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GATE ME 2007

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

If a square matrix $$A$$ is real and symmetric then the eigen values
The number of linearly independent eigen vectors of $$\left[ {\matrix{ 2 &amp...
The minimum value of function $$\,\,y = {x^2}\,\,$$ in the interval $$\,\,\left[...
If $$\,\,\,y = x + \sqrt {x + \sqrt {x + \sqrt {x + .....\alpha } } } \,\,\,$$ t...
$$\mathop {Lim}\limits_{x \to 0} {{{e^x} - \left( {1 + x + {{{x^2}} \over 2}} \r...
The area of a triangle formed by the tips of vectors $$\overrightarrow a ,\overr...
Let $$X$$ and $$Y$$ be two independent random variables. Which one of the relati...
The solution of $${{d\,y} \over {d\,x}} = {y^2}$$ with initial value $$y(0)=1$$ ...
The partial differential equation $$\,\,{{{\partial ^2}\phi } \over {\partial {x...
If $$\phi (x,y)$$ and $$\psi (x,y)$$ are function with continuous 2<sup>nd</sup>...
If $$F(s)$$ is the Laplace transform of the function $$f(t)$$ then Laplace trans...
During inelastic collision of two particles, which one of the following is conse...
A block of mass $$M$$ is related from point $$P$$ on a rough inclined plane with...
Newton's law of viscosity states that the shear stress in a fluid is proportiona...
Oil in a hydraulic cylinder is compressed from an initial volume $$2{m^3}$$ to $...
In a steady flow through a nozzle, the flow velocity on the nozzle axis is given...
Which combination of the following statements about steady incompressible forced...
Oil flows through a $$200mm$$ diameter horizontal cast iron pipe (friction facto...
Consider steady laminar incompressible axi-symmetric fully developed viscous flo...
Consider an incompressible laminar boundary layer flow over a flat plate of leng...
Consider a steady incompressible flow through a channel as shown below. <img cla...
Consider a steady incompressible flow through a channel as shown below. <img cla...
Consider steady one-dimensional heat flow in a plate of $$20mm$$ thickness with ...
Consider steady one-dimensional heat flow in a plate of $$20mm$$ thickness with ...
Building has to be maintained at $${21^ \circ }C$$ (dry bulb) and $${14.5^ \circ...
The temp distribution within the Laminar thermal boundary layer over a heated is...
The average heat transfer coefficient on a thin hot vertical plate suspended in ...
In a counter flow heat exchanger, hot fluid enters at $${65^ \circ }C$$ and cold...
The maximum level of inventory of item is $$100$$ and it is achieved with infin...
In a machine shop, pins of $$15mm$$ diameter are produced at a rate of $$1000$$ ...
Capacities of production of an item over $$3$$ consecutive months in regular tim...
A thin spherical pressure vessel of $$200mm$$ diameter and $$1mm$$ thickness is ...
A bolted joint in shown below. The maximum shear stress, in $$MPa,$$ in bolts $$...
A gear set has a pinion with $$20$$ teeth and a gear with $$40$$ teeth. The pini...
A gear set has a pinion with $$20$$ teeth and a gear with $$40$$ teeth. The pini...
A gear set has a pinion with $$20$$ teeth and a gear with $$40$$ teeth. The pini...
A ball bearing operating at a load $$F$$ has $$8000$$hours of life. The life of ...
A natural feed journal bearing of diameter $$50mm$$ and length $$50mm$$ operatin...
A block brake shows below has a free width of $$300$$ $$mm$$ and a mean coeffici...
Which of the following engineering materials is the most suitable candidate for ...
If a particular $$Fe$$-$$C$$ alloy contains less than $$0.83$$% carbon, it is ca...
A $$200$$ $$mm$$ long down sprue has an area of cross section of $$650$$ $$m{m^2...
Volume of a cube of a side $$''l''$$ and volume of sphere of radius $$' r '$$ ar...
Match the correct combination for following metal working processes. <img class=...
The thickness of metallic sheet is reduced from an initial value of $$16mm$$ to ...
In open die forging, a disc of diameter $$200mm$$ height $$60mm$$ is compressed ...
Which of the following is a solid state welding process.
A $$DC$$ welding machine with a linear power source characteristic provides open...
Two metallic sheets, each of $$2.0$$ $$mm$$ thickness are welded in lap joint co...
A low carbon steel bar of $$147$$ $$mm$$ diameter with length of $$630$$ $$mm$$ ...
A low carbon steel bar of $$147$$ $$mm$$ diameter with length of $$630$$ $$mm$$ ...
In orthogonal turning of a low carbon steel bar of diameter $$150mm$$ with uncoa...
In orthogonal turning of medium carbon steel, the specific machining energy is $...
In orthogonal turning of low carbon steel pipe with principal cutting edge angle...
The force requirement in a blanking operation of low carbon steel sheet is $$5.0...
A hole is specified as $${40^{\matrix{ {0.050} \cr {0.000} \cr } }}\...
Which type of motor is used in axial or spindle drives of $$CNC$$ m/c tools
A steel rod of length $$L$$ and diameter $$D$$, fixed at both ends, is uniformly...
In a simply-supported beam loaded as shown below, the maximum bending moment in ...
A disc of radius' r 'has a hole of radius 'r/2' cut-out as shown. The centroid o...
A machine frame shown in the figure below is subjected to a horizontal force of ...
A machine frame shown in the figure below is subjected to a horizontal force of ...
A uniformly loaded propped cantilever beam and its free body diagram are shown b...
A stepped steel shaft shown below is subjected to $$10$$ N-m torque. If the modu...
A quick return mechanism is shown in below. The crank OS is drive at $$2$$ rev/s...
The input link Q<sub>2</sub>P of a four bar linkage is rotated at $$2$$ rad/s co...
A quick return mechanism is shown in below. The crank OS is drive at $$2$$ rev/s...
The speed of an engine varies from $$210$$ rad/s to $$190$$ rad/s. During cycle ...
For an under damped harmonic oscillator, resonance
The equation of motion of a harmonic oscillator is given by $${{{d^2}x} \over {d...
The natural frequency of the system shown below is <img class="question-image" ...
Water has a critical specific volume of $$0.003155$$ $${m^3}/kg.$$ A closed and ...
A heat transformer is a device that transfers a part of the heat, supplied to it...
An irreversible heat engine extracts heat from a high temperature source at a ra...
Which of the following relationships is valid only for reversible process underg...
Which combination of the following statements is correct? <p>The incorporation o...
A model of a hydraulic turbine is tested at a head of $$1/{4^{th}}$$ of that und...
The inlet angle of runner blades of a Francis turbine is $${90^0}.$$ The blades ...
Match the items in columns $$I$$ and $$II$$. <p><b>Column $$I$$</b> <br>$$P:$$ C...

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