GATE ME 1996
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GATE ME

In the Gauss - elimination for a solving system of linear algebraic equations, triangularization leads to
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The eigen values of $$\left[ {\matrix{ 1 & 1 & 1 \cr 1 & 1 & 1 \cr 1 & 1 & 1 \cr
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If a function is continuous at a point its first derivative
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The expression curl $$\left( {grad\,f} \right)$$ where $$f$$ is a scalar function is
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The particular solution for the differential equation $${{{d^2}y} \over {d{t^2}}} + 3{{dy} \over {dx}} + 2y = 5\cos x$$
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The one dimensional heat conduction partial difference equation $$\,\,{{\partial T} \over {\partial t}} = {{{\partial ^2
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$${i^i}$$, where $$i\, = \,\sqrt { - 1} $$ is given by
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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
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A wheel of mass m and radius r is in accelerated rolling motion without slip under a steady axial torque $$T$$. If the c
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AB and CD tow uniform and identical bars of mass 10kg each, as shown. The hinges at A and B are frictionless. The assemb
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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
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Match 4 correct pairs between List $$I$$ and List $$II$$. No credit will be given for partially correct matching List $
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A fluid is one which can be defined as a substance that:
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The dimension of surface tension is :
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A mercury manometer is used to measure the static pressure at a point in a water pipe as shown in Fig. The level differe
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For laminar flow through a long pipe, the pressure drop per unit length increases.
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For a given heat flow and for the same thickness, the temp drop across the material will be maximum for
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For a current carrying wire of $$20$$ $$mm$$ diameter and having $$k=0.5W/mK$$ is exposed to air $$\left( {h = 20W/{m^2}
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Match List - $${\rm I}$$ with List - $${\rm II}$$ and select the correct answer using the code given below the Lists: L
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In an assembly line for assembling toys, five workers are assigned tasks which take times of $$10, 8, 6, 9$$ and $$10$$
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If at the optimum in a linear programming problem, a dual variable corresponding to a particular primal constraint is ze
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A job shop incurs a cost of Rs.$$60$$/- per day for each day a job is in the shop. At the beginning of a month there are
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A solid shaft can resist a bending moment of $$3.0$$ $$kNm$$ and a twisting moment of $$4.0$$ $$kNm$$ together, then the
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If the ratio of the diameter of river hole to the pitch of rivets is $$0.25$$, then the tearing Efficiency of the joint
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The bolts in a rigid flanged coupling connecting two shafts transmitting power are subjected to
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In spur gears, the circle on which the involute is generated is called the
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In thick film hydrodynamic journal bearings, the coefficient of friction
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Light impurities in the molten metal are prevented from reaching the mold cavity by providing a
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The pouring basin in a sand mold is $$200$$ $$mm$$ diameter $$100$$ $$mm$$ height. The mould cavity is a cube of $$125$$
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A wire of $$0.1mm$$ diameter is drawn from a rod of $$15mm$$ diameter dies giving reductions of $$20\% $$, $$40\% $$ and
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Preheating before welding is done to
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The cross section weld bead is shown in fig the profile of the bead and the fusion zone are taken circular for convenien
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Tool life of a $$10$$ hours is obtained when cutting with a single point tool at $$63m/min.$$ If Taylor's constant $$C=
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The rake angle in drill
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The rake angle in drill
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A $$50$$ $$mm$$ diameter disc is to be punched out from a carbon steel sheet $$1.0$$ $$mm$$ thick. The diameter of the p
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The fit on a hole-shaft system is specified as $$H7$$-$$s6.$$ The type of fit is
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If the two principal strains at a point are 1000 $$ \times $$ 10-6 and -600 $$ \times $$ 10-6, then the maximum shear st
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Two bars AB and BC are connected by a frictionless hinge at B. The assembly is supported and loaded as shown in Fig. Dra
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A thin cylinder of $$100$$mm internal diameter and $$5$$mm thickness is subjected to an internal pressure of $$10$$ MPa
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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
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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
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A mass of $$1$$ kg is suspended by means of $$3$$ springs as shown in Figure. The spring constants $$\,{K_1},\,{K_2}\,\,
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A cylinder of mass 1 kg and radius 1 m is connected by two identical springs at a height of $$0.5m$$ above the center as
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When wet steam flows through a throttle valve and remains wet at exit
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The specific heats of an ideal gas depend on its
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Match List - $${\rm I}$$ with List - $${\rm II}$$ List - $${\rm I}$$ $$A.$$ Cetane number $$B.$$ Approach and range $$C
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For reversible adiabatic compression in a steady flow process, the work transfer per unit mass is
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A solar energy based heat engine which receives $$80$$ $$kJ$$ of heat at $${100^ \circ }C$$ and rejects $$70$$ $$kJ$$ of
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For two cycles coupled in series, the topping cycle has an efficiency of $$30\% $$ and the bottoming cycle has an effici
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An iron cube at a temperature of $$400$$ deg $$C$$ is dropped into an insulated bath containing $$10$$ $$kg$$ water at $
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A steam plant has the boiler efficiency of $$92\% $$, turbine efficiency (mechanical) of $$94\% $$, generator efficiency
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In a hydroelectric station, water is available at the rate of $$175{m^3}/s$$ under a head of $$18m.$$ The turbines run a
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