GATE ME 2009

## GATE ME

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

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

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

View Question 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

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

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

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

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

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

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

View Question 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

View Question Match the following

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

View Question Friction at the tool - chip interface can be reduced by

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

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

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

View Question Match the following

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

View Question