GATE ME 2005
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## GATE ME

$$A$$ is a $$3 \times 4$$ matrix and $$AX=B$$ is an inconsistent system of equations. The highest possible rank of $$A$$
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Which one of the following is an eigen vector of the matrix $$\left[ {\matrix{ 5 &amp; 0 &amp; 0 &amp; 0 \cr 0 & View Question$$\int\limits_{ - a}^a {\left[ {{{\sin }^6}\,x + {{\sin }^7}\,x} \right]dx} $$is equal to View Question By a change of variables$$x(u, v) = uv,\,\,y\left( {u,v} \right) = {v \over u}$$in a double integral, the integr View Question Changing the order of integration in the double integral$${\rm I} = \int\limits_0^8 {\int\limits_{{\raise0.5ex\hbox{$\ View Question Stokes theorem connects View Question A lot had $$10$$% defective items. Ten items are chosen randomly from this lot. The probability that exactly $$2$$ of th View Question A single die is thrown two times. What is the probability that the sum is neither $$8$$ nor $$9?$$ View Question Using given data points tabulated below, a straight line passing through the origin is fitted using least squares method View Question If $${x^2}\left( {{{d\,y} \over {d\,x}}} \right) + 2xy = {{2\ln x} \over x}$$ and $$y(1)=0$$ then what is $$y(e)$$? View Question The complete solution of the ordinary differential equation $${{{d^2}y} \over {d\,{x^2}}} + p{{dy} \over {dx}} + qy = 0 View Question Which of the following is a solution of the differential equation$$\,{{{d^2}y} \over {d{x^2}}} + p{{dy} \over {dx}} + \ View Question Starting from $$\,{x_0} = 1,\,\,$$ one step of Newton - Raphson method in solving the equation $${x^3} + 3x - 7 = 0$$ gi View Question A simple pendulum of length 5m, with a bob of mass 1 kg, is in simple harmonic motion. As it passes through its mean pos View Question The time variation of the position of a particle in rectilinear motion is given by $$x = 2{t^3} + {t^2} + 2t$$. If 'V' i View Question A shell is fired from a cannon. At the instant the shell is just about to leave the barrel, its velocity relative to the View Question An elevator (lift) consists of the elevator cage and a counter weight, of mass m each. The cage and the counterweight ar View Question Two books of mass 1 kg each are kept on a table, one over the other. The coefficient of friction on every pair of contac View Question A 1 kg mass of clay, moving with a velocity of 10 m/s, strikes a stationary wheel and sticks to it. The solid wheel has View Question The velocity components in the $$x$$ and $$y$$ directions of a two dimensional potential flow are $$u$$ and $$v$$, respe View Question A leaf is caught in a whirlpool. At a given instant, the leaf is at a distance of $$120$$ $$m$$ from the centre of the w View Question A venturimeter of $$20$$ $$mm$$ throat diameter is used to measure the velocity of water in a horizontal pipe of $$40$$ View Question A $$U$$-tube manometer with a small quantity of mercury is used to measure the static pressure difference between two lo View Question In case of one dimensional heat conduction in a medium with constant properties, $$T$$ is the temperature at position $$View Question Heat flows through a composite slab, as shown below. The depth of the slab is$$1m.$$the$$k$$values are in$$W/m View Question A small copper ball of $$5$$ $$mm$$ diameter at $$500$$ $$K$$ is dropped into an oil bath whose temperature is $$300$$$
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An un-insulated air conditioning duct of rectangular cross section $$1\,\,m \times 0.5\,m,$$ carrying air at $${20^ \cir View Question An un-insulated air conditioning duct of rectangular cross section$$1\,\,m \times 0.5\,m,$$carrying air at$${20^ \cir
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The following figure was generated from experimental data relating spectral black body emissive power to wave length at
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A solid cylinder (surface $$2$$) is located at the center of a hollow sphere (surface $$1$$). The diameter of the sphere
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Hot oil is cooled from $${80^ \circ }C$$ to $${50^ \circ }C$$ in an oil cooler which uses air as the coolant. The air te
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The distribution of lead-time demand fro an item is as follows: The reorder level is $$1.25$$ times the expected valu
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A project has six activities $$(A$$ to $$F)$$ with respective activity durations $$7,5,6,6,8,4$$ days. The network has t
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The sales of a product during the last four years were $$860, 880, 870$$ and $$890$$ units. The forecast for the fourth
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Consider a single server queuing model with Poisson arrivals $$\left( {\lambda = 4/hour} \right)$$ and exponential serv
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Consider a linear programming problem with two variables and two constraints. The objective function is: Maximize $${x_1 View Question Consider a linear programming problem with two variables and two constraints. The objective function is: Maximize$${x_1
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A company has two factories $${S_1},$$ $${S_2}$$ and two warehouses $${D_1},$$ $${D_2}$$ . the supplies from $${S_1}$$ a
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Which one of the following is criterion in the design of hydrodynamic journal bearings?
