GATE ME 2008
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## GATE ME

The matrix $$\left[ {\matrix{ 1 &amp; 2 &amp; 4 \cr 3 &amp; 0 &amp; 6 \cr 1 &amp; 1 &amp; P \cr } } \ri View Question The eigen vectors of the matrix$$\left[ {\matrix{ 1 &amp; 2 \cr 0 &amp; 2 \cr } } \right]$$are written in View Question For what values of 'a' if any will the following system of equations in$$x, y$$and$$z$$have a solution?$$$2x+3y=4,$
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Consider the shaded triangular region $$P$$ shown in the figure. What is $$\int\!\!\!\int\limits_p {xy\,dx\,dy\,?}$$
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In the Taylor series expansion of $${e^x}$$ about $$x=2,$$ the coefficient of $$\,\,{\left( {x - 2} \right)^4}\,\,$$ is
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The value of $$\,\,\mathop {Lim}\limits_{x \to 8} {{{x^{1/3}} - 2} \over {x - 8}}\,\,$$ is
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Which of the following integrals is unbounded?
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The length of the curve $$\,y = {2 \over 3}{x^{3/2}}$$ between $$x=0$$ &amp; $$x=1$$ is
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Let $$\,\,f = {y^x}.$$ What is $$\,\,{{{\partial ^2}f} \over {\partial x\partial y}}\,\,$$ at $$x=2,$$ $$y=1$$?
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The divergence of the vector field $$\left( {x - y} \right)\widehat i + \left( {y - x} \right)\widehat j + \left( {x + y View Question The directional derivative of the scalar function$$f(x, y, z) = {x^2} + 2{y^2} + z\,\,$$at the point$$P = \left(
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A coin is tossed $$4$$ times. What is the probability of getting heads exactly $$3$$ times?
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It is given that $$y'' + 2y' + y = 0,\,\,\,\,y\left( 0 \right) = 0,y\left( 1 \right) = 0.$$ What is $$y(0.5)$$?
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Given that $$\mathop x\limits^{ \bullet \bullet } + 3x = 0$$ and $$x\left( 0 \right) = 1,\,\,\mathop x\limits^ \bulle View Question The integral$$\oint {f(z)dz} $$evaluated around the unit circle on the complex plane for$$f(z) = {{\cos z} \over z}$$View Question A straight rod length$$L(t),$$hinged at one end freely extensible at the other end, roates through an angle$$\theta \
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Consider a truss $$PQR$$ loaded at $$P$$ with a force $$F$$ as shown in the figure. The tension in the member $$QR$$ is
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A circular disk of radius $$'R'$$ rolls without slipping at a velocity $$v$$. The magnitude of the velocity at point $$' View Question A journal bearing has a shaft diameter of$$40mm$$and a length of$$40mm.$$The shaft is rotating at$$20rad/
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A cubic block of side $$'L'$$ and mass $$'M'$$ is dragged over an oil film across table by a string connects to a hangin
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For a continuity equation given $$\nabla .\overrightarrow V = 0$$ to be valid, $$\overrightarrow V$$ where is the velo
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The gap between a moving circular plate and a stationary surface is being continuously reduced, as the circular plate co
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The gap between a moving circular plate and a stationary surface is being continuously reduced, as the circular plate co
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A two dimensional fluid element rotates like a rigid body. At a point with in the element, the pressure is $$1$$ unit. R
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Steady two dimensional heat conduction takes place in the body shown in the fig below. The normal temperature gradients
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For the three dimensional object shown in the fig below. Five faces are insulated. The sixth face $$(PQRS),$$ which is n
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For flow of fluid over a heated plate, the following fluid properties are known: Viscosity $$=0.001Pa.s;$$ Specific heat
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A hollow enclosure is formed between two infinitely concentric cylinders of radii $$1m$$ and $$2m$$ respectively. Radiat
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The $$LMTD$$ of a counter flow heat exchanger is $${20^ \circ }C$$. The cold fluid enters at $${20^ \circ }C$$ and the h
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For the network below, the objective is to find the length of the shortest path from node $$P$$ to node $$G.$$ Let $${d_ View Question A moving average system is used for forecasting weekly demand.$${F_1}\left( t \right)$$and$${F_2}\left( t \right)$$a View Question In an$$M/M/1$$queuing system, the number of arrivals in an interval of length$$T$$is a Poisson random variable (i.e. View Question Consider the Linear programme$$(LP)$$Max$$4x$$+$$6y$$Subject to$$\eqalign{ &amp; \,\,\,\,\,\,\,\,\,\,\,3x + 2
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Consider the Linear programme $$(LP)$$ Max $$4x$$ + $$6y$$ Subject to \eqalign{ &amp; \,\,\,\,\,\,\,\,\,\,\,3x + 2 View Question For the standard transportation linear programme withm$$sources and$$n$$destinations and total supply equaling tot View Question A set of$$5$$jobs is to be processed on a single machine. The processing time (in days) is given in the table below. T View Question A steel bar of$$10mm\,\, \times \,\,50\,\,mm$$is cantilevered with two$$M12$$bolts ($$P$$and$$Q$$) to support View Question A steel bar of$$10mm\,\, \times \,\,50\,\,mm$$is cantilevered with two$$M12$$bolts ($$P$$and$$Q$$) to support View Question A spur gate has a module of$$3mm,$$number of teeth$$16,$$a face width of$$36mm$$and a pressure angle of$${20^ \ci
