GATE 1996 Mechanical Engineering

In an assembly line for assembling toys, five workers are assigned tasks which take times of $$10, 8, 6, 9$$ and $$10$$ minutes respectively. The balance delay for the line is

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

If a function is continuous at a point its first derivative

For a current carrying wire of $$20$$ $$mm$$ diameter and having $$k=0.5W/mK$$ is exposed to air $$\left( {h = 20W/{m^2}K} \right),$$ maximum heat dissiption occurs when thickness...

In thick film hydrodynamic journal bearings, the coefficient of friction

Preheating before welding is done to

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

The eigen values of $$\left[ {\matrix{ 1 & 1 & 1 \cr 1 & 1 & 1 \cr 1 & 1 & 1 \cr } } \right]$$ are

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

In a hydroelectric station, water is available at the rate of $$175{m^3}/s$$ under a head of $$18m.$$ The turbines run at a speed of $$150$$ $$rpm$$ with overall efficiency of $$82...

A wheel of mass m and radius r is in accelerated rolling motion without slip under a steady axial torque $$T$$. If the coefficient of kinetic friction is $$\mu $$, the friction for...

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

A wire of $$0.1mm$$ diameter is drawn from a rod of $$15mm$$ diameter dies giving reductions of $$20\% $$, $$40\% $$ and $$80\% $$ are available. For minimum error in the final siz...

A $$50$$ $$mm$$ diameter disc is to be punched out from a carbon steel sheet $$1.0$$ $$mm$$ thick. The diameter of the punch should be (Take clearance as $$3\% $$ of sheet thicknes...

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

Tool life of a $$10$$ hours is obtained when cutting with a single point tool at $$63m/min.$$ If Taylor's constant $$C=257.35,$$ tool life on doubling the velocity will be

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

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

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

The pouring basin in a sand mold is $$200$$ $$mm$$ diameter $$100$$ $$mm$$ height. The mould cavity is a cube of $$125$$ $$mm$$ side and must be filled in $$25$$ seconds. The maxim...

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 spring of stiffness k. Assume perfectly elastic impact. Imm...

The rake angle in drill

The rake angle in drill

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

An iron cube at a temperature of $$400$$ deg $$C$$ is dropped into an insulated bath containing $$10$$ $$kg$$ water at $${25^ \circ }C.$$ The water finally reaches a temperature of...

A solar energy based heat engine which receives $$80$$ $$kJ$$ of heat at $${100^ \circ }C$$ and rejects $$70$$ $$kJ$$ of heat to the ambient at $${30^ \circ }C$$ is to be designed....

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

Match List - $${\rm I}$$ with List - $${\rm II}$$ List - $${\rm I}$$ $$A.$$ Cetane number $$B.$$ Approach and range $$C.$$ $${\left( {{{\delta T} \over {\delta P}}} \right)_h} \ne...

The specific heats of an ideal gas depend on its

For two cycles coupled in series, the topping cycle has an efficiency of $$30\% $$ and the bottoming cycle has an efficiency of $$20\% $$. The overall combined cycle efficiency is

A steam plant has the boiler efficiency of $$92\% $$, turbine efficiency (mechanical) of $$94\% $$, generator efficiency of $$92\% $$ and cycle efficiency of $$44\% $$. If $$6\% $$...

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

The dimension of surface tension is :

A thin cylinder of $$100$$mm internal diameter and $$5$$mm thickness is subjected to an internal pressure of $$10$$ MPa and a torque of $$2000$$ Nm. Calculate the magnitudes of the...

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

Match List - $${\rm I}$$ with List - $${\rm II}$$ and select the correct answer using the code given below the Lists: List - $${\rm I}$$ $$A.$$ Grashof number $$B.$$ Schmid number...

If at the optimum in a linear programming problem, a dual variable corresponding to a particular primal constraint is zero, then it means that

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

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

A solid shaft can resist a bending moment of $$3.0$$ $$kNm$$ and a twisting moment of $$4.0$$ $$kNm$$ together, then the maximum torque that can be applied is

Match 4 correct pairs between List $$I$$ and List $$II$$ . No credit will be given for partially correct matching List $$I$$ (a) Collision of particles (b) Stability (C) Satellite...

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

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