GATE ME 2007
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## GATE ME

If a square matrix $$A$$ is real and symmetric then the eigen values
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The number of linearly independent eigen vectors of $$\left[ {\matrix{ 2 &amp; 1 \cr 0 &amp; 2 \cr } } \righ View Question The minimum value of function$$\,\,y = {x^2}\,\,$$in the interval$$\,\,\left[ {1,5} \right]\,\,$$is View Question If$$\,\,\,y = x + \sqrt {x + \sqrt {x + \sqrt {x + .....\alpha } } } \,\,\,$$then$$y(2)=$$__________. View Question$$\mathop {Lim}\limits_{x \to 0} {{{e^x} - \left( {1 + x + {{{x^2}} \over 2}} \right)} \over {{x^3}}} = $$View Question The area of a triangle formed by the tips of vectors$$\overrightarrow a ,\overrightarrow b $$and$$\overrightarrow c View Question Let $$X$$ and $$Y$$ be two independent random variables. Which one of the relations $$b/w$$ expectation $$(E),$$ varianc View Question The solution of $${{d\,y} \over {d\,x}} = {y^2}$$ with initial value $$y(0)=1$$ is bounded in the interval is View Question The partial differential equation $$\,\,{{{\partial ^2}\phi } \over {\partial {x^2}}} + {{{\partial ^2}\phi } \over {\pa View Question If$$\phi (x,y)$$and$$\psi (x,y)$$are function with continuous 2nd derivatives then$$\phi (x,y)\, + \,i\psi (x,y)$$View Question If$$F(s)$$is the Laplace transform of the function$$f(t)$$then Laplace transform of$$\int\limits_0^t {f\left( x \ri View Question During inelastic collision of two particles, which one of the following is conserved? View Question A block of mass $$M$$ is related from point $$P$$ on a rough inclined plane with inclination angle $$\theta$$, shown in View Question Newton's law of viscosity states that the shear stress in a fluid is proportional to : View Question Oil in a hydraulic cylinder is compressed from an initial volume $$2{m^3}$$ to $$1.96{m^3}$$. If the pressure of oil in View Question In a steady flow through a nozzle, the flow velocity on the nozzle axis is given by $$u = {u_0}\left( {1 + 3x/L} \right) View Question Which combination of the following statements about steady incompressible forced vortex flow is correct? P: Shear stres View Question Consider steady laminar incompressible axi-symmetric fully developed viscous flow through a straight circular pipe of co View Question Oil flows through a$$200mm$$diameter horizontal cast iron pipe (friction factor,$$f=0.0225$$) of length$$500m.$$The View Question Consider an incompressible laminar boundary layer flow over a flat plate of length$$L, aligned with the direction of View Question Consider a steady incompressible flow through a channel as shown below. The velocity profile is uniform with a value o View Question Consider a steady incompressible flow through a channel as shown below. The velocity profile is uniform with a value o View Question Consider steady one-dimensional heat flow in a plate of20mm$$thickness with a uniform heat generation of$$80MW/{m^3 View Question Consider steady one-dimensional heat flow in a plate of $$20mm$$ thickness with a uniform heat generation of $$80MW/{m^3 View Question Building has to be maintained at$${21^ \circ }C$$(dry bulb) and$${14.5^ \circ }C$$(wet bulb). The dew point temp und View Question The temp distribution within the Laminar thermal boundary layer over a heated isothermal flat plate is given by$$\left View Question The average heat transfer coefficient on a thin hot vertical plate suspended in still air can be determined from observa View Question In a counter flow heat exchanger, hot fluid enters at $${65^ \circ }C$$ and cold fluid leaves at $${30^ \circ }C.$$ mass View Question The maximum level of inventory of item is $$100$$ and it is achieved with infinite replenishment rate. The inventory be View Question In a machine shop, pins of $$15mm$$ diameter are produced at a rate of $$1000$$ per month and the same is consumed at a View Question Capacities of production of an item over $$3$$ consecutive months in regular time are $$100,$$ $$100$$ and $$80$$ and in View Question A thin spherical pressure vessel of $$200mm$$ diameter and $$1mm$$ thickness is subjected to an internal pressure varyin View Question A bolted joint in shown below. The maximum shear stress, in $$MPa,$$ in bolts $$A$$ and $$B$$ respectively are View Question A gear set has a pinion with $$20$$ teeth and a gear with $$40$$ teeth. The pinion runs at $$30rev/s$$ and transmits a p View Question A gear set has a pinion with $$20$$ teeth and a gear with $$40$$ teeth. The pinion runs at $$30rev/s$$ and transmits a p View Question A gear set has a pinion with $$20$$ teeth and a gear with $$40$$ teeth. The pinion runs at $$30rev/s$$ and transmits a p View Question A ball bearing operating at a load $$F$$ has $$8000$$hours of life. The life of the bearing, in hours, when the load is View Question A natural feed journal bearing of diameter $$50mm$$ and length $$50mm$$ operating at $$20$$ revolutions/sec carries a lo View Question A block brake shows below has a free width of $$300$$ $$mm$$ and a mean coefficient of friction of $$0.25$$. For an acti View Question Which of the following engineering materials is the most suitable