket peripheral speed is $$10$$ $$m/s,$$ the water jet velocity is $$25$$ $$m/s$$ and volumetric flow rate of the jet is $$0.1{m^3}/s.$$ If the jet deflect...
A football was inflated to a gauge pressure of $$1$$ bar when the ambient temperature was $${15^ \circ }C$$. When the game started next day, the air temperature at the stadium was...
In an orthogonal machining operation: $$\,\,\,\,\,\,\,\,\,\,$$Uncut thickness $$\,\,\,\,\,$$ $$= 0.5$$ $$mm$$ $$\,\,\,\,\,\,\,\,\,\,$$Cutting speed $$\,\,\,\,\,\,\,\,\,\,$$ $$= 20$...
In arc welding process, the voltage and current are $$25V$$ and $$300A$$ respectively. The arc heat transfer efficiency is $$0.85$$ and welding speed is $$8$$ $$mm/sec$$. The net h...
The velocity profile in fully developed laminar flow in a pipe of diameter $$D$$ is given by $$u = {u_0}\left( {1 - 4{r^2}/{D^2}} \right),$$ where $$r$$ is the radial distance from...
In an orthogonal machining operation: $$\,\,\,\,\,\,\,\,\,\,$$Uncut thickness $$\,\,\,\,\,$$ $$= 0.5$$ $$mm$$ $$\,\,\,\,\,\,\,\,\,\,$$Cutting speed $$\,\,\,\,\,\,\,\,\,\,$$ $$= 20$...
The solution of the differential equation $${{dy} \over {dx}} + 2xy = {e^{ - {x^2}}}\,\,$$ with $$y(0)=1$$ is
A large hydraulic turbine is to generate $$300$$ $$kW$$ at $$1000$$ $$rpm$$ under a head of $$40$$ $$m$$. for initial testing, a $$1:4$$ scale model of the turbine operates under a...
Eigen values of a matrix $$S = \left[ {\matrix{ 3 & 2 \cr 2 & 3 \cr } } \right]$$ are $$5$$ and $$1.$$ What are the eigen values of the matrix $${S^2} = SS?$$
A cylindrical shafts is subjected to an alternating stress of $$100MPa.$$ Fatigue strength to sustain $$1000$$ cycles is $$490MPa.$$ If the corrected endurance strength is $$70MPa,...
In a sand casting operation, the total liquid head is maintained constant such that it is equal to the mould height. The time taken to fill the mould with a top gate is $${t_A}.$$...
A steel bar of 40 mm × 40 mm square cross-section is subjected to an axial compressive load of 200 kN. If the length of the bar is 2m and E = 200 GPa. The decrement in length of th...
A pin-ended column of length $$L,$$ modulus of elasticity $$E$$ and second moment of the cross-sectional area $$I$$ is loaded centrally by a compressive load $$P.$$ The critical bu...
Match the items in columns $$I$$ and $$II$$ Column $$I$$ $$P.$$ Addendum $$Q.$$ Instantaneous center of velocity $$R.$$ Section modulus $$S.$$ Prince circle Column $$II$$ $$1.$$ Ca...
The number of inversions for a slider crank mechanism is
A simply supported beam of span length $$6$$m and $$75$$ mm diameter carries a udl of $$1.5$$ kN/m What is the maximum value of bending moment?
In a four-bar linkage, $$S$$ denotes the shortest link length, $$L$$ is the longest link length, $$P$$ and $$Q$$ are the lengths of other two links. At least one of the three movin...
For a circular shaft of diameter $$'d'$$ subjected to torque $$T,$$ the maximum value of the shear stress is
A simply supported beam of span length $$6$$m and $$75$$ mm diameter carries a udl of $$1.5$$ kN/m What is the maximum value of bending stress?
If $${C_f}$$ is the coefficient of speed fluctuation of a flywheel then the ratio of $${\omega _{\max }}/{\omega _{\min }}$$ will be
For a four bar linkage in Toggle position, the value of mechanical advantage is
A vibratory system consists of a mass $$12.5$$ kg, a spring of stiffness $$1000$$ $$N/m,$$ and a dashpot with damping coefficient of $$15$$ $$Ns/m.$$ The value of logarithmic decre...
A machine of $$250$$ kg mass is supported on springs of total stiffness $$100$$ kN/m. Machine has an unbalanced rotating force of $$350$$ N at speed of $$3600$$ rpm. Assuming a dam...
A vibratory system consists of a mass $$12.5$$ kg, a spring of stiffness $$1000$$ $$N/m,$$ and a dashpot with damping coefficient of $$15$$ $$Ns/m.$$ The value of critical damping...
Determine the correctness or otherwise of the following Assertion $$(a)$$ and the Reason$$(r).$$ Assertion(A): In a power plant working on a Rankine cycle, the regenerative feed wa...