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GATE ME 2008

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

The matrix $$\left[ {\matrix{ 1 & 2 & 4 \cr 3 & 0 & 6 \...
The eigen vectors of the matrix $$\left[ {\matrix{ 1 & 2 \cr 0 &...
For what values of <b>'a'</b> if any will the following system of equations in $...
Consider the shaded triangular region $$P$$ shown in the figure. What is $$\int\...
The value of $$\,\,\mathop {Lim}\limits_{x \to 8} {{{x^{1/3}} - 2} \over {x - 8}...
In the Taylor series expansion of $${e^x}$$ about $$x=2,$$ the coefficient of $$...
Which of the following integrals is unbounded?
The length of the curve $$\,y = {2 \over 3}{x^{3/2}}$$ between $$x=0$$ &amp; $$...
Let $$\,\,f = {y^x}.$$ What is $$\,\,{{{\partial ^2}f} \over {\partial x\partial...
The divergence of the vector field $$\left( {x - y} \right)\widehat i + \left( {...
The directional derivative of the scalar function $$f(x, y, z)$$$$ = {x^2} + 2{y...
A coin is tossed $$4$$ times. What is the probability of getting heads exactly $...
It is given that $$y'' + 2y' + y = 0,\,\,\,\,y\left( 0 \right) = 0,y\left( 1 \ri...
Given that $$\mathop x\limits^{ \bullet \bullet } + 3x = 0$$ and $$x\left( 0 ...
The integral $$\oint {f(z)dz} $$ evaluated around the unit circle on the complex...
A straight rod length $$L(t),$$ hinged at one end freely extensible at the other...
Consider a truss $$PQR$$ loaded at $$P$$ with a force $$F$$ as shown in the figu...
A circular disk of radius $$'R'$$ rolls without slipping at a velocity $$v$$. Th...
A journal bearing has a shaft diameter of $$40$$ $$mm$$ and a length of $$40mm.$...
A cubic block of side $$'L'$$ and mass $$'M'$$ is dragged over an oil film acros...
For a continuity equation given $$\nabla .\overrightarrow V = 0$$ to be valid, ...
The gap between a moving circular plate and a stationary surface is being contin...
The gap between a moving circular plate and a stationary surface is being contin...
A two dimensional fluid element rotates like a rigid body. At a point with in th...
Steady two dimensional heat conduction takes place in the body shown in the fig ...
For the three dimensional object shown in the fig below. Five faces are insulate...
For flow of fluid over a heated plate, the following fluid properties are known:...
A hollow enclosure is formed between two infinitely concentric cylinders of radi...
The $$LMTD$$ of a counter flow heat exchanger is $${20^ \circ }C$$. The cold flu...
For the network below, the objective is to find the length of the shortest path ...
A moving average system is used for forecasting weekly demand. $${F_1}\left( t \...
In an $$M/M/1$$ queuing system, the number of arrivals in an interval of length ...
Consider the Linear programme $$(LP)$$ <br>Max $$4x$$ + $$6y$$ <br>Subject to ...
Consider the Linear programme $$(LP)$$ <br>Max $$4x$$ + $$6y$$ <br>Subject to ...
For the standard transportation linear programme with $$m$$ sources and $$n$$ de...
A set of $$5$$ jobs is to be processed on a single machine. The processing time ...
A steel bar of $$10$$ $$mm\,\, \times \,\,50\,\,mm$$ is cantilevered with two $$...
A steel bar of $$10$$ $$mm\,\, \times \,\,50\,\,mm$$ is cantilevered with two $$...
A spur gate has a module of $$3mm,$$ number of teeth $$16,$$ a face width of $$3...
Match the type of gears with their most appropriate description <p><b>Type of g...
A journal bearing has a shaft diameter of $$40mm$$ and a length of $$40mm.$$ The...
One tooth of gear having $$4$$ module and $$32$$ teeth is shown in the figure. A...
A clutch has outer and inner diameters $$100mm$$ and $$40mm$$ respectively. Assu...
While cooling, a cubical casting of side $$40mm$$ undergoes $$3\% ,\,\,4\% $$ an...
In a single pass rolling operation, a $$20mm$$ thick plate with plate width of $...
In arc welding of a butt joint, the welding speed is to be selected such that hi...
In a single point turning tool, the side rake angle and orthogonal rake angle ar...
Orthogonal turning is performed on a cylindrical work piece with shear strength ...
Orthogonal turning is performed on a cylindrical work piece with shear strength ...
Internal gear cutting operation can be performed by
The figure shows an incomplete schematic of a conventional lathe to be used for ...
In the deep drawing of cups, blanks show a tendency to wrinkle up around the pe...
A displacement sensor (a dial indicator) measures the lateral displacement of a ...
For generating coon's surface we require
In the feed drive of a point to point open loop $$CNC$$ drive, a stepper motor r...
In the feed drive of a point to point open loop $$CNC$$ drive, a stepper motor r...
A two dimensional fluid element rotates like a rigid body. At a point within the...
A solid circular shaft of diameter 100 mm is subjected to an axial stress of 50 ...
For the component loaded with a force $$F$$ as shown in the figure, the axial st...
A compression spring is made of music wire of $$20$$ mm diameter having a shear ...
A cantilever type gate hinged at $$Q$$ is shown in the figure. $$P$$ and $$R$$ a...
The rod $$PQ$$ of length $$L$$ and with flexural rigidity $$EI$$ is hinged at bo...
A cylindrical container of radius $$R=1$$m, wall thickness $$1$$mm is filled wit...
A cylindrical container of radius $$R=1$$m, wall thickness $$1$$mm is filled wit...
The strain energy stored in the beam with flexural rigidity $$EI$$ and loaded as...
A planar mechanism has 8 links and 10 rotary joints. The number of degrees of fr...
A uniform rigid rod of mass $$m =1kg$$ and length $$L=1$$ m is hinged at its ce...
The natural frequency of the spring mass system shown in the figure is closest t...
In the figure shown, the system is a pure substance kept in a piston- cylinder a...
In the figure shown, the system is a pure substance kept in a piston- cylinder a...
In the figure shown, the system is a pure substance kept in a piston- cylinder a...
A balloon containing an ideal gas is initially kept in an evacuated and insulate...
A rigid, insulated tank is initially evacuated. The tank is connected with a sup...
In a steady state steady flow process taking place in a device with a single inl...
$$2$$ moles of oxygen are mixed adiabatically with another $$2$$ moles of oxygen...
A cycle device operates between three thermal reservoirs, as shown in the figure...
$$A$$ gas expands in a frictionless piston-cylinder arrangement. The expansion p...
A thermal power plant operates on a regenerative cycle with a single open feed w...
Water having a density of $$1000\,\,kg/{m^3},$$ issues from a Nozzle with a velo...

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