GATE ME 2006

## GATE ME

Eigen values of a matrix $$S = \left[ {\matrix{
3 & 2 \cr
2 & 3 \cr
} } \right]$$ are $$5$$ and $$1.

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Multiplication of matrices $$E$$ and $$F$$ is $$G.$$ Matrices $$E$$ and $$G$$ are
$$E = \left[ {\matrix{
{\cos \thet

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For $$\,\,\,{{{d^2}y} \over {d{x^2}}} + 4{{dy} \over {dx}} + 3y = 3{e^{2x}},\,\,$$ the particular integral is

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The solution of the differential equation $${{dy} \over {dx}} + 2xy = {e^{ - {x^2}}}\,\,$$ with $$y(0)=1$$ is

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If point A is in equilibrium under the action of the applied forces, the values of tensions and T AB and TAC are respec

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For a Newtonian fluid:

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In a two-dimensional velocity field with velocities $$u$$ and $$v$$ along $$x$$ and $$y$$ directions respectively, the c

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A two-dimensional flow field has velocities along the $$x$$ and $$y$$ directions given by $$u = {x^2}t$$ and $$v = - 2x

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The velocity profile in fully developed laminar flow in a pipe of diameter $$D$$ is given by $$u = {u_0}\left( {1 - 4{r^

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A siphon draws water from a reservoir and discharges it out at atmospheric pressure. Assuming ideal fluid and the reserv

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A smooth flat plate with a sharp leading edge is placed along a gas stream flowing at $$U = 10\,m/s.$$ The thickness of

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A smooth flat plate with a sharp leading edge is placed along a gas stream flowing at $$U = 10\,m/s.$$ The thickness of

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In a composite slab, the temperature at the interface (Tinter) between two materials is equal to the average of the temp

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With an increase in the thickness of insulation around a circular pipe, heat loss to surroundings due to

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A $$100$$ $$W$$ electric bulb was switched on in a $$2.5 \times 3 \times 3m$$ size thermally insulated room having tempe

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Consider the following data for an item.
Annual demand: $$2500$$ units per year Ordering cost: Rs.100 per order Invento

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A stockist wishes to optimize the number of perishable items he needs to stock in any month in his store. The demand dis

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Consider a $$PERT$$ network for a project involving six tasks ($$a$$ to $$f$$)
The expected completion time of the pro

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Consider a $$PERT$$ network for a project involving six tasks ($$a$$ to $$f$$)
The standard deviation of the critical

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The table gives details of an assembly line.
What is the line efficiency of the assembly line?

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The number of customers arriving at a railway reservation counter is Poisson distributed with an arrival rate of eight c

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A firm is required to procure three items $$(P, Q$$ and $$R).$$ The prices quoted for these items (in Rs.) by suppliers

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A cylindrical shafts is subjected to an alternating stress of $$100MPa.$$ Fatigue strength to sustain $$1000$$ cycles is

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A $$60mm$$ long and $$6mm$$ thick fillet weld carries a steady load of $$15kN$$ along the weld. The shear strength of t

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Twenty degree full depth involute profiled $$19$$-tooth pinion and $$37$$-tooth gear are in mesh. If the module is $$5mm

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A disk clutch is required to transmit $$5$$ $$kW$$ at $$2000$$ $$rpm$$ the disk has a friction lining with Coefficient o

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An expendable pattern is used in

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In a sand casting operation, the total liquid head is maintained constant such that it is equal to the mould height. The

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A $$4$$ $$mm$$ thick sheet is rolled with $$300$$ $$mm$$ diameter rolls to reduce thickness without any change in its wi

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In a wire drawing operation, diameter of a steel wire is reduced from $$10$$ $$mm$$ to $$8$$ $$mm.$$ the mean flow stres

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In arc welding process, the voltage and current are $$25V$$ and $$300A$$ respectively. The arc heat transfer efficiency

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In an orthogonal machining operation:
$$\,\,\,\,\,\,\,\,\,\,$$Uncut thickness $$\,\,\,\,\,$$ $$= 0.5$$ $$mm$$
$$\,\,\,\

