GATE ME 2015 Set 3

## GATE ME

The lowest eigen value of the $$2 \times 2$$ matrix $$\left[ {\matrix{
4 & 2 \cr
1 & 3 \cr
} } \righ

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For a given matrix $$P = \left[ {\matrix{
{4 + 3i} & { - i} \cr
i & {4 - 3i} \cr
} } \right],$$ whe

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The value of $$\mathop {Lim}\limits_{x \to 0} \left( {{{ - \sin x} \over {2\sin x + x\cos x}}} \right)\,\,\,$$ is ______

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Let $$\phi $$ be an arbitrary smooth real valued scalar function and $$\overrightarrow V $$ be an arbitrary smooth vecto

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The value of $$\int\limits_C {\left[ {\left( {3x - 8{y^2}} \right)dx + \left( {4y - 6xy} \right)dy} \right],\,\,} $$ (wh

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If $$P(X)$$ $$ = $$ $$1/4,$$ $$P(Y) = 1/3,$$ and $$\,\,P\left( {X \cap Y} \right) = 1/12,\,\,$$ the value of $$P(Y/X)$$

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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

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Newton-Raphson method is used to find the roots of the equation, $${\,{x^3} + 2{x^2} + 3x - 1 = 0}$$ If the initial gue

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Using a unit step size, the value of integral $$\int\limits_1^2 {x\,\ln \,xdx\,\,\,} $$ by trapezoidal rule is _________

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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

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The annual requirement of rivets at a ship manufacturing company is $$2000$$ $$kg.$$ The rivets are supplied in units of

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In the notation $$(a/b/c) : (d/e/f)$$ for summarizing the characteristics of queuing situation, the letters $$‘b’$$ and

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For the linear programming problem:
$$\eqalign{
& Maximize\,\,\,\,\,Z = 3{x_1} + 2{x_2} \cr
& 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

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In full mould (cavity-less) casting process, the Pattern is made of

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The dimensions of a cylindrical side riser (height $$=$$ diameter) for a
$$25cm \times 15cm \times 5cm$$ steel casting

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Ratio of solidification time of a cylindrical casting (height $$=$$ radius) to that of a cubic casting of side two times

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In a rolling operation using rolls of diameter $$500mm,$$ if a thick plate cannot be reduced to less than $$20mm$$ in on

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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

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In a machining operation, if the generatrix and directrix both are straight lines, the surface obtained is

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A shaft of length $$90$$ $$mm$$ has a tapered portion of length $$55$$ $$mm.$$ The diameter of the taper is $$80$$ $$mm$

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In a $$CNC$$ milling operation, the tool has to machine the circular arc from point $$(20, 20)$$ to $$(10, 10)$$ at sequ

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For the overhanging beam shown in figure, the magnitude of maximum bending moment (in kN-m) is ________

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For the same material and the mass, which of the following configurations of flywheel will have maximum mass moment of i

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The value of moment of inertia of the section shown in the figure about the axis-$$XX$$ is
$$All$$ $$dimensions$$ $$a

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A cylindrical tank with closed ends is filled with compressed air at a pressure of $$500 kP$$a. The inner radius of the

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In the figure, link $$2$$ rotates with constant angular velocity $${{\omega _2}}$$. A slider link $$3$$ moves outwards w

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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

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The number of degrees of freedom of the linkage shown in the figure is

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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.

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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

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Which of the following statements are TRUE for damped vibrations?
$$P.$$ For a system having critical damping, the value

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Figure shows a single degree of freedom system. The system consists of a mass less rigid bar $$OP$$ hinged at $$O$$ and

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A rigid container of volume $$0.5$$ $${m^3}$$ contains $$1.0$$ $$kg$$ of water at $${120^ \circ }C$$
$$\left( {{V_f} =

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Steam enters a turbine at $$30bar,$$ $${300^ \circ }C$$ $$\left( {u = 2750\,\,kJ/kg,\,\,h = 2993\,\,kJ/kg} \right)$$ and

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A mixture of ideal gases has the following composition by mass:
If the universal gas constant is $$8314$$ $$J/kmol$$-

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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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