candidate for hot chamber die casting View Question If a particular $$Fe$$-$$C$$ alloy contains less than $$0.83$$% carbon, it is called View Question Volume of a cube of a side $$''l''$$ and volume of sphere of radius $$' r '$$ are equal. Both the cube and the sphere ar View Question A $$200$$ $$mm$$ long down sprue has an area of cross section of $$650$$ $$m{m^2}$$ where the pouring basin meets the do View Question The thickness of metallic sheet is reduced from an initial value of $$16mm$$ to a final value of $$10mm$$ in one single View Question In open die forging, a disc of diameter $$200mm$$ height $$60mm$$ is compressed without any barreling effect. The final View Question Match the correct combination for following metal working processes. View Question Which of the following is a solid state welding process. View Question A $$DC$$ welding machine with a linear power source characteristic provides open circuit voltage of $$80V$$ and short ci View Question Two metallic sheets, each of $$2.0$$ $$mm$$ thickness are welded in lap joint configuration by resistance spot welding View Question A low carbon steel bar of $$147$$ $$mm$$ diameter with length of $$630$$ $$mm$$ is being turned with uncoated carbide in View Question A low carbon steel bar of $$147$$ $$mm$$ diameter with length of $$630$$ $$mm$$ is being turned with uncoated carbide in View Question In orthogonal turning of a low carbon steel bar of diameter $$150mm$$ with uncoated carbide tool, the cutting velocity i View Question In orthogonal turning of medium carbon steel, the specific machining energy is $$2$$ $$kJ/m{m^3},$$ the cutting velocity View Question In orthogonal turning of low carbon steel pipe with principal cutting edge angle of $$90,$$ the main cutting force is $$View Question The force requirement in a blanking operation of low carbon steel sheet is$$5.0kN.$$The thickness of the sheet is View Question A hole is specified as$${40^{\matrix{ {0.050} \cr {0.000} \cr } }}\,\,mm.$$The mating shaft has a clearanc View Question Which type of motor is used in axial or spindle drives of$$CNC$$m/c tools View Question A steel rod of length$$L$$and diameter$$D$$, fixed at both ends, is uniformly heated to a temperature rise of$$\Delt View Question In a simply-supported beam loaded as shown below, the maximum bending moment in N-m is View Question A disc of radius' r 'has a hole of radius 'r/2' cut-out as shown. The centroid of the remaining disc (shaded portion) at View Question A machine frame shown in the figure below is subjected to a horizontal force of $$600$$ $$N$$ parallel to $$Z$$-directio View Question A machine frame shown in the figure below is subjected to a horizontal force of $$600$$ $$N$$ parallel to $$Z$$-directio View Question A uniformly loaded propped cantilever beam and its free body diagram are shown below. The reactions are View Question A stepped steel shaft shown below is subjected to $$10$$ N-m torque. If the modulus of rigidity is $$80$$ GPa, the strai View Question A quick return mechanism is shown in below. The crank OS is drive at $$2$$ rev/s in counter clockwise direction If the View Question The input link Q2P of a four bar linkage is rotated at $$2$$ rad/s counter clockwise direction as shown below. The angul View Question A quick return mechanism is shown in below. The crank OS is drive at $$2$$ rev/s in counter clockwise direction The ang View Question The speed of an engine varies from $$210$$ rad/s to $$190$$ rad/s. During cycle the change in kinetic energy is found to View Question For an under damped harmonic oscillator, resonance View Question The equation of motion of a harmonic oscillator is given by $${{{d^2}x} \over {d{t^2}}} + 2\xi {\omega _n}{{dx} \over {d View Question The natural frequency of the system shown below is View Question Water has a critical specific volume of$$0.003155{m^3}/kg.$$A closed and rigid steel tank of volume$$0.025{m^3}
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A heat transformer is a device that transfers a part of the heat, supplied to it at an intermediate temperature, to a hi
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An irreversible heat engine extracts heat from a high temperature source at a rate of $$100kW$$ and rejects heat to a si
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Which of the following relationships is valid only for reversible process undergone by a closed system of simple compres
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Which combination of the following statements is correct? The incorporation of re-heater in a steam power plant. $$P:$$
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The inlet angle of runner blades of a Francis turbine is $${90^0}.$$ The blades are so shaped that the tangential compon
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A model of a hydraulic turbine is tested at a head of $$1/{4^{th}}$$ of that under which the full scale turbine works. T
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Match the items in columns $$I$$ and $$II$$. Column $$I$$ $$P:$$ Centrifugal compressor $$Q:$$ Centrifugal pump $$R:$$ P
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