GATE ME 2011
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## 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 $${x_1} + {x_2} = 0 View Question A series expansion for the function$$\sin \theta $$is _______. View Question If$$f(x)$$is even function and a is a positive real number , then$$\int\limits_{ - a}^a {f\left( x \right)dx\,\,} $View Question What is $$\mathop {Lim}\limits_{\theta \to 0} {{\sin \theta } \over \theta }\,\,$$ equal to ? View Question An unbiased coin is tossed five times. The outcome of each loss is either a head or a tail. Probability of getting at le View Question Consider the differential equation $${{dy} \over {dx}} = \left( {1 + {y^2}} \right)x\,\,.$$ The general solution with c View Question The integral $$\,\int\limits_1^3 {{1 \over x}\,\,dx\,\,\,}$$ when evaluated by using simpson's $$1/{3^{rd}}$$ rule on t View Question The product of two complex numbers $$1 + i\,\,\,\,\&amp; \,\,\,\,2 - 5\,i$$ is View Question The coefficient of restitution of a perfectly plastic impact is View Question 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 View Question A 1 kg block is resting on a surface with coefficient of friction $$\mu$$ $$=0.1.$$ A force of $$0.8$$ $$N$$ is applied View Question A streamline and an equipotential line in a flow field View Question Figure shows the schematic for the measurement of velocity of air (density $$= 1.2\,\,kg/{m^3}$$ ) through a constant - View Question A pipe of $$25$$ $$mm$$ outer diameter carries steam. The heat transfer coefficient between the cylinder and surrounding View Question A spherical steel ball of $$12mm$$ diameter is initially at $$100K.$$ It is slowly cooled in a surrounding of $$300K.$$ View Question The ratios of the laminar hydrodynamic boundary layer thickness to thermal boundary layer thickness of flows of two flui View Question In a condenser of a power plant, the steam condenses at a temperature of $${60^ \circ }C.$$ The cooling water enters at View Question The word Kanban is most appropriately associated with View Question Cars arrive at a service station according to Poisson's distribution with a mean rate of $$5$$ per hour. The service tim View Question One unit of product $${P_1}$$ requires $$3$$ $$kg$$ of resource $${R_1}$$ and $$1$$ $$kg$$ of resource $${R_2}$$. One un View Question One unit of product $${P_1}$$ requires $$3$$ $$kg$$ of resource $${R_1}$$ and $$1$$ $$kg$$ of resource $${R_2}$$. One un View Question Match the following criteria of material failure, under biaxial stresses $${\sigma _1}$$and $${\sigma _2}$$ and yield st View Question Two identical ball bearings $$P$$ and $$Q$$ are operating at loads $$30kN$$ and $$45kN$$ respectively. The ratio of the View Question Green sand mould indicates that View Question A cubic casting of $$50mm$$ side undergoes volumetric solidification shrinkage and volumetric solid contraction of $$4\% View Question The maximum possible draft in cold rolling of sheet increases with the View Question Which one among the following welding processes uses non-consumable electrode? View Question A single-point cutting tool with$${12^0}$$rake angle is used to machine a steel work-piece. The depth of cut,$$i.e$$View Question The shear strength of a sheet metal is$$300MPa.$$The blanking force required to produce a blank of$$100mm$$diam View Question A hole is dimension$$\phi {9^{\matrix{ { + 0.015} \cr { + 0\,\,\,\,\,\,\,\,\,\,} \cr } }}\,mm.$$The corres View Question A simply supported beam$$PQ$$is loaded by a moment of$$1kN-m$$at the mid-span of the beam as shown in the figur View Question A torque$$T$$is applied at the free end of a stepped rod of circular cross-sections as shown in the figure. The shear View Question A column has a rectangular cross-section of 10 mm$$ \times $$20 mm and a length of 1 m. The slenderness ratio of the c View Question A double - parallelogram mechanism is shown in the figure. Note that PQ is a single link. The mobility of the mechanism View Question For the four - bar linkage shown in the figure, the angular velocity of link AB is$$1$$rad/s. The length of link CD is View Question A disc of mass m is attached to a spring of stiffness$$k$$as shown in the figure. The disc rolls without slipping on View Question A mass of$$1$$kg is attached to two identical springs each with stiffness$$k=20kN/m$$as shown in the figure. Under f View Question The temperature and pressure of air in a large reservoir are$$400K$$and$$3$$bar respectively. A converging dive View Question The temperature and pressure of air in a large reservoir are$$400K$$and$$3$$bar respectively. A converging dive View Question The contents of a well-insulated tank are heated by a resistor of$$23\Omega $$in which$$10A$$current is flowing. Con View Question A pump handling a liquid raises its pressure from$$1$$bar to$$30bar.$$Take the density of the liquid as$$990$$View Question Heat and work are View Question In an experimental set-up, air flows between two stations$$P$$and$$Q$$adiabatically. The direction of flow depends o View Question In an experimental set-up, air flows between two stations$$P$$and$$Q$$adiabatically. The direction of flow depends o View Question The values of enthalpy of steam at the inlet and outlet of a steam turbine in a Rankine cycle are$$2800kJ/kg$\$ and
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