GATE 2009 Mechanical Engineering
36 questions across 1 session
The divergence of the vector field $$\,3xz\widehat i + 2xy\widehat j - y{z^2}\widehat k$$ at a point $$(1,1,1)$$ is equal to
Radiative heat transfer is intended between the inner surfaces of two very largen isothermal parallel metal plates. While the upper plate (designated as plate $$1$$) is a black sur...
Radiative heat transfer is intended between the inner surfaces of two very largen isothermal parallel metal plates. While the upper plate (designated as plate $$1$$) is a black sur...
A company uses $$2555$$ units of an item annually. Delivery lead time is $$8$$ days. The recorder point (in number of units) to achieve optimum inventory is
In a parallel flow heat exchanger operating under steady state, the heat capacity rates (product of specific heat at constant pressure and mass flow rate) of the hot and cold fluid...
For a matrix $$\left[ M \right] = \left[ {\matrix{ {{3 \over 5}} & {{4 \over 5}} \cr x & {{3 \over 5}} \cr } } \right].$$ The transpose of the matrix is equal to the inverse of the...
The standard deviation of a uniformly distributed random variable $$b/w$$ $$0$$ and $$1$$ is
What are the upper and lower limits of the shaft represented by $$60{f_8}$$? Use the following data: Diameter $$60$$ lies in the diameter step of $$50-80$$ $$mm$$ Fundamental toler...
A forged steel link with uniform diameter of $$30mm$$ at the centre is subjected to an axial force that varies from $$40kN$$ in compression to $$160kN$$ in tension. The tensile $$\...
The minimum shear strain in orthogonal turning with a cutting tool of zero rake angle is
The solution of $$x{{dy} \over {dx}} + y = {x^4}$$ with condition $$y\left( 1 \right) = {6 \over 5}$$
You are asked to evaluate assorted fluid flows for their suitability in a given laboratory application. The following three flow choices. Expressed in terms of the two - dimensiona...
The expected time $$\left( {{t_e}} \right)$$ of a $$PERT$$ activity in terms of optimistic time $$\left( {{t_0}} \right)$$, pessimistic $$\left( {{t_p}} \right)$$ and most likely t...
Consider the following Linear Programming problem $$(LLP)$$ Maximize: $$Z = 3{x_1} + 2{x_2}$$ $$\,\,$$ Subject $$\,\,$$ to $$\eqalign{ & \,\,\,\,\,\,\,{x_1} \le 4 \cr & \,\,\,\,\,\...
If a closed system is undergoing an irreversible process, the entropy of the system
A compressor undergoes a reversible, steady flow process. The gas at inlet and outlet of the compressor is designated as state $$1$$ and state $$2$$ respectively. Potential and kin...
A frictionless piston-cylinder device contains a gas initially at $$0.8MPa$$ and $$0.015$$ $${m^3}.$$ It expands quasi-statically at constant temperature to a final volume of $$0.0...
A $${20^ \circ }$$ full depth involute spur pinion of $$4mm$$ module and $$21$$ teeth is to transmit $$15kW$$ at $$960rpm.$$ Its face width is $$25mm.$$ Given that the tooth geomet...
Friction at the tool - chip interface can be reduced by
Which of the following forecasting methods takes a fraction of forecast error into account for the next period forecast?
If three coins are tossed simultaneously, the probability of getting at least one head is
The inverse Laplace transform of $${1 \over {\left( {{s^2} + s} \right)}}$$ is
Consider steady, incompressible and irrotational flow through a reducer in a horizontal pipe where the diameter is reduced from $$20cm$$ to $$10cm.$$ The pressure in the $$20cm$$ p...
An analytic function of a complex variable $$z = x + i\,y$$ is expressed as $$f\left( z \right) = u\left( {x,y} \right) + i\,\,v\,\,\left( {x,y} \right)$$ where $$i = \sqrt { - 1}...
The area enclosed between the curves $${y^2} = 4x\,\,$$ and $${{x^2} = 4y}$$ is
A coolant fluid at $${30^ \circ }C$$ flows over a heated flat plate maintained at a constant temperature of $${100^ \circ }C$$. The boundary layer temp distribution at a given loca...
A $${20^ \circ }$$ full depth involute spur pinion of $$4mm$$ module and $$21$$ teeth is to transmit $$15kW$$ at $$960rpm.$$ Its face width is $$25mm.$$ The tangential force transm...
The distance between the origin and the point nearest to it on the surface $$\,\,{z^2} = 1 + xy\,\,$$ is
Water at $${25^0}C$$ is flowing through a $$1.0km$$ long $$G.I.$$ pipe of $$200mm$$ diameter at the rate of $$0.07$$ $${m^3}/s.$$ If value of Darcy friction factor for this pipe is...
Two streams of liquid metal, which are not hot enough to fuse properly, result into a casting defect known as
A solid circular shaft of diameter $$d$$ is subjected to a combined bending moment, $$M$$ and torque, $$T.$$ The material property to be used for designing the shaft using the rela...
An automotive engine weighing $$240$$ kg is supported on four springs with linear characteristics. Each of the front two springs have a stiffness of $$16$$ MN/m while the stiffness...
The rotor shaft of a large electric motor supported between short bearings at both the ends shows a deflection of $$1.8$$ mm in the middle of the rotor. Assuming the rotor to be pe...
A vehicle suspension system consists of a spring and a damper. The stiffness of the spring is $$3.6$$ kN/m and the damping constant of the damper is $$400$$ Ns/m. If the mass is $$...
Match the approaches given below to perform stated kinematics/dynamics analysis of machine Analysis $$P.$$ Continuous relative rotation $$Q.$$ Velocity and acceleration $$R.$$ Mobi...
If the principal stresses in a plane stress problem are $${\sigma _1}$$ $$= 100$$ MPa, $${\sigma _2}$$ $$= 40$$ MPa, the magnitude of the maximum shear stress (in MPa) wil be