GATE ME 2014 Set 1

## GATE ME

Given that the determinant of the matrix $$\left[ {\matrix{
1 & 3 & 0 \cr
2 & 6 & 4 \cr
{ -

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Which one of the following describes the relationship among the three vectors, $$\widehat i + \widehat j + \widehat k,\

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$$\mathop {Lt}\limits_{x \to 0} {{x - \sin x} \over {1 - \cos x}}$$ is

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The integral $$\,\,\oint\limits_C {\left( {ydx - xdy} \right)\,\,} $$ is evaluated along the circle $${x^2} + {y^2} = {1

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In the following table, $$x$$ is a discrete random variable and $$p(x)$$ is the probability density. The standard devia

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The matrix form of the linear system $${{dx} \over {dt}} = 3x - 5y$$ and $$\,{{dy} \over {dt}} = 4x + 8y\,\,$$ is

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If $$\,y = f\left( x \right)\,\,$$ is the solution of $${{{d^2}y} \over {d{x^2}}} = 0$$ with the boundary conditions $

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Using the trapezoidal rule, and dividing the interval of integration into three equal sub-intervals, the definite integ

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The argument of the complex number $${{1 + i} \over {1 - i}},$$ where $$i = \sqrt { - 1} ,$$ is

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A circular object of radius r rolls without slipping on a horizontal level floor with the center having velocity $$V$. T

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A block weighing 200N is in contact with a level plane whose coefficients of static and kinetic friction are 0.4 and 0.2

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A block R of mass 100 kg is placed on a block S of mass 150 kg as shown in the figure. Block R is tied to the wall by a

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A rigid link PQ of length 2 m rotates about the pinned end Q with a constant angular acceleration of 12 rad/s2 . When th

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In a simple concentric shaft-bearing arrangement, the lubricant flows in the $$2$$ $$mm$$ gap between the shaft and the

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For a completely submerged body with center of gravity $$'G'$$ and center of buoyancy $$'B',$$ the condition of stabilit

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An ideal water jet with volume flow rate of $$0.05{m^3}/s$$ strikes a flat plane placed normal to its path and exerts a

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Water flows through a pipe having an inner radius of $$10$$ $$mm$$ at the rate of $$36$$ $$kg/hr$$ at $${25^ \circ }C$$.

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For a fully developed flow of water in a pipe having diameter $$10$$ $$cm,$$ velocity $$0.1$$ $$m/s$$ and kinematic visc

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Consider one dimensional steady state heat conduction across a wall (as shown in figure below) of thickness $$30$$ $$mm$

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The non-dimensional fluid temperature profile near the surface of a convectively cooled flat plate is given by $${{{T_w}

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In exponential smoothening method, which one of the following is true?

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The jobs arrive at a facility, for service, in a random manner. The probability distribution of number of arrivals of jo

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Jobs arrive at a facility at an average rate of $$5$$ in an $$8$$ hour shift. The arrival of the jobs follows Poisson di

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The state of stress at a point is given by $$\,\,{\sigma _x} = - 6\,MPa,\,\,{\sigma _y} = 4\,\,MPa,$$ and $${\tau _{xy}

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A pair of spur gears with module $$5$$ $$mm$$ and a center distance of $$450mm$$ is used for a speed reduction of $$5:1$

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A hydrodynamic journal bearing is subject to $$2000$$ $$N$$ load at a rotational speed of $$2000$$ $$rpm.$$ Both bearing

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An aluminium alloy (density $$2600$$ $$kg/{m^3}$$ ) casting is to be produced. A cylindrical hole of $$100$$ $$mm$$ diam

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A metal rod of initial length $${L_0}$$ is subjected to a drawing process. The length of the rod at any instant is given

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The major difficulty during welding of aluminium is due to its

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In solid-state welding, the contamination layers between the surfaces to be welded are removed by

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If the Taylor's tool life exponent $$n$$ is $$0.2,$$ and the tool changing time is $$1.5$$ $$min,$$ then the tool life (

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The main cutting force acting on a tool during the turning (orthogonal cutting) operation of a metal is $$400N.$$ The tu

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During pure orthogonal turning operation of a hollow cylindrical pipe, it is found that the thickness of the chip produc

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Which one of the following instruments is widely used to check and calibrate geometric features of machine tools during

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For machining a rectangular island represented by coordinates
$$P(0,0), Q(100,0), R(100,50)$$ and $$S(0,50)$$ on a cast

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For the given assembly : $$25$$ $$H7/g8,$$ match Group $$A$$ with Group $$B$$

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A metallic rod of $$500$$mm length and $$50$$mm diameter, when subjected to a tensile force of $$100$$kN at the ends, ex

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A circular rod of length $$‘L’$$ and area of cross-section $$‘A’$$ has a modulus of elasticity $$‘E’$$ and coefficient o

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A metallic rod of $$500$$mm length and $$50$$mm diameter, when subjected to a tensile force of $$100$$kN at the ends, ex

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Consider a cantilever beam, having negligible mass and uniform flexural rigidity, with length $$0.01m$$. The frequency

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A rigid uniform rod $$AB$$ of length $$L$$ and mass $$m$$ is hinged at $$C$$ such that $$AC = L/3, CB = 2L/3.$$ Ends $$A

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$$1.5$$ $$kg$$ of water is in saturated liquid state at $$2$$ bar
$$\left( {{v_f} = 0.001061\,\,{m^3}/kg,\,\,{u_f} = 50

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A reversible heat engine receives $$2$$ $$kJ$$ of heat from a reservoir at $$1000$$ $$K$$ and a certain amount of heat f

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The maximum theoretical work obtainable, when a system interacts to equilibrium with a reference environment, is called

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In a power plant, water (density $$ = 1000\,\,kg/{m^3}$$ ) is pumped from $$80$$ $$kPa$$ to $$3$$ $$MPa$$. The pump has

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An ideal reheat Rankine cycle operates between the pressure limits of $$10$$ $$kPa$$ and $$8$$ $$MPa,$$ with reheat bein

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