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A band brake consists of a lever attached to one end of the band. The other end of the band is fixed to the ground. The
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A band brake consists of a lever attached to one end of the band. The other end of the band is fixed to the ground. The
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A mould has a downsprue whose length is $$20$$ $$cm$$ and the cross sectional area at the base of the down sprue is $$1\ View Question Match List -$${\rm I}$$(products) with List -$${\rm II}$$(casting process) and select the correct answer using the c View Question The strength of a brazed joint View Question Spot welding of two$$1mm$$thick sheets of steel (density$$ = 8000kg/{m^3}$$) is carried out successfully by pas View Question The figure below shows a graph, which qualitatively relates cutting speed and cost per piece produced. The three curve View Question Two tools$$P$$and$$Q$$have signature$${5^ \circ } - {5^ \circ } - {6^ \circ } - {6^ \circ } - {8^ \circ } - {30^ \c
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A $$600$$ $$mm$$ $$\times \,\,30\,\,mm$$ flat surface of a plate is to be finish machined on a shaper. The plate has b
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A $$2$$ $$mm$$ thick metal sheet is to be bent at an angle of one radian with a bend radius of $$100$$ $$mm.$$ If the st
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In order to have interference fit, it is essential that the lower limit of the shaft should be
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Which among the $$NC$$ operations given below are continuous path operations? Arc Welding $$(A$$ $$W)$$, Milling $$(M), View Question The tool of an$$NC$$machine has to move along a circular arc from$$(5,5)$$to$$(10,10)$$while performing an operati View Question A cantilever beam carries the anti-symmetric load shown, where wo is the peak intensity of the distributed load. Qualita View Question A beam is made up of two identical bars AB and BC, by hinging them together at B. The end A is built-in (cantilevered) a View Question A mass less beam has a loading pattern as shown in figure. The beam is rectangular cross-section with a width of 30 mm a View Question A weighing machine consists of a 2 kg pan resting on a spring in this condition, with the pan resting on the spring, the View Question A cantilever beam has the square cross section of 10 mm$$ \times $$10 mm. It carries a transverse load of 10 N. Consid View Question A mass less beam has a loading pattern as shown in figure. The beam is rectangular cross-section with a width of 30 mm a View Question The two shafts$$AB$$and$$BC$$, of equal length and diameters$$d$$and$$2d$$, are made of the same material. They ar View Question Two identical cantilever beams are supported as shown, with their free ends in contact through a rigid roller. After the View Question The number of degrees of freedom of a planar linkage with 8 links and 9 simple revolute joints is View Question An instantaneous configuration of a four-bar mechanism, whose plane is horizontal, is shown in the figure below. At this View Question An instantaneous configuration of a four-bar mechanism, whose plane is horizontal, is shown in the figure below. At this View Question An instantaneous configuration of a four-bar mechanism, whose plane is horizontal, is shown in the figure below. At this View Question There are four samples P, Q, R and S, with natural frequencies 64, 96, 128 and 256 Hz, respectively. There are mounted o View Question In a spring-mass system, the mass is 0.1 kg and the stiffness of the spring is 1 kN/m. By introducing a damper, the freq View Question The following table of properties was printed out for saturated liquid and saturated vapour of ammonia. The titles for o View Question The following table of properties was printed out for saturated liquid and saturated vapour of ammonia. The titles for o View Question Nitrogen at an initial state of$$10$$bar,$$1{m^3}$$and$$300K$$is expanded isothermally to a final volume of  View Question The following four figures have been drawn to represent a fictitious thermodynamic cycle, on the$$P$$-$$v$$and$$T$$- View Question A vapor absorption refrigeration system is a heat pump with three thermal reservoirs as shown in the figure. A refrigera View Question In the velocity diagram shown below,$$u=$$blade velocity,$$C=$$absolute fluid velocity and$$W =  relative veloci
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