GATE ME 2011

## GATE ME

Eigen values of a real symmetric matrix are always

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Consider the following system of equations
$$2{x_1} + {x_2} + {x_3} = 0,\,\,{x_2} - {x_3} = 0$$ and $${x_1} + {x_2} = 0

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A series expansion for the function $$\sin \theta $$ is _______.

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If $$f(x)$$ is even function and a is a positive real number , then $$\int\limits_{ - a}^a {f\left( x \right)dx\,\,} $

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What is $$\mathop {Lim}\limits_{\theta \to 0} {{\sin \theta } \over \theta }\,\,$$ equal to ?

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An unbiased coin is tossed five times. The outcome of each loss is either a head or a tail. Probability of getting at le

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Consider the differential equation $${{dy} \over {dx}} = \left( {1 + {y^2}} \right)x\,\,.$$ The general solution with c

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The integral $$\,\int\limits_1^3 {{1 \over x}\,\,dx\,\,\,} $$ when evaluated by using simpson's $$1/{3^{rd}}$$ rule on t

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The product of two complex numbers $$1 + i\,\,\,\,\& \,\,\,\,2 - 5\,i$$ is

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The coefficient of restitution of a perfectly plastic impact is

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A stone with mass of $$0.1$$kg is catapulted as shown in the figure. The total force $${F_x}$$ (in N) exerted by the rub

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A 1 kg block is resting on a surface with coefficient of friction $$\mu $$ $$=0.1.$$ A force of $$0.8$$ $$N$$ is applied

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A streamline and an equipotential line in a flow field

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Figure shows the schematic for the measurement of velocity of air (density $$ = 1.2\,\,kg/{m^3}$$ ) through a constant -

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A pipe of $$25$$ $$mm$$ outer diameter carries steam. The heat transfer coefficient between the cylinder and surrounding

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A spherical steel ball of $$12mm$$ diameter is initially at $$100K.$$ It is slowly cooled in a surrounding of $$300K.$$

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The ratios of the laminar hydrodynamic boundary layer thickness to thermal boundary layer thickness of flows of two flui

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In a condenser of a power plant, the steam condenses at a temperature of $${60^ \circ }C.$$ The cooling water enters at

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The word Kanban is most appropriately associated with

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Cars arrive at a service station according to Poisson's distribution with a mean rate of $$5$$ per hour. The service tim

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One unit of product $${P_1}$$ requires $$3$$ $$kg$$ of resource $${R_1}$$ and $$1$$ $$kg$$ of resource $${R_2}$$. One un

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One unit of product $${P_1}$$ requires $$3$$ $$kg$$ of resource $${R_1}$$ and $$1$$ $$kg$$ of resource $${R_2}$$. One un

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Match the following criteria of material failure, under biaxial stresses $${\sigma _1}$$and $${\sigma _2}$$ and yield st

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Two identical ball bearings $$P$$ and $$Q$$ are operating at loads $$30kN$$ and $$45kN$$ respectively. The ratio of the

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Green sand mould indicates that

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A cubic casting of $$50mm$$ side undergoes volumetric solidification shrinkage and volumetric solid contraction of $$4\%

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The maximum possible draft in cold rolling of sheet increases with the

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Which one among the following welding processes uses non-consumable electrode?

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A single-point cutting tool with $${12^0}$$ rake angle is used to machine a steel work-piece. The depth of cut, $$i.e$$

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The shear strength of a sheet metal is $$300MPa.$$ The blanking force required to produce a blank of $$100$$ $$mm$$ diam

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A hole is dimension $$\phi {9^{\matrix{
{ + 0.015} \cr
{ + 0\,\,\,\,\,\,\,\,\,\,} \cr
} }}\,mm.$$ The corres

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A simply supported beam $$PQ$$ is loaded by a moment of $$1$$ $$kN-m$$ at the mid-span of the beam as shown in the figur

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A torque $$T$$ is applied at the free end of a stepped rod of circular cross-sections as shown in the figure. The shear

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A column has a rectangular cross-section of 10 mm $$ \times $$ 20 mm and a length of 1 m. The slenderness ratio of the c

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A double - parallelogram mechanism is shown in the figure. Note that PQ is a single link. The mobility of the mechanism

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For the four - bar linkage shown in the figure, the angular velocity of link AB is $$1$$ rad/s. The length of link CD is

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A disc of mass m is attached to a spring of stiffness $$k$$ as shown in the figure. The disc rolls without slipping on

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A mass of $$1$$ kg is attached to two identical springs each with stiffness $$k=20kN/m$$ as shown in the figure. Under f

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The temperature and pressure of air in a large reservoir are $$400$$ $$K$$ and $$3$$ bar respectively. A converging dive

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The temperature and pressure of air in a large reservoir are $$400$$ $$K$$ and $$3$$ bar respectively. A converging dive

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The contents of a well-insulated tank are heated by a resistor of $$23\Omega $$ in which $$10A$$ current is flowing. Con

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A pump handling a liquid raises its pressure from $$1$$ bar to $$30$$ $$bar.$$ Take the density of the liquid as $$990$$

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Heat and work are

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In an experimental set-up, air flows between two stations $$P$$ and $$Q$$ adiabatically. The direction of flow depends o

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In an experimental set-up, air flows between two stations $$P$$ and $$Q$$ adiabatically. The direction of flow depends o

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The values of enthalpy of steam at the inlet and outlet of a steam turbine in a Rankine cycle are $$2800$$ $$kJ/kg$$ and

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