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## GATE ME 2005

Exam Held on Thu Jan 01 1970 00:00:00 GMT+0000 (Coordinated Universal Time)
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## GATE ME

$$A$$ is a $$3 \times 4$$ matrix and $$AX=B$$ is an inconsistent system of equat...
Which one of the following is an eigen vector of the matrix $$\left[ {\matrix{ ...$$\int\limits_{ - a}^a {\left[ {{{\sin }^6}\,x + {{\sin }^7}\,x} \right]dx} $$i... By a change of variables$$x(u, v) = uv,\,\,y\left( {u,v} \right) = {v \ove...
Changing the order of integration in the double integral <br>$${\rm I} = \int\l... Stokes theorem connects A lot had$$10$$% defective items. Ten items are chosen randomly from this lot. ... A single die is thrown two times. What is the probability that the sum is neithe... Using given data points tabulated below, a straight line passing through the ori... If$${x^2}\left( {{{d\,y} \over {d\,x}}} \right) + 2xy = {{2\ln x} \over x}$$a... The complete solution of the ordinary differential equation$${{{d^2}y} \over {d...
Which of the following is a solution of the differential equation $$\,{{{d^2}y} ... Starting from$$\,{x_0} = 1,\,\,$$one step of Newton - Raphson method in solvin... A simple pendulum of length 5m, with a bob of mass 1 kg, is in simple harmonic m... The time variation of the position of a particle in rectilinear motion is given ... A shell is fired from a cannon. At the instant the shell is just about to leave ... An elevator (lift) consists of the elevator cage and a counter weight, of mass m... Two books of mass 1 kg each are kept on a table, one over the other. The coeffic... A 1 kg mass of clay, moving with a velocity of 10 m/s, strikes a stationary whee... The velocity components in the$$x$$and$$y$$directions of a two dimensional p... A leaf is caught in a whirlpool. At a given instant, the leaf is at a distance o... A venturimeter of$$20mm$$throat diameter is used to measure the velocity ... A$$U$$-tube manometer with a small quantity of mercury is used to measure the s... In case of one dimensional heat conduction in a medium with constant properties,... Heat flows through a composite slab, as shown below. The depth of the slab is$$...
A small copper ball of $$5$$ $$mm$$ diameter at $$500$$ $$K$$ is dropped into an...
An un-insulated air conditioning duct of rectangular cross section $$1\,\,m \tim... An un-insulated air conditioning duct of rectangular cross section$$1\,\,m \tim...
The following figure was generated from experimental data relating spectral blac...
A solid cylinder (surface $$2$$) is located at the center of a hollow sphere (su...
Hot oil is cooled from $${80^ \circ }C$$ to $${50^ \circ }C$$ in an oil cooler w...
The distribution of lead-time demand fro an item is as follows: <img class="que...
A project has six activities $$(A$$ to $$F)$$ with respective activity durations...
The sales of a product during the last four years were $$860, 880, 870$$ and $$8... Consider a single server queuing model with Poisson arrivals$$\left( {\lambda ...
Consider a linear programming problem with two variables and two constraints. Th...
Consider a linear programming problem with two variables and two constraints. Th...
A company has two factories $${S_1},$$ $${S_2}$$ and two warehouses $${D_1},$$ \$...
Which one of the following is criterion in the design of hydrodynamic journal be...
A band brake consists of a lever attached to one end of the band. The other end ...
A band brake consists of a lever attached to one end of the band. The other end ...
A mould has a downsprue whose length is $$20$$ $$cm$$ and the cross sectional ar...
Match <b>List - $${\rm I}$$</b> (products) with <b>List - $${\rm II}$$</b> (cast...
The strength of a brazed joint
Spot welding of two $$1$$ $$mm$$ thick sheets of steel (density $$= 8000kg/{m^3... The figure below shows a graph, which qualitatively relates cutting speed and co... Two tools$$P$$and$$Q$$have signature$${5^ \circ } - {5^ \circ } - {6^ \circ...
A $$600$$ $$mm$$ $$\times \,\,30\,\,mm$$ flat surface of a plate is to be fini...
A $$2$$ $$mm$$ thick metal sheet is to be bent at an angle of one radian with a ...
In order to have interference fit, it is essential that the lower limit of the s...
Which among the $$NC$$ operations given below are continuous path operations? A...
The tool of an $$NC$$ machine has to move along a circular arc from $$(5,5)$$ to...
A cantilever beam carries the anti-symmetric load shown, where w<sub>o</sub> is ...
A beam is made up of two identical bars AB and BC, by hinging them together at B...
A mass less beam has a loading pattern as shown in figure. The beam is rectangul...
A weighing machine consists of a 2 kg pan resting on a spring in this condition,...
A cantilever beam has the square cross section of 10 mm $$\times$$ 10 mm. It c...
A mass less beam has a loading pattern as shown in figure. The beam is rectangul...
The two shafts $$AB$$ and $$BC$$, of equal length and diameters $$d$$ and $$2d$$...
Two identical cantilever beams are supported as shown, with their free ends in c...
The number of degrees of freedom of a planar linkage with 8 links and 9 simple r...
An instantaneous configuration of a four-bar mechanism, whose plane is horizonta...
An instantaneous configuration of a four-bar mechanism, whose plane is horizonta...
An instantaneous configuration of a four-bar mechanism, whose plane is horizonta...
There are four samples P, Q, R and S, with natural frequencies 64, 96, 128 and 2...
In a spring-mass system, the mass is 0.1 kg and the stiffness of the spring is 1...
The following table of properties was printed out for saturated liquid and satur...
The following table of properties was printed out for saturated liquid and satur...
Nitrogen at an initial state of $$10$$ bar, $$1{m^3}$$ and $$300$$ $$K$$ is expa...
The following four figures have been drawn to represent a fictitious thermodynam...
A vapor absorption refrigeration system is a heat pump with three thermal reserv...
In the velocity diagram shown below, $$u=$$ blade velocity, $$C=$$ absolute flu...

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