GATE 2005 Mechanical Engineering
43 questions across 1 session
A lot had $$10$$% defective items. Ten items are chosen randomly from this lot. The probability that exactly $$2$$ of the chosen items are defective is
The strength of a brazed joint
A simple pendulum of length 5m, with a bob of mass 1 kg, is in simple harmonic motion. As it passes through its mean position, the bob has a speed of 5m/s. the net force on the bob...
In case of one dimensional heat conduction in a medium with constant properties, $$T$$ is the temperature at position $$x,$$ at time $$t.$$ Then $${{\partial T} \over {\partial t}}...
A mould has a downsprue whose length is $$20$$ $$cm$$ and the cross sectional area at the base of the down sprue is $$1\,\,c{m^2}.$$ The down sprue feeds a horizontal runner leadin...
Which among the $$NC$$ operations given below are continuous path operations? Arc Welding $$(A$$ $$W)$$, Milling $$(M),$$ Drilling $$(D),$$ Punching in Sheet Metal $$(P)$$ Laser Cu...
Hot oil is cooled from $${80^ \circ }C$$ to $${50^ \circ }C$$ in an oil cooler which uses air as the coolant. The air temperature rises from $${30^ \circ }C$$ to $${40^ \circ }C$$....
The time variation of the position of a particle in rectilinear motion is given by $$x = 2{t^3} + {t^2} + 2t$$. If 'V' is the velocity and 'a' acceleration of the particle in consi...
$$A$$ is a $$3 \times 4$$ matrix and $$AX=B$$ is an inconsistent system of equations. The highest possible rank of $$A$$ is
Which one of the following is criterion in the design of hydrodynamic journal bearings?
Stokes theorem connects
Two books of mass 1 kg each are kept on a table, one over the other. The coefficient of friction on every pair of contacting surfaces is 0.3. the lower book is pulled with a horizo...
A solid cylinder (surface $$2$$) is located at the center of a hollow sphere (surface $$1$$). The diameter of the sphere is $$1m,$$ while the cylinder has a diameter and length of...
Starting from $$\,{x_0} = 1,\,\,$$ one step of Newton - Raphson method in solving the equation $${x^3} + 3x - 7 = 0$$ gives the next value $${x_1}$$ as
An un-insulated air conditioning duct of rectangular cross section $$1\,\,m \times 0.5\,m,$$ carrying air at $${20^ \circ }C$$ with a velocity of $$10 m/s,$$ is exposed to an ambie...
A venturimeter of $$20$$ $$mm$$ throat diameter is used to measure the velocity of water in a horizontal pipe of $$40$$ $$mm$$ diameter. If the pressure difference between the pipe...
A company has two factories $${S_1},$$ $${S_2}$$ and two warehouses $${D_1},$$ $${D_2}$$ . the supplies from $${S_1}$$ and $${S_2}$$ are $$50$$ and $$40$$ units respectively. Wareh...
A single die is thrown two times. What is the probability that the sum is neither $$8$$ nor $$9?$$
The tool of an $$NC$$ machine has to move along a circular arc from $$(5,5)$$ to $$(10,10)$$ while performing an operation. The center of the arc is at $$(10,5).$$ Which one of the...
A leaf is caught in a whirlpool. At a given instant, the leaf is at a distance of $$120$$ $$m$$ from the centre of the whirlpool. The whirlpool can be described by the following ve...
The sales of a product during the last four years were $$860, 880, 870$$ and $$890$$ units. The forecast for the fourth year was $$876$$ units. If the forecast for the fifth year,...
Which of the following is a solution of the differential equation $$\,{{{d^2}y} \over {d{x^2}}} + p{{dy} \over {dx}} + \left( {q + 1} \right)y = 0?$$ Where $$p=4, q=3$$
Two tools $$P$$ and $$Q$$ have signature $${5^ \circ } - {5^ \circ } - {6^ \circ } - {6^ \circ } - {8^ \circ } - {30^ \circ } - 0$$ and $${5^ \circ } - {5^ \circ } - {7^ \circ } -...
