GATE 2012 Mechanical Engineering
39 questions across 1 session
In a $$DC$$ $$arc$$ welding operating, the length characteristic was obtained as $${V_{arc}} = 20 + 5l$$ where the $$arc$$ length $$l$$ was varied between $$5mm$$ and $$7mm.$$ Here...
A $$CNC$$ vertical milling machine has to cut a straight slot of $$10$$ $$mm$$ width and $$2$$ $$mm$$ depth by a cutter of $$10$$ $$mm$$ diameter between points $$(0, 0)$$ and $$(1...
Consider the differential equation $$\,\,{x^2}{{{d^2}y} \over {d{x^2}}} + x{{dy} \over {dx}} - 4y = 0\,\,\,$$ with the boundary conditions of $$\,\,y\left( 0 \right) = 0\,\,\,$$ an...
$$\,\mathop {Lim}\limits_{x \to 0} \left( {{{1 - \cos x} \over {{x^2}}}} \right)$$ is
Calculate the punch size in $$mm,$$ for a circular blanking operation for which details are given below. Size of the blank $$25$$ $$mm$$ Thickness of the sheet $$2$$ $$mm$$ Radial...
$$x+2y+z=4, 2x+y+2z=5, x-y+z=1$$ The system of algebraic equations given above has
At $$x=0,$$ the function $$f\left( x \right) = {x^3} + 1$$ has
Consider the function $$f\left( x \right) = \left| x \right|$$ in the interval $$\,\, - 1 \le x \le 1.\,\,\,$$ At the point $$x=0, f(x)$$ is
A solid circular shaft needs to be designed to transmit a torque of $$50$$ $$N.m.$$ If the allowable shear stress of the material is $$140$$ $$MPa,$$ assuming a factor of safety of...
In an interchangeable assembly, shafts of size $${25.000^{\matrix{ { + 0.040} \cr { - 0.010} \cr } }}\,\,mm$$ mate with holes of size $${25.000^{\matrix{ { + 0.030} \cr { + 0.020}...
A solid cylinder of diameter $$100$$ $$mm$$ and height $$50$$ $$mm$$ is forged between two frictionless flat dies to a height of $$25$$ $$mm.$$ The percentage change in diameter is
Which one of the following configurations has the highest fin effectiveness?
In a single pass drilling operation, a through hole of $$15$$ $$mm$$ diameter is to be drilled in a steel plate of $$50$$ $$mm$$ thickness. Drill spindle speed is $$500$$ $$rpm,$$...
An automobile plant contracted to buy shock absorbers from two suppliers $$X$$ and $$Y$$. $$X$$ supplies $$60$$% and $$Y$$ supplies $$40$$% of the shock absorbers. All shock absorb...
For the matrix $$A = \left[ {\matrix{ 5 & 3 \cr 1 & 3 \cr } } \right],$$ ONE of the normalized eigen vectors is given as
A box contains $$4$$ red balls and $$6$$ black balls. Three balls are selected randomly from the box one after another, without replacement. The probability that the selected set c...
Air enters an adiabatic nozzle at $$300$$ $$kPa,$$ $$500$$ $$K$$ with a velocity of $$10$$ $$m/s.$$ It leaves the nozzle at $$100$$ $$kPa$$ with a velocity of $$180$$ $$m/s.$$ The...
An ideal gas of mass $$m$$ and temperature $${T_1}$$ undergoes a reversible isothermal process from an initial pressure $${P_1}$$ to final pressure $$P{}_2.$$ The heat loss during...
A political party orders an arch for the entrance to the ground in which the annual convention is being held. The profile of the arch follows the equation $$y = 2x\,\,\, - 0.1{x^2}...
Steam enters an adiabatic turbine operating at steady state with an enthalpy of $$3251.0kJ/kg$$ and leaves as a saturated mixture at $$15$$ $$kPa$$ with quality (dryness fraction )...
Water $$\left( {{C_p} = 4.18\,kJ/kg.K} \right)$$ at $${80^ \circ }C$$ enters a counter flow heat exchanger with a mass flow rate of $$0.5kg/s.$$ Air $$\left( {{C_p} = 1\,kJ/kg.\,K}...
An incompressible fluid flows over a flat plate with zero pressure gradient. The boundary layer thickness is $$1mm$$ at a location where the Reynolds number is $$1000$$. If the vel...
For an opaque surface, the absorptivity $$\left( \alpha \right),$$ transmissivity $$\left( \tau \right)$$ and reflectivity $$\left( \rho \right)$$ are related by the equation:
For the spherical surface $${x^2} + {y^2} + {z^2} = 1,$$ the unit outward normal vector at the point $$\left( {{1 \over {\sqrt 2 }},{1 \over {\sqrt 2 }},0} \right)$$ is given by
Which one of the following is NOT a decision taken during the aggregate production planning stage?
The homogeneous state of stress for a metal part undergoing plastic deformation is $$$T = \left( {\matrix{ {10} & 5 & 0 \cr 5 & {20} & 0 \cr 0 & 0 & { - 10} \cr } } \right)$$$ Wher...
In a single pass rolling process using $$410mm$$ diameter steel rollers, a strip of width $$140mm$$ and thickness $$8mm$$ undergoes $$10\% $$ reduction of thickness. The angle of b...
The area enclosed between the straight line $$y=x$$ and the parabola $$y = {x^2}$$ in the $$x-y$$ plane is
The inverse Laplace transform of the function $$F\left( s \right) = {1 \over {s\left( {s + 1} \right)}}$$ is given by
A circular solid disc of uniform thickness $$20mm,$$ radius $$200mm$$ and $$mass$$ $$20kg,$$ is used as a fly wheel. If it rotates at $$600$$ $$rpm,$$ the kinetic energy of the fly...
A $$200$$ mm long, stress free rod at room temperature is held between two immovable rigid walls. The temperature of the rod is uniformly raised by $$250$$ o C. If the Young's modu...
The following are the data for two crossed helical gears used for speed reduction: Gear $$I:$$ Pitch circle diameter in the plane of rotation 80mm and helix angle 30 o Gear $$II:$$...
A solid steel cube constrained on all six faces is heated so that the temperature rises uniformly by $$\Delta T.$$ If the thermal coefficient of the material is $$\alpha $$, young'...
A cantilever beam of length $$L$$ is subjected to a moment $$M$$ at the free end. The moment of inertia of the beam cross section about the neutral axis is $$I$$ and the Young’s mo...
A solid circular shaft needs to be designed to transmit a torque of 50N.m. If the allowable shear stress of the material is $$140$$MPa, assuming a factor of safety of $$2,$$ the mi...
The state of stress at a point under plane stress condition is $${\sigma _{xx}} = 40\,$$ MPa, $${\sigma _{yy}} = 100\,$$ MPa & $${\tau _{xy}} = 40$$ MPa. The radius of the Mohr's c...
For a long slender column of uniform cross section, the ratio of critical buckling load for the case with both ends clamped to the case with both ends hinged is
A thin walled spherical shell is subjected to an internal pressure. If the radius of the shell is increased by 1% and the thickness is reduced by 1%, with the internal pressure rem...
Air enters an adiabatic nozzle at $$300$$ $$kPa,$$ $$500$$ $$K$$ with a velocity of $$10$$ $$m/s.$$ It leaves the nozzle at $$100$$ $$kPa$$ with a velocity of $$180$$ $$m/s.$$ The...