GATE ME 2015 Set 1

## GATE ME

If any two columns of a determinant $$P = \left| {\matrix{
4 & 7 & 8 \cr
3 & 1 & 5 \cr
9 &a

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Consider a spatial curve in three -dimensional space given in parametric form by $$\,\,x\left( t \right)\,\, = \,\,\cos

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The value of $$\mathop {Lim}\limits_{x \to 0} \,{{1 - \cos \left( {{x^2}} \right)} \over {2{x^4}}}$$ is

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Consider an ant crawling along the curve $$\,{\left( {x - 2} \right)^2} + {y^2} = 4,$$ where $$x$$ and $$y$$ are in mete

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The velocity field on an incompressible flow is given by
$$V = \left( {{a_1}x + {a_2}y + {a_3}z} \right)i + \left( {{b_

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The probability of obtaining at least two $$'SIX'$$ in throwing a fair dice $$4$$ times is

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Ram and Ramesh appeared in an interview for two vacancies in the same department. The probability of Ram's selection is

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Among the four normal distributions with probability density functions as shown below, which one has the lowest variance

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Find the solution of $${{{d^2}y} \over {d{x^2}}} = y$$ which passes through origin and the point $$\left( {ln2,{3 \over

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Simpson's $${1 \over 3}$$ rule is used to integrate the function $$f\left( x \right) = {3 \over 5}{x^2} + {9 \over 5}\,\

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Given two complex numbers $${z_1} = 5 + \left( {5\sqrt 3 } \right)i$$ and $${z_2} = {2 \over {\sqrt 3 }} + 2i,$$ the arg

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The Laplace Transform of $$f\left( t \right) = {e^{2t}}\sin \left( {5t} \right)\,u\left( t \right)$$ is

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Two identical trusses support a load of 100 N as shown in the figure. The length of each truss is 1.0m; cross-sectional

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For the truss shown in figure, the magnitude of the force in member PR and the support reaction at R are respectively

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A ball of mass 0.1 kg, initially at rest, is dropped from height of 1m. Ball hits the ground and bounces off the ground.

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The velocity field on an incompressible flow is given by
$$V = \left( {{a_1}x + {a_2}y + {a_3}z} \right)i + \left( {{b_

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Match the following pairs:

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Water $$\left( {\rho = 1000kg/{m^3}} \right)$$ flows through a venturimeter with inlet diameter $$80$$ $$mm$$ and throa

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Consider fully developed flow in a circular pipe with negligible entrance length effects. Assuming the mass flow rate, d

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Air ( $${\rho = 1.2\,\,kg/{m^3}}$$ and kinematic viscosity, $${v = 2 \times {{10}^{ - 5}}{m^2}/s}$$ ) with a velocity o

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A $$10$$ $$mm$$ diameter electrical conductor is covered by an insulation of $$2$$ $$mm$$ thickness. The conductivity of

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The Blasius equation related to boundary layer theory is a

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For flow of viscous fluid over a flat plate, if the fluid temperature is the same as the plate temperature, the thermal

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For flow through a pipe of radius $$R,$$ the velocity and temperature distribution are as follows:
$$U\left( {r,x} \righ

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Following data refers to the activities of a project, where, node $$1$$ refers to the start and node $$5$$ refers to the

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For a canteen, the actual demand for disposable cups was $$500$$ units in January and $$600$$ units in February. The for

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A machine element is subjected to the following bi-axial state of stress: $$\,\,{\sigma _x} = 80MPa;\,\,{\sigma _y} = 20

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Which one of the following is the most conservative fatigue failure criterion?

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A horizontal plate has been joined to a vertical post using four rivets arranged as shown in the figure. The magnitude o

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The solidification time of a casting is proportional to $${\left( {{V \over A}} \right)^2},$$ Where $$V$$ is the volume

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Match the following products with preferred manufacturing process:

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In a slab rolling operation, the maximum thickness reduction $$\left( {\Delta {h_{\max }}} \right)$$ is given by $$\Delt

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In a linear arc welding process, the heat input per unit length is inversely proportional to

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A $$DC$$ welding power source has a linear voltage-current $$(V$$-$$I)$$ characteristic with open circuit voltage of $$8

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Under certain cutting conditions, doubling the cutting speed reduces the tool life to $${\left( {{1 \over {16}}} \right)

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An orthogonal turning operation is carried out under the following conditions; rake angle $$ = {5^ \circ },$$ spindle ro

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Holes of diameter $${25.0^{\matrix{
{ + 0.040} \cr
{ + 0.020} \cr
} }}\,\,mm$$ are assembled interchangeably

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The function of interpolator in a $$CNC$$ machine controller is to

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In the assembly shown below, the part dimensions are:
$$\eqalign{
& {L_1} = {22.0^{ \pm 0.01}}\,\,mm, \cr
&am

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A triangular facet in a $$CAD$$ model has vertices: $${P_1}\left( {0,0,0} \right);\,\,{P_2}\left( {1,1,0} \right)$$ and

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Consider a stepped shaft subjected to a twisting moment applied at $$B$$ as shown in the figure. Assume shear modulus, $

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A cantilever beam with flexural rigidity of 200 N.m2 is loaded as shown in the figure. The deflection (in mm) at the tip

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Consider a steel (Young’s modulus $$E = 200$$ $$GP$$a) column hinged on both sides. Its height is $$1.0$$ $$m$$ and cros

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A wheel of radius r rolls without slipping on a horizontal surface shown below. If the velocity of point P is 10m/s in t

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A pinion with radius $${r_1}$$, and inertia $${{\rm I}_1}$$ is driving a gear with radius $${r_2}$$ and inertia $${{\rm

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Consider a slider crank mechanism with nonzero masses and inertia. A constant torque $$\tau $$ is applied on the crank a

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A mobile phone has a small motor with an eccentric mass used for vibrator mode. The location of the eccentric mass on mo

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A precision instrument package (m = 1kg) needs to be mounted on a surface vibrating at 60 Hz. It is desired that only 5%

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Considering massless rigid rod and small oscillations, the natural frequency (in rad/s) of vibration of the system shown

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For an ideal gas with constant values of specific heats, for calculation of the specific enthalpy,

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Temperature of nitrogen in a vessel of volume $$2{m^3}$$ is $$288$$ $$K.$$ $$A$$ $$U$$-tube manometer connected to the v

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A well insulated rigid container of volume $$1{m^3}$$ contains $$1.0$$ $$kg$$ of an ideal gas $$\left[ {{C_p} =1000\,\,\

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A Carnot engine $$(CE$$-$$1)$$ works between two temperature reservoirs $$A$$ and $$B,$$ where $${T_A} = 900K$$ and $${T

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Steam enters a well insulated turbine and expands isentropically throughout. At an intermediate pressure, $$20$$ percent

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