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

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

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

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

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

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

For a Newtonian fluid:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

An expendable pattern is used in

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

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

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

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

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

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

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

Ring gage is used to measure

$$NC$$ contouring is an example of

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

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

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

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

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

The number of inversions for a slider crank mechanism is

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

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

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

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

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

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

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

The differential equation governing the vibrating system is

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

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

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

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

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

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

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

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

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

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

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

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

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