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 $$\left[ {\matrix{ 1 &amp; 1 &amp; 1 \cr 1 &amp; 1 &amp; 1 \cr 1 &amp; 1 &amp; 1 \cr View Question If a function is continuous at a point its first derivative View Question The expression curl$$\left( {grad\,f} \right)$$where$$f$$is a scalar function is View Question The particular solution for the differential equation$${{{d^2}y} \over {d{t^2}}} + 3{{dy} \over {dx}} + 2y = 5\cos x$$View Question The one dimensional heat conduction partial difference equation$$\,\,{{\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 $View Question A fluid is one which can be defined as a substance that: View Question The dimension of surface tension is : View Question A mercury manometer is used to measure the static pressure at a point in a water pipe as shown in Fig. The level differe View Question For laminar flow through a long pipe, the pressure drop per unit length increases. View Question For a given heat flow and for the same thickness, the temp drop across the material will be maximum for View Question For a current carrying wire of $$20$$ $$mm$$ diameter and having $$k=0.5W/mK$$ is exposed to air $$\left( {h = 20W/{m^2} View Question Match List -$${\rm I}$$with List -$${\rm II}$$and select the correct answer using the code given below the Lists: L View Question In an assembly line for assembling toys, five workers are assigned tasks which take times of$$10, 8, 6, 9$$and$$10$$View Question If at the optimum in a linear programming problem, a dual variable corresponding to a particular primal constraint is ze View Question A job shop incurs a cost of Rs.$$60$$/- per day for each day a job is in the shop. At the beginning of a month there are View Question A solid shaft can resist a bending moment of$$3.0kNm$$and a twisting moment of$$4.0kNm$$together, then the View Question If the ratio of the diameter of river hole to the pitch of rivets is$$0.25$$, then the tearing Efficiency of the joint View Question The bolts in a rigid flanged coupling connecting two shafts transmitting power are subjected to View Question In spur gears, the circle on which the involute is generated is called the View Question In thick film hydrodynamic journal bearings, the coefficient of friction View Question Light impurities in the molten metal are prevented from reaching the mold cavity by providing a View Question The pouring basin in a sand mold is$$200mm$$diameter$$100mm$$height. The mould cavity is a cube of$$125$$View Question A wire of$$0.1mm$$diameter is drawn from a rod of$$15mm$$diameter dies giving reductions of$$20\% $$,$$40\% $$and View Question Preheating before welding is done to View Question The cross section weld bead is shown in fig the profile of the bead and the fusion zone are taken circular for convenien View Question Tool life of a$$10$$hours is obtained when cutting with a single point tool at$$63m/min.$$If Taylor's constant$$C= View Question The rake angle in drill View Question The rake angle in drill View Question A $$50$$ $$mm$$ diameter disc is to be punched out from a carbon steel sheet $$1.0$$ $$mm$$ thick. The diameter of the p View Question The fit on a hole-shaft system is specified as $$H7$$-$$s6.$$ The type of fit is View Question If the two principal strains at a point are 1000 $$\times$$ 10-6 and -600 $$\times$$ 10-6, then the maximum shear st View Question Two bars AB and BC are connected by a frictionless hinge at B. The assembly is supported and loaded as shown in Fig. Dra View Question A thin cylinder of $$100$$mm internal diameter and $$5$$mm thickness is subjected to an internal pressure of $$10$$ MPa View Question 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 View Question 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 View Question A mass of $$1$$ kg is suspended by means of $$3$$ springs as shown in Figure. The spring constants $$\,{K_1},\,{K_2}\,\, View Question A cylinder of mass 1 kg and radius 1 m is connected by two identical springs at a height of$$0.5m$$above the center as View Question When wet steam flows through a throttle valve and remains wet at exit View Question The specific heats of an ideal gas depend on its View Question Match List -$${\rm I}$$with List -$${\rm II}$$List -$${\rm I}A.$$Cetane number$$B.$$Approach and range$$C View Question For reversible adiabatic compression in a steady flow process, the work transfer per unit mass is View Question A solar energy based heat engine which receives $$80$$ $$kJ$$ of heat at $${100^ \circ }C$$ and rejects $$70$$ $$kJ$$ of View Question For two cycles coupled in series, the topping cycle has an efficiency of $$30\%$$ and the bottoming cycle has an effici View Question 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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