GATE ME 2015 Set 3
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## GATE ME

The lowest eigen value of the $$2 \times 2$$ matrix $$\left[ {\matrix{ 4 &amp; 2 \cr 1 &amp; 3 \cr } } \righ View Question For a given matrix$$P = \left[ {\matrix{ {4 + 3i} &amp; { - i} \cr i &amp; {4 - 3i} \cr } } \right],$$whe View Question The value of$$\mathop {Lim}\limits_{x \to 0} \left( {{{ - \sin x} \over {2\sin x + x\cos x}}} \right)\,\,\,$$is ______ View Question Let$$\phi $$be an arbitrary smooth real valued scalar function and$$\overrightarrow V $$be an arbitrary smooth vecto View Question The value of$$\int\limits_C {\left[ {\left( {3x - 8{y^2}} \right)dx + \left( {4y - 6xy} \right)dy} \right],\,\,} $$(wh View Question If$$P(X) = 1/4,P(Y) = 1/3,$$and$$\,\,P\left( {X \cap Y} \right) = 1/12,\,\,$$the value of$$P(Y/X)$$View Question A coin is tossed thrice. Let$$X$$be the event that head occurs in each of the first two tosses. Let$$Y$$be the event View Question Newton-Raphson method is used to find the roots of the equation,$${\,{x^3} + 2{x^2} + 3x - 1 = 0}$$If the initial gue View Question Using a unit step size, the value of integral$$\int\limits_1^2 {x\,\ln \,xdx\,\,\,} $$by trapezoidal rule is _________ View Question Laplace transform of the function$$f(t)$$is given by$$f\left( s \right) = L\left\{ {f\left( t \right)} \right\} = \in
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A weight of 500N is supported by two metallic ropes as shown in the figure. The values of tensions T1 and T2 are respect
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A bullet spins as the shot is fired from a gun. For this purpose, two helical slots as shown in the figure are cut in th
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Which of the following statement are TRUE, when the cavitation parameter $$\sigma = 0?$$ (i) The local pressure is red
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A Prandtl tube (Pitot-static tube with $$C=1$$) is used to measure the velocity of water. The differential manometer rea
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Three parallel pipes connected at the two ends have flow-rates $$\,\,\,{Q_1},\,\,\,{Q_2},\,\,\,\,$$ and $${Q_3}$$ respec
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Couette flow is characterized by
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A brick wall $$\,\left( {k = 0.9{W \over {m.K}}} \right)$$ of thickness $$0.18$$ $$m$$ separates the warm air in a room
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The ratio of momentum diffusivity $$\left( \upsilon \right)$$ to thermal diffusivity $$\left( \alpha \right),$$ is ca
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A solid sphere $$1$$ of radius $$'r'$$ is placed inside a hollow, closed hemispherical surface $$2$$ of radius $$'4r'.$$
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Saturated vapor is condensed to saturated liquid in a condenser. The heat capacity ratio is $${c_r} = {{{c_{\min }}} \ov View Question The annual requirement of rivets at a ship manufacturing company is$$2000kg.$$The rivets are supplied in units of View Question In the notation$$(a/b/c) : (d/e/f)$$for summarizing the characteristics of queuing situation, the letters$$‘b’$$and View Question For the linear programming problem:$$\eqalign{ &amp; Maximize\,\,\,\,\,Z = 3{x_1} + 2{x_2} \cr &amp; Subject\,\,
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For the given fluctuating fatigue load, the values of stress amplitude and stress ratio are respectively.
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A cantilever bracket is bolted to a column using three $$M12 \times 1.75$$ bolts $$P, Q$$ and $$R.$$ The value of maximu
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For ball bearings, the fatigue life $$L$$ measured in number of revolutions and the radial load $$F$$ are related by $$F View Question In full mould (cavity-less) casting process, the Pattern is made of View Question The dimensions of a cylindrical side riser (height$$=$$diameter) for a$$25cm \times 15cm \times 5cm$$steel casting View Question Ratio of solidification time of a cylindrical casting (height$$=$$radius) to that of a cubic casting of side two times View Question In a rolling operation using rolls of diameter$$500mm,$$if a thick plate cannot be reduced to less than$$20mm$$in on View Question Which two of the following joining processes are autogeneous?$$(i)$$Diffusion welding$$(ii)$$Electro slag welding$$
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Orthogonal turning of a mild steel tube with a tool of rake angle $${10^0}$$ is carried out at a feed of $$0.14$$ $$mm/r View Question In a machining operation, if the generatrix and directrix both are straight lines, the surface obtained is View Question A shaft of length$$90mm$$has a tapered portion of length$$55mm.$$The diameter of the taper is$$80mm$View Question In a $$CNC$$ milling operation, the tool has to machine the circular arc from point $$(20, 20)$$ to $$(10, 10)$$ at sequ View Question For the overhanging beam shown in figure, the magnitude of maximum bending moment (in kN-m) is ________ View Question For the same material and the mass, which of the following configurations of flywheel will have maximum mass moment of i View Question The value of moment of inertia of the section shown in the figure about the axis-$$XX$$ is $$All$$ $$dimensions$$ $$a View Question A cylindrical tank with closed ends is filled with compressed air at a pressure of$$500 kP$$a. The inner radius of the View Question In the figure, link$$2$$rotates with constant angular velocity$${{\omega _2}}$$. A slider link$$3$$moves outwards w View Question Figure shows a wheel rotating about O2. Two points A and B located along the radius of wheel have speeds of 80 m/s and 1 View Question The number of degrees of freedom of the linkage shown in the figure is View Question A gear train is made up of five spur gears as shown in the figure. Gear$$2$$is driver and gear$$6$$is driven member. View Question The torque (in N-m) exerted on the crank shaft of a two stroke engine can be described as is the crank angle as$$\,\,T View Question Which of the following statements are TRUE for damped vibrations? $$P.$$ For a system having critical damping, the value View Question Figure shows a single degree of freedom system. The system consists of a mass less rigid bar $$OP$$ hinged at $$O$$ and View Question A rigid container of volume $$0.5$$ $${m^3}$$ contains $$1.0$$ $$kg$$ of water at $${120^ \circ }C$$ $$\left( {{V_f} = View Question Steam enters a turbine at$$30bar,{300^ \circ }C\left( {u = 2750\,\,kJ/kg,\,\,h = 2993\,\,kJ/kg} \right)$$and View Question A mixture of ideal gases has the following composition by mass: If the universal gas constant is$$8314J/kmol$$- View Question One side of a wall is maintained at$$400K$$and the other at$$300K.$$The rate of heat transfer through the wall is$
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