GATE ME 2006

## GATE ME

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

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

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

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

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

View Question For a Newtonian fluid:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

View Question An expendable pattern is used in

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

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

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

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

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

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

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

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

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

View Question Ring gage is used to measure

View Question $$NC$$ contouring is an example of

View Question 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

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

View Question 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

View Question 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

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

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

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

View Question The number of inversions for a slider crank mechanism is

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

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

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

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

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

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

View Question The differential equation governing the vibrating system is

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

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

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

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

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

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

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

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

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

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

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

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

View Question 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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