GATE 2009 Production & Industrial
23 questions across 1 session
A disc of $$200$$ $$mm$$ diameter is blanked from a strip of an aluminium alloy of thickness $$3.2$$ $$mm.$$ The material shear strength to fracture is $$150$$ $$MPa.$$ The blankin...
The total derivative of the function $$'xy'$$ is
The homogeneous part of the differential equation $$\,{{{d^2}y} \over {d{x^2}}} + p{{dy} \over {dx}} + qy = r\,\,$$ ( $$p, q, r$$ are constants) has real distinct roots if
The solution of the differential equation $${{{d^2}y} \over {d{x^2}}} = 0$$ with boundary conditions (i) $${{dy} \over {dx}} = 1$$ at $$x=0$$ (ii) $${{dy} \over {dx}} = 1$$ at $$x=...
The value of the determinant $$\left| {\matrix{ 1 & 3 & 2 \cr 4 & 1 & 1 \cr 2 & 1 & 3 \cr } } \right|$$ is
The value of $${x_3}$$ obtained by solving the following system of linear equations is $$${x_1} + 2{x_2} - 2{x_3} = 4$$$ $$$2{x_1} + {x_2} + {x_3} = - 2$$$ $$$ - {x_1} + {x_2} - {x...
During the numerical solution of a first order differential equation using the Euler (also known as Euler Cauchy) method with step size $$h,$$ the local truncation error is of the...
The line integral of the vector function $$\overrightarrow F = 2x\widehat i + {x^2}\widehat j\,\,$$ along the $$x$$ - axis from $$x=1$$ to $$x=2$$ is
The pressure drop for laminar flow of a liquid in a smooth pipe at normal temperature and pressure is
Heat is being transferred convectively from a cylindrical nuclear reactor fuel rod of $$50mm$$ diameter to water at $${70^ \circ }C$$, under steady state condition, the rate of hea...
Anisotropy in rolled components is caused by
Using direct extrusion process, a round billet of $$100$$ $$mm$$ length and $$50mm$$ diameter is extruded. Considering an ideal deformation process (no friction and no redundant wo...
An orthogonal operation is carried out at $$20m/min$$ cutting speed, using a cutting tool of rake angle $$15deg$$. The chip thickness is $$0.4mm$$ and uncut chip thickness is $$0.2...
In an orthogonal machining operation , the tool life obtained is $$10min$$ at a cutting speed of $$10m/min,$$ while at $$75m/min$$ cutting speed, the tool life is $$30min$$. The va...
Hot chamber die casting is NOT suited for
An autocollimator is used to
Autogeneous gas tungsten arc welding of a steel plate is carried out with welding current of $$500A,$$ voltage of $$20V,$$ and weld speed of $$20mm/min.$$ Consider the heat transfe...
Resistance spot welding of two steel sheets is carried out in lap joint configuration by using a welding current of $$3$$ $$KA$$ and a weld time of $$0.2s.$$ A molten weld nugget o...
Resistance spot welding of two steel sheets is carried out in lap joint configuration by using a welding current of $$3$$ $$KA$$ and a weld time of $$0.2s.$$ A molten weld nugget o...
A titanium sheet of $$5.0mm$$ thickness is cut by wire cut $$EDM$$ process using a wire of $$1.0mm$$ diameter. A uniform spark gap of $$0.5mm$$ on both sides of the wire is maintai...
The total angular movement (in degrees) of a lead screw with a pitch of $$5.0mm$$ to drive the work table by a distance of $$200mm$$ in a $$NC$$ machine is
An orthogonal operation is carried out at $$20m/min$$ cutting speed, using a cutting tool of rake angle $$15deg$$. The chip thickness is $$0.4mm$$ and uncut chip thickness is $$0.2...
A solid cylinder of diameter $$D$$ and height equal to $$D,$$ and a solid cube of side $$L$$ are being sand cast by using the same material. Assuming there is no super-heat in both...