The particular solution for the differential equation $${{{d^2}y} \over {d{t^2}}} + 3{{dy} \over {dx}} + 2y = 5\cos x$$

The eigen values of $$\left[ {\matrix{ 1 & 1 & 1 \cr 1 & 1 & 1 \cr 1 & 1 & 1 \cr

In the Gauss - elimination for a solving system of linear algebraic equations, triangularization leads to

If a function is continuous at a point its first derivative

The expression curl $$\left( {grad\,f} \right)$$ where $$f$$ is a scalar function is

The one dimensional heat conduction partial difference equation $$\,\,{{\partial T} \over {\partial t}} = {{{\partial ^2

$${i^i}$$, where $$i\, = \,\sqrt { - 1} $$ is given by

A wheel of mass m and radius r is in accelerated rolling motion without slip under a steady axial torque $$T$$. If the c

AB and CD tow uniform and identical bars of mass 10kg each, as shown. The hinges at A and B are frictionless. The assemb

Match 4 correct pairs between List $$I$$ and List $$II$$. No credit will be given for partially correct matching List $

A rod of length 1m is sliding in a corner as shown in. At an instant when the rod makes an angle of 60 degrees with the

A ball A of mass m falls under gravity from a height h and strikes another ball B of mass m which supported at rest on a

For laminar flow through a long pipe, the pressure drop per unit length increases.

A fluid is one which can be defined as a substance that:

The dimension of surface tension is :

A mercury manometer is used to measure the static pressure at a point in a water pipe as shown in Fig. The level differe

For a given heat flow and for the same thickness, the temp drop across the material will be maximum for

For a current carrying wire of $$20$$ $$mm$$ diameter and having $$k=0.5W/mK$$ is exposed to air $$\left( {h = 20W/{m^2}

Match List - $${\rm I}$$ with List - $${\rm II}$$ and select the correct answer using the code given below the Lists: L

In an assembly line for assembling toys, five workers are assigned tasks which take times of $$10, 8, 6, 9$$ and $$10$$

If at the optimum in a linear programming problem, a dual variable corresponding to a particular primal constraint is ze

A job shop incurs a cost of Rs.$$60$$/- per day for each day a job is in the shop. At the beginning of a month there are

A solid shaft can resist a bending moment of $$3.0$$ $$kNm$$ and a twisting moment of $$4.0$$ $$kNm$$ together, then the

If the ratio of the diameter of river hole to the pitch of rivets is $$0.25$$, then the tearing Efficiency of the joint

The bolts in a rigid flanged coupling connecting two shafts transmitting power are subjected to

In spur gears, the circle on which the involute is generated is called the

In thick film hydrodynamic journal bearings, the coefficient of friction

The pouring basin in a sand mold is $$200$$ $$mm$$ diameter $$100$$ $$mm$$ height. The mould cavity is a cube of $$125$$

Light impurities in the molten metal are prevented from reaching the mold cavity by providing a

A wire of $$0.1mm$$ diameter is drawn from a rod of $$15mm$$ diameter dies giving reductions of $$20\% $$, $$40\% $$ and

Preheating before welding is done to

The cross section weld bead is shown in fig the profile of the bead and the fusion zone are taken circular for convenien

Tool life of a $$10$$ hours is obtained when cutting with a single point tool at $$63m/min.$$ If Taylor's constant $$C=

The rake angle in drill

The rake angle in drill

A $$50$$ $$mm$$ diameter disc is to be punched out from a carbon steel sheet $$1.0$$ $$mm$$ thick. The diameter of the p

The fit on a hole-shaft system is specified as $$H7$$-$$s6.$$ The type of fit is

If the two principal strains at a point are 1000 $$ \times $$ 10-6 and -600 $$ \times $$ 10-6, then the maximum shear st

Two bars AB and BC are connected by a frictionless hinge at B. The assembly is supported and loaded as shown in Fig. Dra

A thin cylinder of $$100$$mm internal diameter and $$5$$mm thickness is subjected to an internal pressure of $$10$$ MPa

A rod of length $$1$$ $$m$$ is sliding in a corner as shown in Fig.$$2.7.$$ At an instant when the rod makes an angle of

Below Fig show a planetary gear train. Gears 2, 4 and 5 have 24, 40 and 144 teeth respectively. Gear 5 is fixed. Gear 2

A mass of $$1$$ kg is suspended by means of $$3$$ springs as shown in Figure. The spring constants $$\,{K_1},\,{K_2}\,\,

A cylinder of mass 1 kg and radius 1 m is connected by two identical springs at a height of $$0.5m$$ above the center as

When wet steam flows through a throttle valve and remains wet at exit

The specific heats of an ideal gas depend on its

Match List - $${\rm I}$$ with List - $${\rm II}$$ List - $${\rm I}$$ $$A.$$ Cetane number $$B.$$ Approach and range $$C

For reversible adiabatic compression in a steady flow process, the work transfer per unit mass is

A solar energy based heat engine which receives $$80$$ $$kJ$$ of heat at $${100^ \circ }C$$ and rejects $$70$$ $$kJ$$ of

For two cycles coupled in series, the topping cycle has an efficiency of $$30\% $$ and the bottoming cycle has an effici

An iron cube at a temperature of $$400$$ deg $$C$$ is dropped into an insulated bath containing $$10$$ $$kg$$ water at $

A steam plant has the boiler efficiency of $$92\% $$, turbine efficiency (mechanical) of $$94\% $$, generator efficiency

In a hydroelectric station, water is available at the rate of $$175{m^3}/s$$ under a head of $$18m.$$ The turbines run a