GATE ME 2015 Set 1
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## GATE ME

If any two columns of a determinant $$P = \left| {\matrix{ 4 &amp; 7 &amp; 8 \cr 3 &amp; 1 &amp; 5 \cr 9 &a View Question Consider a spatial curve in three -dimensional space given in parametric form by$$\,\,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 $$V = \left( {{a_1}x + {a_2}y + {a_3}z} \right)i + \left( {{b_ View Question The probability of obtaining at least two$$'SIX'$$in throwing a fair dice$$4$$times is View Question Ram and Ramesh appeared in an interview for two vacancies in the same department. The probability of Ram's selection is View Question Among the four normal distributions with probability density functions as shown below, which one has the lowest variance View Question Find the solution of$${{{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 $$f\left( x \right) = {3 \over 5}{x^2} + {9 \over 5}\,\ View Question Given two complex numbers$${z_1} = 5 + \left( {5\sqrt 3 } \right)i$$and$${z_2} = {2 \over {\sqrt 3 }} + 2i,$$the arg View Question The Laplace Transform of$$f\left( t \right) = {e^{2t}}\sin \left( {5t} \right)\,u\left( t \right)$$is View Question Two identical trusses support a load of 100 N as shown in the figure. The length of each truss is 1.0m; cross-sectional View Question For the truss shown in figure, the magnitude of the force in member PR and the support reaction at R are respectively View Question A ball of mass 0.1 kg, initially at rest, is dropped from height of 1m. Ball hits the ground and bounces off the ground. View Question Match the following pairs: View Question The velocity field on an incompressible flow is given by$$V = \left( {{a_1}x + {a_2}y + {a_3}z} \right)i + \left( {{b_
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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: $$U\left( {r,x} \righ View Question Following data refers to the activities of a project, where, node$$1$$refers to the start and node$$5$$refers to the View Question For a canteen, the actual demand for disposable cups was$$500$$units in January and$$600$$units in February. The for View Question A machine element is subjected to the following bi-axial state of stress:$$\,\,{\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 $$\Delt View Question In a linear arc welding process, the heat input per unit length is inversely proportional to View Question A$$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 $${\left( {{1 \over {16}}} \right) View Question An orthogonal turning operation is carried out under the following conditions; rake angle$$ = {5^ \circ },$$spindle ro View Question Holes of diameter$${25.0^{\matrix{ { + 0.040} \cr { + 0.020} \cr } }}\,\,mm$$are assembled interchangeably View Question The function of interpolator in a$$CNC$$machine controller is to View Question In the assembly shown below, the part dimensions are:$$\eqalign{ &amp; {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, $View Question A cantilever beam with flexural rigidity of 200 N.m2 is loaded as shown in the figure. The deflection (in mm) at the tip View Question Consider a steel (Young’s modulus $$E = 200$$ $$GP$$a) column hinged on both sides. Its height is $$1.0$$ $$m$$ and cros View Question 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 View Question A pinion with radius $${r_1}$$, and inertia $${{\rm I}_1}$$ is driving a gear with radius $${r_2}$$ and inertia $${{\rm View Question Consider a slider crank mechanism with nonzero masses and inertia. A constant torque$$\tau $$is applied on the crank a View Question A precision instrument package (m = 1kg) needs to be mounted on a surface vibrating at 60 Hz. It is desired that only 5% View Question A mobile phone has a small motor with an eccentric mass used for vibrator mode. The location of the eccentric mass on mo View Question Considering massless rigid rod and small oscillations, the natural frequency (in rad/s) of vibration of the system shown View Question For an ideal gas with constant values of specific heats, for calculation of the specific enthalpy, View Question Temperature of nitrogen in a vessel of volume$$2{m^3}$$is$$288K.AU$$-tube manometer connected to the v View Question A well insulated rigid container of volume$$1{m^3}$$contains$$1.0kg$$of an ideal gas$$\left[ {{C_p} =1000\,\,\ View Question A Carnot engine $$(CE$$-$$1)$$ works between two temperature reservoirs $$A$$ and $$B,$$ where $${T_A} = 900K$$ and $${T View Question Steam enters a well insulated turbine and expands isentropically throughout. At an intermediate pressure,$$20$\$ percent
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