GATE 2007 Mechanical Engineering
61 questions across 1 session
In orthogonal turning of a low carbon steel bar of diameter $$150mm$$ with uncoated carbide tool, the cutting velocity is $$90m/min,$$ The feed is $$0.24mm/rev$$ and the depth of c...
Which of the following is a solid state welding process.
Two metallic sheets, each of $$2.0$$ $$mm$$ thickness are welded in lap joint configuration by resistance spot welding at a welding current of $$10$$ $$KA$$ and welding time of $$1...
Capacities of production of an item over $$3$$ consecutive months in regular time are $$100,$$ $$100$$ and $$80$$ and in overtime are $$20,$$ $$20$$ and $$40.$$ The demands over th...
The temp distribution within the Laminar thermal boundary layer over a heated isothermal flat plate is given by $$\left( {T - {T_w}} \right)/\left( {{T_\infty } - {T_w}} \right) =...
The number of linearly independent eigen vectors of $$\left[ {\matrix{ 2 & 1 \cr 0 & 2 \cr } } \right]$$ is
Consider steady laminar incompressible axi-symmetric fully developed viscous flow through a straight circular pipe of constant cross - sectional area at a Reynolds number of $$5.$$...
If $$\,\,\,y = x + \sqrt {x + \sqrt {x + \sqrt {x + .....\alpha } } } \,\,\,$$ then $$y(2)=$$ __________.
A hole is specified as $${40^{\matrix{ {0.050} \cr {0.000} \cr } }}\,\,mm.$$ The mating shaft has a clearance fit with minimum clearance of $$0.01mm.$$ The tolerance on the shaft i...
If a square matrix $$A$$ is real and symmetric then the eigen values
The average heat transfer coefficient on a thin hot vertical plate suspended in still air can be determined from observations of the change in plate temperature with time as it coo...
In open die forging, a disc of diameter $$200mm$$ height $$60mm$$ is compressed without any barreling effect. The final diameter of the disc is $$400mm.$$ The true strain is
A thin spherical pressure vessel of $$200mm$$ diameter and $$1mm$$ thickness is subjected to an internal pressure varying from $$4$$ to $$8MPa.$$ Assume that the yield, ultimate an...
The solution of $${{d\,y} \over {d\,x}} = {y^2}$$ with initial value $$y(0)=1$$ is bounded in the interval is
In orthogonal turning of low carbon steel pipe with principal cutting edge angle of $$90,$$ the main cutting force is $$1000$$$$N$$ and the feed force is $$800N.$$ The shear angle...
Newton's law of viscosity states that the shear stress in a fluid is proportional to :
Volume of a cube of a side $$''l''$$ and volume of sphere of radius $$' r '$$ are equal. Both the cube and the sphere are solid and same material. They are being cast. The ratio of...
The partial differential equation $$\,\,{{{\partial ^2}\phi } \over {\partial {x^2}}} + {{{\partial ^2}\phi } \over {\partial {y^2}}} + {{\partial \phi } \over {\partial x}} + {{\p...
The maximum level of inventory of item is $$100$$ and it is achieved with infinite replenishment rate. The inventory becomes zero over one and half month due to consumption at a un...
In a steady flow through a nozzle, the flow velocity on the nozzle axis is given by $$u = {u_0}\left( {1 + 3x/L} \right),\,\,$$ where $$x$$ is the distance along the axis of the no...
A low carbon steel bar of $$147$$ $$mm$$ diameter with length of $$630$$ $$mm$$ is being turned with uncoated carbide insert. The observed tool lives are $$24$$ and $$12$$ for cutt...
Oil flows through a $$200mm$$ diameter horizontal cast iron pipe (friction factor, $$f=0.0225$$) of length $$500m.$$ The volumetric flow rate is $$0.2{m^3}/s.$$ The head loss (in $...
A low carbon steel bar of $$147$$ $$mm$$ diameter with length of $$630$$ $$mm$$ is being turned with uncoated carbide insert. The observed tool lives are $$24$$ and $$12$$ for cutt...
Consider steady one-dimensional heat flow in a plate of $$20mm$$ thickness with a uniform heat generation of $$80MW/{m^3}.$$ The left and right faces are kept at constant temperatu...
In a counter flow heat exchanger, hot fluid enters at $${65^ \circ }C$$ and cold fluid leaves at $${30^ \circ }C.$$ mass flow rate of the hot fluid is $$1$$ $$Kg/s$$ and that of co...
In a machine shop, pins of $$15mm$$ diameter are produced at a rate of $$1000$$ per month and the same is consumed at a rate of $$500$$ per month. The production and consumption co...
A $$DC$$ welding machine with a linear power source characteristic provides open circuit voltage of $$80V$$ and short circuit current of $$800A,$$ during welding with the machine ,...
The thickness of metallic sheet is reduced from an initial value of $$16mm$$ to a final value of $$10mm$$ in one single pass rolling with a pair of cylindrical rollers each of diam...
A gear set has a pinion with $$20$$ teeth and a gear with $$40$$ teeth. The pinion runs at $$30rev/s$$ and transmits a power of $$20KW$$. The teeth are on the $${20^ \circ }$$ full...
During inelastic collision of two particles, which one of the following is conserved?
