GATE 2004 Mechanical Engineering

In a $$2-D$$ $$CAD$$ package, clockwise circular arc of radius, $$5,$$ specified from $${P_1}\left( {15,10} \right)$$ to $${P_2}\left( {10,15} \right)$$ will have its center at

In a machining operation, doubling the cutting speed reduces the tool life to $$1/{8^{th}}$$ of the original value. The exponent $$n$$ in Taylor's tool life equation $$V{T^n} = C,$...

Through holes of $$10$$ $$mm$$ diameter are to be drilled in steel plate of $$20$$ $$mm$$ thickness. Drill spindle speed is $$300$$ $$rpm,$$ feed $$0.2$$ $$mm/rev$$ and drill point...

The sum of the eigen values of the matrix $$\left[ {\matrix{ 1 & 1 & 3 \cr 1 & 5 & 1 \cr 3 & 1 & 1 \cr } } \right]$$ is

If $$\,\,\,x = a\left( {\theta + Sin\theta } \right)$$ and $$y = a\left( {1 - Cos\theta } \right)$$ then $$\,\,{{dy} \over {dx}} = \,\_\_\_\_\_.$$

Gray cast iron blocks $$200 \times 100 \times 10\,\,mm$$ are to be cast in sand moulds. Shrinkage allowance for pattern making is $$1$$%. The ratio of the volume of pattern to that...

A spherical thermocouple junction of diameter $$0.706 mm$$ is to be used for the measurement of temperature of a gas stream. The convective heat transfer co-efficient on the bead s...

A maintenance service facility has Poisson arrival rates, negative exponential service time and operates on a ‘first come first served’ queue discipline. Breakdowns occur on an ave...

The volume of an object expressed in spherical co-ordinates is given by $$V = \int\limits_0^{2\pi } {\int\limits_0^{{\raise0.5ex\hbox{$\scriptstyle \pi $} \kern-0.1em/\kern-0.15em...

During the execution of a CNC part program block $$NO20\,\,\,\,GO2\,\,\,\,X45.0\,\,\,\,Y25.0\,\,\,\,R5.0.$$ The type of tool motion will be

At a hydro electric power plant site, available head and flow rate are $$24.5$$ $$m$$ and $$10.1{m^3}/s$$ respectively. If the turbine to be installed is required to run at $$4.0$$...

In a condenser, water enters at $${30^ \circ }C$$ and flows at the rate $$1500$$ $$Kg/hr.$$ The condensing steam is at a temperature of $${120^ \circ }C$$ and cooling water leaves...

A company produces two types of toys: $$P$$ and $$Q.$$ Production time of $$Q$$ is twice that of $$P$$ and the company has a maximum of $$2000$$ time units per day. The supply of r...

A company has an annual demand of $$1000$$ units, ordering cost of Rs.$$100$$/order and carrying cost of Rs.$$100$$/unit –year. If the stock-out costs are estimated to be nearly Rs...

For what value of $$x$$ will the matrix given below become singular? $$\left[ {\matrix{ 8 & x & 0 \cr 4 & 0 & 2 \cr {12} & 6 & 0 \cr } } \right]$$

$$10$$ $$mm$$ diameter holes are to be punched in a steel sheet of $$3$$ $$mm$$ thickness. Shear strength of the material is $$400\,\,N/m{m^2}$$ and penetration is $$40\% $$. Shear...

A hole of diameter $${25.00^{ + 0.01}}\,\,mm$$ is to be inspected by using GO / NO GO gages. The size of the GO plug gage should be

A centrifugal pump is required to pump water to an open water tank situated $$4$$ $$km$$ away from the location of the pump through a pipe of diameter $$0.2$$ $$m$$ having Darcy’s...

A fluid flow is represented by the velocity field $$\overrightarrow V = ax\,\overrightarrow i + ay\,\overrightarrow j ,$$ where a constant . The equation of stream line passing thr...

For air flow over a flat plate, velocity $$(U)$$ and boundary layer thickness $$\left( \delta \right)$$ can be expressed respectively, as $$${U \over {{U_\infty }}} = {3 \over 2}{y...

A steel billet of $$2000$$ $$kg$$ mass is to be cooled from $$1250$$ $$K$$ to $$450$$ $$K.$$ The heat released during this process is to be used as a source of energy. The ambient...

A gas contained in a cylinder is compressed, the work required for compression being $$5000$$ $$kJ.$$ During the process, heat interaction of $$200$$ $$kJ$$ causes the surroundings...

A solar collector receiving solar radiation at the rate of $$0.6$$$$kW/{m^2}$$ transforms it to the internal energy of a fluid at an overall efficiency of $$50\% $$. The fluid heat...

A heat engine having an efficiency of $$70\% $$ is used to drive a refrigerator having a coefficient of performance of $$5.$$ The energy absorbed from low temperature reservoir by...

One dimensional unsteady state heat transfer equation for a sphere with heat generation at the rate $$'{q_g}',$$ can be written as

Two 1 mm thick steel sheets are to be spot welded at a current of $$5000$$ $$A.$$ Assuming effective resistance to be $$200$$ micro-ohms and current flow time of $$0.2$$ second, he...

In an orthogonal cutting test on mild steel, the following data were obtained Cutting speed: $$40$$ $$m/min,$$ Depth of cut: $$0.3$$ $$mm,$$ Tool rake angle : $$ + {5^ \circ },$$ C...

An incompressible fluid (kinematic viscosity $$ = 7.4 \times {10^{ - 7}}\,\,{m^2}/s,$$ specific gravity, $$0.88$$) is held between two parallel plates. If the top plate is moved wi...

Misrun is a casting defect which occurs due to

For a fluid flow through a divergent pipe of length $$L$$ having inlet and outlet radii of $${R_1}$$ and $${R_2}$$ respectively and a constant flow rate of $$Q,$$ assuming the velo...

In a rolling process, sheet of $$25$$ $$mm$$ thickness is rolled to $$20$$ $$mm$$ thickness. Roll is of diameter $$600$$ $$mm$$ and it rotates at $$100$$ $$rpm.$$ The roll strip co...

Two mating spur gears have $$40$$ and $$120$$ teeth respectively. The pinion rotates at $$1200$$ $$rpm$$ and transmits a torque of $$20N.m.$$ The torque transmitted by gear is

In $$PERT$$ analysis a critical activity has

For a product, the forecast and the actual sales for December $$2002$$ were $$25$$ and $$20$$ respectively. If the exponential smoothing constant $$(\alpha )$$ is taken as $$0.2,$$...

A closed cylinder having a radius $$R$$ and height $$H$$ is filled with oil of density $$\rho .$$ If the cylinder is rotated about its axis at an angular velocity of $$\omega $$ ,...

A vibrating machine is isolated from the floor using springs. If the ratio of excitation frequency of vibration of machine to the natural frequency of the isolation system is equal...

A uniform, slender cylindrical rod is made of a homogeneous and isotropic material. The rod rests on a frictionless surface. The rod is heated uniformly. If the radial and longitud...

Match the following with respect to spatial mechanism. Type of Joint $$P.$$ Revolute $$Q.$$ Cylindrical $$R.$$ Spherical Motion constrained $$1.$$ Three $$2.$$ Five $$3.$$ Four $$4...

In terms of Poisson's ratio $$\left( \mu \right)$$ the ratio of Young's Modulus $$(E)$$ to Shear Modulus $$(G)$$ of elastic materials is

A solid circular shaft of $$60$$ mm diameter transmits a torque of $$1600$$ N - m. The value of maximum shear developed is