GATE ME 2014 Set 1

## GATE ME

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

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

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

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

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

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

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

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

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

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

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

View Question 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

View Question 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

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

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

View Question 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

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

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

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

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

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

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

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

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

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

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

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

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

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

View Question The major difficulty during welding of aluminium is due to its

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

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

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

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

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

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

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

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

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

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

View Question 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

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

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

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

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

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

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