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Match the type of gears with their most appropriate description Type of gear (P)$$\,\,\,\,\,$$ Helical (Q)$$\,\,\,\,\, View Question A journal bearing has a shaft diameter of$$40mm$$and a length of$$40mm.$$The shaft is rotating at$$20rad/s$$a View Question One tooth of gear having$$4$$module and$$32$$teeth is shown in the figure. Assume that the gear tooth and the corres View Question A clutch has outer and inner diameters$$100mm$$and$$40mm$$respectively. Assuming a uniform pressure of$$2MPa$$and View Question While cooling, a cubical casting of side$$40mm$$undergoes$$3\% ,\,\,4\% $$and$$5\% $$volume shrinkage during the l View Question In a single pass rolling operation, a$$20mm$$thick plate with plate width of$$100mm$$, is reduced to$$18mm$$thick. View Question In arc welding of a butt joint, the welding speed is to be selected such that highest cooling rate is achieved. Melting View Question In a single point turning tool, the side rake angle and orthogonal rake angle are equal.$$\varphi $$is the principle c View Question Orthogonal turning is performed on a cylindrical work piece with shear strength of$$250Mpa.$$The following conditions View Question Orthogonal turning is performed on a cylindrical work piece with shear strength of$$250Mpa.$$The following conditions View Question Internal gear cutting operation can be performed by View Question The figure shows an incomplete schematic of a conventional lathe to be used for cutting threads with different pitches. View Question In the deep drawing of cups, blanks show a tendency to wrinkle up around the periphery (flange). The most likely cause View Question A displacement sensor (a dial indicator) measures the lateral displacement of a mandrel on the taper hole inside a drill View Question For generating coon's surface we require View Question In the feed drive of a point to point open loop$$CNC$$drive, a stepper motor rotating at$$200steps/rev$$drives a tab View Question In the feed drive of a point to point open loop$$CNC$$drive, a stepper motor rotating at$$200steps/rev$$drives a tab View Question A two dimensional fluid element rotates like a rigid body. At a point within the element, the pressure is$$1$$unit. Ra View Question A solid circular shaft of diameter 100 mm is subjected to an axial stress of 50 MPa. It further subjected to a torque of View Question For the component loaded with a force$$F$$as shown in the figure, the axial stress at the corner point$$P$$is View Question A compression spring is made of music wire of$$20$$mm diameter having a shear strength and shear modulus of$$800$$MP View Question A cantilever type gate hinged at$$Q$$is shown in the figure.$$P$$and$$R$$are the centers of gravity of the cantile View Question The rod$$PQ$$of length$$L$$and with flexural rigidity$$EI$$is hinged at both ends. For what minimum force$$F$$is View Question A cylindrical container of radius$$R=1$$m, wall thickness$$1$$mm is filled with water upto a depth of$$2$$m and suspe View Question A cylindrical container of radius$$R=1$$m, wall thickness$$1$$mm is filled with water upto a depth of$$2$$m and suspe View Question The strain energy stored in the beam with flexural rigidity$$EI$$and loaded as shown in the figure is View Question A planar mechanism has 8 links and 10 rotary joints. The number of degrees of freedom of the mechanism, using Gruebler's View Question A uniform rigid rod of mass$$m =1kg$$and length$$L=1$$m is hinged at its centre &amp; laterally supported at one e View Question The natural frequency of the spring mass system shown in the figure is closest to View Question In the figure shown, the system is a pure substance kept in a piston- cylinder arrangement. The system is initially a tw View Question In the figure shown, the system is a pure substance kept in a piston- cylinder arrangement. The system is initially a tw View Question In the figure shown, the system is a pure substance kept in a piston- cylinder arrangement. The system is initially a tw View Question A balloon containing an ideal gas is initially kept in an evacuated and insulated room. The balloon ruptures and the gas View Question A rigid, insulated tank is initially evacuated. The tank is connected with a supply line through which air ( assumed to View Question In a steady state steady flow process taking place in a device with a single inlet and a single outlet, the work done pe View Question$$2$$moles of oxygen are mixed adiabatically with another$$2$$moles of oxygen in mixing chamber, so that the final to View Question A cycle device operates between three thermal reservoirs, as shown in the figure. Heat is transferred to/from the cyclic View Question$$A$$gas expands in a frictionless piston-cylinder arrangement. The expansion process is very slow, and is resisted by View Question A thermal power plant operates on a regenerative cycle with a single open feed water heater, as shown in the figure. For View Question Water having a density of$$1000\,\,kg/{m^3},$$issues from a Nozzle with a velocity of$$10m/s and the jet strik
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