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## GATE ME 2015 Set 3

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

The lowest eigen value of the $$2 \times 2$$ matrix $$\left[ {\matrix{ 4 &amp... For a given matrix$$P = \left[ {\matrix{ {4 + 3i} &amp; { - i} \cr i &a...
The value of $$\mathop {Lim}\limits_{x \to 0} \left( {{{ - \sin x} \over {2\sin ... Let$$\phi $$be an arbitrary smooth real valued scalar function and$$\overrigh...
The value of $$\int\limits_C {\left[ {\left( {3x - 8{y^2}} \right)dx + \left( {4... If$$P(X) = 1/4,P(Y) = 1/3,$$and$$\,\,P\left( {X \cap Y} \righ...
A coin is tossed thrice. Let $$X$$ be the event that head occurs in each of the ...
Newton-Raphson method is used to find the roots of the equation, $${\,{x^3} + 2... Using a unit step size, the value of integral$$\int\limits_1^2 {x\,\ln \,xdx\,\...
Laplace transform of the function $$f(t)$$ is given by $$f\left( s \right) = L\l... A weight of 500N is supported by two metallic ropes as shown in the figure. The ... A bullet spins as the shot is fired from a gun. For this purpose, two helical sl... Which of the following statement are TRUE, when the cavitation parameter$$\sigm...
A Prandtl tube (Pitot-static tube with $$C=1$$) is used to measure the velocity ...
Three parallel pipes connected at the two ends have flow-rates $$\,\,\,{Q_1},\,\... Couette flow is characterized by A brick wall$$\,\left( {k = 0.9{W \over {m.K}}} \right)$$of thickness$$0.18$$... The ratio of momentum diffusivity$$\left( \upsilon \right)$$to thermal diffus... A solid sphere$$1$$of radius$$'r'$$is placed inside a hollow, closed hemisph... Saturated vapor is condensed to saturated liquid in a condenser. The heat capaci... The annual requirement of rivets at a ship manufacturing company is$$2000k...
In the notation $$(a/b/c) : (d/e/f)$$ for summarizing the characteristics of que...
For the linear programming problem: <br>\eqalign{ &amp; Maximize\,\,\,\,\,Z... For the given fluctuating fatigue load, the values of stress amplitude and stres... A cantilever bracket is bolted to a column using threeM12 \times 1.75$$bolts... For ball bearings, the fatigue life$$L$$measured in number of revolutions and ... In full mould (cavity-less) casting process, the Pattern is made of The dimensions of a cylindrical side riser (height$$=$$diameter) for a <br>$$...
Ratio of solidification time of a cylindrical casting (height $$=$$ radius) to t...
In a rolling operation using rolls of diameter $$500mm,$$ if a thick plate canno...
Which two of the following joining processes are autogeneous? <br>$$(i)$$ Diffus...
Orthogonal turning of a mild steel tube with a tool of rake angle $${10^0}$$ is ...
In a machining operation, if the generatrix and directrix both are straight line...
A shaft of length $$90$$ $$mm$$ has a tapered portion of length $$55$$ $$mm.$$ T...
In a $$CNC$$ milling operation, the tool has to machine the circular arc from po...
For the overhanging beam shown in figure, the magnitude of maximum bending momen...
For the same material and the mass, which of the following configurations of fly...
The value of moment of inertia of the section shown in the figure about the axis...
A cylindrical tank with closed ends is filled with compressed air at a pressure ...
In the figure, link $$2$$ rotates with constant angular velocity $${{\omega _2}}... Figure shows a wheel rotating about O<sub>2</sub>. Two points A and B located al... The number of degrees of freedom of the linkage shown in the figure is <img clas... A gear train is made up of five spur gears as shown in the figure. Gear$$2$$is... The torque (in N-m) exerted on the crank shaft of a two stroke engine can be des... Which of the following statements are TRUE for damped vibrations? <p>$$P.$$For ... Figure shows a single degree of freedom system. The system consists of a mass le... A rigid container of volume$$0.5{m^3}$$contains$$1.0kg$$of water a... Steam enters a turbine at$$30bar,{300^ \circ }C\left( {u = 2750\,\,kJ...
A mixture of ideal gases has the following composition by mass: <img class="que...
One side of a wall is maintained at $$400K$$ and the other at $$300K.$$ The rate...

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