If a particular $$Fe$$-$$C$$ alloy contains less than $$0.83$$% carbon, it is called
Consider steady one-dimensional heat flow in a plate of $$20mm$$ thickness with a uniform heat generation of $$80MW/{m^3}.$$ The left and right faces are kept at constant temperatu...
Let $$X$$ and $$Y$$ be two independent random variables. Which one of the relations $$b/w$$ expectation $$(E),$$ variance $$\left( {{V_{ar}}} \right)$$ and covariance $$\left( {{C_...
In orthogonal turning of medium carbon steel, the specific machining energy is $$2$$ $$kJ/m{m^3},$$ the cutting velocity, feed and depth of cut are $$120m/min,$$ $$0.2mm/rev$$ and...
An irreversible heat engine extracts heat from a high temperature source at a rate of $$100kW$$ and rejects heat to a sink at a rate of $$50kW.$$ The entire work output of the heat...
Water has a critical specific volume of $$0.003155$$ $${m^3}/kg.$$ A closed and rigid steel tank of volume $$0.025{m^3}$$ contains a mixture of water and steam at $$0.1MPa.$$ The m...
A gear set has a pinion with $$20$$ teeth and a gear with $$40$$ teeth. The pinion runs at $$30rev/s$$ and transmits a power of $$20KW$$. The teeth are on the $${20^ \circ }$$ full...
Which combination of the following statements is correct? The incorporation of re-heater in a steam power plant. $$P:$$ always increases the thermal efficiency of the plant. $$Q:$$...
Which of the following relationships is valid only for reversible process undergone by a closed system of simple compressible substance (neglect changes in kinetic and potential en...
A gear set has a pinion with $$20$$ teeth and a gear with $$40$$ teeth. The pinion runs at $$30rev/s$$ and transmits a power of $$20KW$$. The teeth are on the $${20^ \circ }$$ full...
A heat transformer is a device that transfers a part of the heat, supplied to it at an intermediate temperature, to a high temperature reservoir while rejecting the remaining part...
Building has to be maintained at $${21^ \circ }C$$ (dry bulb) and $${14.5^ \circ }C$$ (wet bulb). The dew point temp under these conditions is $${10.17^0}C$$. The outside temp is $...
$$\mathop {Lim}\limits_{x \to 0} {{{e^x} - \left( {1 + x + {{{x^2}} \over 2}} \right)} \over {{x^3}}} = $$
A model of a hydraulic turbine is tested at a head of $$1/{4^{th}}$$ of that under which the full scale turbine works. The diameter of the model is half of that of the full scale t...
The inlet angle of runner blades of a Francis turbine is $${90^0}.$$ The blades are so shaped that the tangential component of velocity at blade outlet is zero. The flow velocity r...
Which combination of the following statements about steady incompressible forced vortex flow is correct? P: Shear stress is zero at all points in the flow. Q: Velocity is directly...
The area of a triangle formed by the tips of vectors $$\overrightarrow a ,\overrightarrow b $$ and $$\overrightarrow c $$ is
Consider an incompressible laminar boundary layer flow over a flat plate of length $$L$$, aligned with the direction of an incoming uniform free stream. If $$F$$ is the ratio of th...
A ball bearing operating at a load $$F$$ has $$8000$$hours of life. The life of the bearing, in hours, when the load is doubled to $$2F$$ is
The minimum value of function $$\,\,y = {x^2}\,\,$$ in the interval $$\,\,\left[ {1,5} \right]\,\,$$ is
If $$\phi (x,y)$$ and $$\psi (x,y)$$ are function with continuous 2 nd derivatives then $$\phi (x,y)\, + \,i\psi (x,y)$$ can be expressed as an analytic function of x +iy ($$i = \s...
Which type of motor is used in axial or spindle drives of $$CNC$$ m/c tools
The force requirement in a blanking operation of low carbon steel sheet is $$5.0$$ $$kN.$$ The thickness of the sheet is $$'t'$$ and diameter of the blanked part is $$'d'.$$ For th...
If $$F(s)$$ is the Laplace transform of the function $$f(t)$$ then Laplace transform of $$\int\limits_0^t {f\left( x \right)dx} $$ is
Which of the following engineering materials is the most suitable candidate for hot chamber die casting
A natural feed journal bearing of diameter $$50mm$$ and length $$50mm$$ operating at $$20$$ revolutions/sec carries a load of $$2kN$$. The lubricant used has a viscosity of $$20mPa...
Oil in a hydraulic cylinder is compressed from an initial volume $$2{m^3}$$ to $$1.96{m^3}$$. If the pressure of oil in the cylinder changes from $$40$$ $$MPa$$ to $$80$$ $$MPa$$ d...
A steel rod of length $$L$$ and diameter $$D$$, fixed at both ends, is uniformly heated to a temperature rise of $$\Delta T.$$ The Young's modulus is $$E$$ and the coefficient of l...
The speed of an engine varies from $$210$$ rad/s to $$190$$ rad/s. During cycle the change in kinetic energy is found to be $$400$$ Nm. The inertia of the flywheel in kgm 2 is
The equation of motion of a harmonic oscillator is given by $${{{d^2}x} \over {d{t^2}}} + 2\xi {\omega _n}{{dx} \over {dt}} + \omega _n^2\,x = 0\,\,\,$$ and the initial conditions...
For an under damped harmonic oscillator, resonance