GATE 2013 Mechanical Engineering
39 questions across 1 session
A steel bar $$200$$ $$mm$$ in diameter is turned at a feed of $$0.25$$ $$mm/rev$$ with a depth of cut of $$4$$ $$mm.$$ The rotational speed of the work piece is $$160$$ $$rpm.$$ Th...
In a rolling process, the state of stress of the material undergoing deformation is
Cylindrical pins of $${25^{\matrix{ { + 0.020} \cr { + 0.010} \cr } }}\,\,mm$$ diameter are electroplated in a shop. Thickness of the plating is $$30 \pm 0.2$$ micron. Neglecting g...
The eigen values of a symmetric matrix are all
A linear programming problem is shown below. $$\eqalign{ & Maximize\,\,\,\,3x + 7y \cr & Subject\,\,to\,\,\,3x + 7y \le 10 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,4x...
Two large diffuse gray parallel plates, separated by a small distance, have surface temperatures of $$400$$ $$K$$ and $$300$$ $$K.$$ If the emissivities of the surfaces are $$0.8$$...
Water (specific heat, $${c_p} = 4.18\,\,kJ/kgK$$ ) enters a pipe at a rate of $$0.01$$ $$kg/s$$ and temperature of $${20^ \circ }C.$$ The pipe, of diameter $$50$$ $$mm$$ and length...
The partial differential equation $$\,\,{{\partial u} \over {\partial t}} + u{{\partial u} \over {\partial x}} = {{{\partial ^2}u} \over {\partial {x^2}}}\,\,\,$$ is a
A bar is subjected to fluctuating tensile load from $$20$$ $$kN$$ to $$100$$ $$kN.$$ The material has yield strength of $$240$$ $$MPa$$ and endurance limit in reversed bending is $...
Let $$X$$ be a normal random variable with mean $$1$$ and variance $$4.$$ The probability $$P\left\{ {X < 0} \right\}$$ is
In a $$CAD$$ package, mirror image of a $$2D$$ points $$P(5, 10)$$ is to be obtained about a line which passes through the origin and makes an angle of $${45^ \circ }$$ countercloc...
The value of the definite integral $$\int_1^e {\sqrt x \ln \left( x \right)dx} $$ is
A cylinder contains $$5\,\,{m^3}$$ of an ideal gas at a pressure of $$1$$ bar. This gas is compressed in a reversible isothermal process till its pressure increases to $$5$$ bar. T...
Consider one-dimensional steady state heat conduction along x-axis $$\left( {0 \le x \le L} \right),$$ through a planewall with the boundary surfaces $$(x=0$$ and $$x=L)$$ maintain...
In order to have maximum power from a Pelton turbine, the bucket speed must be
The pressure, temperature and velocity of air flowing in a pipe are $$5$$ $$bar,$$ $$500$$ $$K$$ and $$50$$ $$m/s,$$ respectively. The specific heats of air at constant pressure an...
A cube shaped casting solidifies in $$5$$ min. The solidification time in min for a cube of the same material, which is $$8$$ times heavier than the original casting, will be
In simple exponential smoothing forecasting, to give higher weightage to recent demand information, the smoothing constant must be close to
Choose the CORRECT set of functions, which are linearly dependent.
Water (specific heat, $${c_p} = 4.18\,\,kJ/kgK$$ ) enters a pipe at a rate of $$0.01$$ $$kg/s$$ and temperature of $${20^ \circ }C.$$ The pipe, of diameter $$50$$ $$mm$$ and length...
The function $$f(t)$$ satisfies the differential equation $${{{d^2}f} \over {d{t^2}}} + f = 0$$ and the auxiliary conditions, $$f\left( 0 \right) = 0,\,{{df} \over {dt}}\left( 0 \r...
A steel ball of diameter $$60$$ $$mm$$ is initially in thermal equilibrium at $${1030^ \circ }C$$ in a furnace. It is suddenly removed from the furnace and cooled in ambient air at...
Two cutting tools are being compared for a machining operation. The tool life equations are: $$\eqalign{ & \,\,\,\,\,\,\,\,\,\,\,\,Carbi{\mathop{\rm de}\nolimits} \,\,tool:\,\,\,\,...
For a ductile material, toughness is a measure of
The following surface integral is to be evaluated over a sphere for the given steady velocity vector field $$F = xi + yj + zk$$ defined with respect to a Cartesian coordinate syste...
The probability that a student knows the correct answer to a multiple choice question is $${2 \over 3}$$. If the student does not know the answer, then the student guesses the answ...
Customers arrive at a ticket counter at a rate of $$50$$ per hr and tickets are issued in the order of their arrival. The average time taken for issuing a ticket is $$1$$ $$min.$$...
A metric thread of pitch $$2$$ $$mm$$ and thread angle 60° is inspected for its pitch diameter using 3-wire method. The diameter of the best size wire in mm is $${60^ \circ }$$ is...
For steady, fully developed flow inside a straight pipe of diameter $$D,$$ neglecting gravity effects, the pressure drop $$\Delta p$$ over a length $$L$$ and the wall shear stress...
In orthogonal turning of a bar of $$100$$ $$mm$$ diameter with a feed of $$0.25$$ $$min/rev,$$ depth of cut of $$4$$ $$mm$$ and cutting velocity of $$90$$ $$m/min,$$ it is observed...
Water is coming out from a tap and falls vertically downwards. At the tap opening, the stream diameter is $$20$$ $$mm$$ with uniform velocity of $$2$$ $$m/s.$$ Acceleration due to...
In orthogonal turning of a bar of $$100$$ $$mm$$ diameter with a feed of $$0.25$$ $$min/rev,$$ depth of cut of $$4$$ $$mm$$ and cutting velocity of $$90$$ $$m/min,$$ it is observed...
The solution to the differential equation $$\,{{{d^2}u} \over {d{x^2}}} - k{{du} \over {dx}} = 0\,\,\,$$ where $$'k'$$ is a constant, subjected to the boundary conditions $$\,\,u\l...
A simply supported beam of length $$L$$ is subjected to a varying distributed load $$\sin \left( {3\pi x/L} \right)N{m^{ - 1}},$$ where the distance $$x$$ is measured from the left...
A long thin walled cylindrical shell, closed at both the ends, is subjected to an internal pressure. The ratio of the hoop stress (circumferential stress) to longitudinal stress de...
If two nodes are observed at a frequency of $$1800$$ rpm during whirling of a simply supported long slender rotating shaft, the first critical speed of the shaft in rpm is
A flywheel connected to a punching machine has to supply energy of $$400$$ Nm while running at a mean angular speed of $$20$$ rad/s. If the total fluctuation of speed is not to exc...
Two threaded bolts A and B of same material and length are subjected to identical tensile load. If the elastic strain energy stored in bolt A is 4 times that of bolt B and the mean...
A single degree of freedom system having mass $$1$$ $$kg$$ and stiffness $$10$$ $$kN/m$$ initially at rest is subjected to an impulse force of magnitude $$5$$ $$kN$$ for $${10^{ -...