By a change of variables $$x(u, v) = uv,$$ $$\,\,y\left( {u,v} \right) = {v \over u}$$ in a double integral, the integral $$f(x, y)$$ changes to $$\,\,\,f\left( {uv,{\raise0.5ex\hb...
Which one of the following is an eigen vector of the matrix $$\left[ {\matrix{ 5 & 0 & 0 & 0 \cr 0 & 5 & 0 & 0 \cr 0 & 0 & 2 & 1 \cr 0 & 0 & 3 & 1 \cr } } \right]$$ is
Nitrogen at an initial state of $$10$$ bar, $$1{m^3}$$ and $$300$$ $$K$$ is expanded isothermally to a final volume of $$2{m^3}$$. The $$p$$-$$v$$-$$T$$ relation is $$\left( {p + {...
The velocity components in the $$x$$ and $$y$$ directions of a two dimensional potential flow are $$u$$ and $$v$$, respectively. Then $${{\partial u} \over {\partial y}}$$ is equal...
Spot welding of two $$1$$ $$mm$$ thick sheets of steel (density $$ = 8000kg/{m^3}$$ ) is carried out successfully by passing a certain amount of current for $$0.1$$ second through...
A small copper ball of $$5$$ $$mm$$ diameter at $$500$$ $$K$$ is dropped into an oil bath whose temperature is $$300$$ $$K.$$ the thermal conductivity of copper is $$400$$ $$W/m.$$...
$$\int\limits_{ - a}^a {\left[ {{{\sin }^6}\,x + {{\sin }^7}\,x} \right]dx} $$ is equal to
If $${x^2}\left( {{{d\,y} \over {d\,x}}} \right) + 2xy = {{2\ln x} \over x}$$ and $$y(1)=0$$ then what is $$y(e)$$?
An un-insulated air conditioning duct of rectangular cross section $$1\,\,m \times 0.5\,m,$$ carrying air at $${20^ \circ }C$$ with a velocity of $$10 m/s,$$ is exposed to an ambie...
Consider a linear programming problem with two variables and two constraints. The objective function is: Maximize $${x_1} + {x_2}.$$ The corner points of the feasible region are $$...
A project has six activities $$(A$$ to $$F)$$ with respective activity durations $$7,5,6,6,8,4$$ days. The network has three paths $$A-B,C-D$$ and $$E-F.$$ All the activities can b...
Consider a single server queuing model with Poisson arrivals $$\left( {\lambda = 4/hour} \right)$$ and exponential service $$\left( {\mu = 4/hour} \right)$$. The number in the syst...
The complete solution of the ordinary differential equation $${{{d^2}y} \over {d\,{x^2}}} + p{{dy} \over {dx}} + qy = 0$$ is $$\,y = {c_1}\,{e^{ - x}} + {C_2}\,{e^{ - 3x}}\,\,$$ th...
Consider a linear programming problem with two variables and two constraints. The objective function is: Maximize $${x_1} + {x_2}.$$ The corner points of the feasible region are $$...
A $$600$$ $$mm$$ $$ \times \,\,30\,\,mm$$ flat surface of a plate is to be finish machined on a shaper. The plate has been fixed with the $$600$$ $$mm$$ side along the tool travel...
Changing the order of integration in the double integral $${\rm I} = \int\limits_0^8 {\int\limits_{{\raise0.5ex\hbox{$\scriptstyle x$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\...
In order to have interference fit, it is essential that the lower limit of the shaft should be
A weighing machine consists of a 2 kg pan resting on a spring in this condition, with the pan resting on the spring, the length of the spring is 200 mm. When a mass of 20 kg is pla...
There are four samples P, Q, R and S, with natural frequencies 64, 96, 128 and 256 Hz, respectively. There are mounted on test setups for conducting vibration experiments. If a lou...
In a spring-mass system, the mass is 0.1 kg and the stiffness of the spring is 1 kN/m. By introducing a damper, the frequency of oscillation is found to be 90% of the original valu...