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In an orthogonal machining operation:
$$\,\,\,\,\,\,\,\,\,\,$$Uncut thickness $$\,\,\,\,\,$$ $$= 0.5$$ $$mm$$
$$\,\,\,\

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In an orthogonal machining operation:
$$\,\,\,\,\,\,\,\,\,\,$$Uncut thickness $$\,\,\,\,\,$$ $$= 0.5$$ $$mm$$
$$\,\,\,\

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If each abrasive grain is viewed as a cutting tool, then which of the following represents the cutting parameters in com

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Match the items in column $${\rm I}$$ and $${\rm I}$$ $${\rm I}$$

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Ring gage is used to measure

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$$NC$$ contouring is an example of

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A bar having a cross-sectional area of 700 mm2 is subjected to axial loads at the positions indicated. The value of stre

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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

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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 v

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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

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For a circular shaft of diameter $$'d'$$ subjected to torque $$T,$$ the maximum value of the shear stress is

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A pin-ended column of length $$L,$$ modulus of elasticity $$E$$ and second moment of the cross-sectional area $$I$$ is l

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For a four bar linkage in Toggle position, the value of mechanical advantage is

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The number of inversions for a slider crank mechanism is

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Match the items in column $$I$$ and $$II$$
List $$I$$
$$P.$$ Higher kinematic pair
$$Q.$$ Lower kinematic pair
$$R.$$ Qu

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In a four-bar linkage, $$S$$ denotes the shortest link length, $$L$$ is the longest link length, $$P$$ and $$Q$$ are the

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Match the items in columns $$I$$ and $$II$$
Column $$I$$
$$P.$$ Addendum
$$Q.$$ Instantaneous center of velocity
$$R.$$

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A planetary gear train has four gears and one carrier. Angular velocities of the gears are $${\omega _1},{\omega _2},{\o

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A planetary gear train has four gears and one carrier. Angular velocities of the gears are $${\omega _1},{\omega _2},{\o

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If $${C_f}$$ is the coefficient of speed fluctuation of a flywheel then the ratio of $${\omega _{\max }}/{\omega _{\min

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The differential equation governing the vibrating system is

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A machine of $$250$$ kg mass is supported on springs of total stiffness $$100$$ kN/m. Machine has an unbalanced rotating

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A vibratory system consists of a mass $$12.5$$ kg, a spring of stiffness $$1000$$ $$N/m,$$ and a dashpot with damping co

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A vibratory system consists of a mass $$12.5$$ kg, a spring of stiffness $$1000$$ $$N/m,$$ and a dashpot with damping co

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Given below is an extract from steam tables.
Specific enthalpy of water in $$kJ/kg$$ at $$150$$ bar and $$ {45^ \circ

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Match items from groups, $${\rm I},$$ $${\rm II},$$ $${\rm III},$$ $${\rm IV}$$ and $$V$$

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A football was inflated to a gauge pressure of $$1$$ bar when the ambient temperature was $${15^ \circ }C$$. When the ga

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A football was inflated to a gauge pressure of $$1$$ bar when the ambient temperature was $${15^ \circ }C$$. When the ga

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A $$100$$ $$W$$ electric bulb was switched on in a $$2.5\,m \times 3m \times 3m$$ size thermally insulated room having

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Determine the correctness or otherwise of the following Assertion $$(a)$$ and the Reason$$(r).$$
Assertion(A): In a pow

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Assertion (A): Condenser is an essential equipment in a steam power plant.
Reason(R): For the same mass flow rate and t

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In a Pelton wheel, the bucket peripheral speed is $$10$$ $$m/s,$$ the water jet velocity is $$25$$ $$m/s$$ and volumetri

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A large hydraulic turbine is to generate $$300$$ $$kW$$ at $$1000$$ $$rpm$$ under a head of $$40$$ $$m$$. for initial te

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A horizontal shaft centrifugal pump lifts ware at 65°C. The suction nozzle is one meter below pump centerline. The press

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