GATE ME 2009

## GATE ME

For a matrix $$\left[ M \right] = \left[ {\matrix{
{{3 \over 5}} & {{4 \over 5}} \cr
x & {{3 \over 5}}

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The area enclosed between the curves $${y^2} = 4x\,\,$$ and $${{x^2} = 4y}$$ is

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The distance between the origin and the point nearest to it on the surface $$\,\,{z^2} = 1 + xy\,\,$$ is

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The divergence of the vector field $$\,3xz\widehat i + 2xy\widehat j - y{z^2}\widehat k$$ at a point $$(1,1,1)$$ is equa

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If three coins are tossed simultaneously, the probability of getting at least one head is

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The standard deviation of a uniformly distributed random variable $$b/w$$ $$0$$ and $$1$$ is

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The solution of $$x{{dy} \over {dx}} + y = {x^4}$$ with condition $$y\left( 1 \right) = {6 \over 5}$$

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The inverse Laplace transform of $${1 \over {\left( {{s^2} + s} \right)}}$$ is

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An analytic function of a complex variable $$z = x + i\,y$$ is expressed as
$$f\left( z \right) = u\left( {x,y} \right)

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A block weighing 981 $$N$$ is resting on a horizontal surface. The coefficient of friction between the block and the hor

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A uniform rigid rod of mass $$M$$ and length $$L$$ is hinged at one end as shown in theadjacent figure. A force P is app

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You are asked to evaluate assorted fluid flows for their suitability in a given laboratory application. The following th

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Consider steady, incompressible and irrotational flow through a reducer in a horizontal pipe where the diameter is reduc

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The velocity profile of a fully developed laminar flow in a straight circular pipe, as shown in the figure, is given by

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Water at $${25^0}C$$ is flowing through a $$1.0km$$ long $$G.I.$$ pipe of $$200mm$$ diameter at the rate of $$0.07$$ $${

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Consider steady-state heat conduction across the thickness in a plane composite wall as shown in fig exposed to convecti

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A coolant fluid at $${30^ \circ }C$$ flows over a heated flat plate maintained at a constant temperature of $${100^ \cir

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Radiative heat transfer is intended between the inner surfaces of two very largen isothermal parallel metal plates. Whil

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Radiative heat transfer is intended between the inner surfaces of two very largen isothermal parallel metal plates. Whil

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In a parallel flow heat exchanger operating under steady state, the heat capacity rates (product of specific heat at con

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A company uses $$2555$$ units of an item annually. Delivery lead time is $$8$$ days. The recorder point (in number of un

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The expected time $$\left( {{t_e}} \right)$$ of a $$PERT$$ activity in terms of optimistic time $$\left( {{t_0}} \right)

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Consider the following network
The optimistic time, most likely time and pessimistic time of all the activities are
giv

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Consider the following network
The optimistic time, most likely time and pessimistic time of all the activities are
giv

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Which of the following forecasting methods takes a fraction of forecast error into account for the next period forecast?

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Consider the following Linear Programming problem $$(LLP)$$
Maximize: $$Z = 3{x_1} + 2{x_2}$$
$$\,\,$$ Subject $$\,\,$$

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Six jobs arrived in a sequence as given below:
Average flow time (in days) for the above jobs using Shortest Processi

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A forged steel link with uniform diameter of $$30mm$$ at the centre is subjected to an axial force that varies from $$40

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A $${20^ \circ }$$ full depth involute spur pinion of $$4mm$$ module and $$21$$ teeth is to transmit $$15kW$$ at $$960rp

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A $${20^ \circ }$$ full depth involute spur pinion of $$4mm$$ module and $$21$$ teeth is to transmit $$15kW$$ at $$960rp

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Two streams of liquid metal, which are not hot enough to fuse properly, result into a casting defect known as

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Match the following

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The minimum shear strain in orthogonal turning with a cutting tool of zero rake angle is

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Friction at the tool - chip interface can be reduced by

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In a machining experiment, tool life was found to vary with the cutting speed in the following manner
The exponent $$(

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In a machining experiment, tool life was found to vary with the cutting speed in the following manner
What is percenta

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What are the upper and lower limits of the shaft represented by $$60{f_8}$$?
Use the following data:
Diameter $$60$$ lie

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Match the following

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If the principal stresses in a plane stress problem are $${\sigma _1}$$ $$= 100$$ MPa, $${\sigma _2}$$ $$= 40$$ MPa, th

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A solid circular shaft of diameter $$d$$ is subjected to a combined bending moment, $$M$$ and torque, $$T.$$ The materia

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A solid shaft of diameter, $$d$$ and length, $$L$$ is fixed at both the ends. A torque, $${T_0}$$ is applied at a distan

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A triangular-shaped cantilever beam of uniform- thickness is shown in the figure. The young's modulus of the material of

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A frame of two arms of equal length $$L$$ is shown in the adjacent figure. The flexural rigidity of each arm of the fram

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A triangular-shaped cantilever beam of uniform- thickness is shown in the figure. The young's modulus of the material of

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A simple quick return mechanism is shown in the figure. The forward to return ratio of the quick return mechanism is 2 :

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Match the approaches given below to perform stated kinematics/dynamics analysis of machine
Analysis
$$P.$$ Continuous re

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An epicyclic gear train is shown schematically in the adjacent figure The sun gear 2 on the input shaft is a 20 teeth ex

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The rotor shaft of a large electric motor supported between short bearings at both the ends shows a deflection of $$1.8$

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An automotive engine weighing $$240$$ kg is supported on four springs with linear characteristics. Each of the front two

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A vehicle suspension system consists of a spring and a damper. The stiffness of the spring is $$3.6$$ kN/m and the damp

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A compressor undergoes a reversible, steady flow process. The gas at inlet and outlet of the compressor is designated as

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A frictionless piston-cylinder device contains a gas initially at $$0.8MPa$$ and $$0.015$$ $${m^3}.$$ It expands quasi-s

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If a closed system is undergoing an irreversible process, the entropy of the system

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The inlet and the outlet conditions of steam for an adiabatic steam turbine are as indicated in the figure. The notation

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The inlet and the outlet conditions of steam for an adiabatic steam turbine are as indicated in the figure. The notation

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