GATE ME 2015 Set 2

## GATE ME

At least one eigenvalue of a singular matrix is

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At $$x=0,$$ the function $$f\left( x \right) = \left| x \right|$$ has

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Curl of vector $$\,V\left( {x,y,x} \right) = 2{x^2}i + 3{z^2}j + {y^3}k\,\,$$ at $$x=y=z=1$$ is

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The surface integral $$\,\,\int {\int\limits_s {{1 \over \pi }} } \left( {9xi - 3yj} \right).n\,dS\,\,$$ over the spher

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The chance of a student passing an exam is $$20$$% The chance of a student passing the exam and getting above $$90$$% ma

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Consider the following differential equation $${{dy} \over {dt}} = - 5y;$$ initial condition: $$y=2$$ at $$t=0.$$
The

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The values of function $$(x)$$ at $$5$$ discrete points are given below:
Using Trapezodial rule with step size of $$0.

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Laplace transform of $$\cos \left( {\omega t} \right)$$ is

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The Laplace transform of $${e^{i5t}}$$ where $$i = \sqrt { - 1} ,$$

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A small ball of mass 1 kg moving with a velocity of 12 m/s undergoes a direct central impact with a stationary ball of m

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The initial velocity of an object is $$40$$ $$m/s.$$ The acceleration a of the object is given by the following expressi

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For the truss shown in the figure, the magnitude of the force (in kN) in the member SR is

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If the fluid velocity for a potential flow is given by $$V\left( {x,y} \right) = u\left( {x,y} \right)i + v\left( {x,y}

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For a fully developed laminar flow of water (dynamic viscosity $$0.001$$ $$Pa$$-s) through a pipe of radius $$5$$ $$cm,$

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The head loss for a laminar incompressible flow through a horizontal circular pipe is $${h_1}$$. Pipe length and fluid r

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Within a boundary layer for a steady incompressible flow, the Bernoulli equation

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If a foam insulation is added to a $$4cm$$ outer diameter pipe as shown as figure, the critical radius of insulation (i

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A cylindrical uranium fuel rod of radius 5 mm in a nuclear reactor is generating heat at the rate of $$4 \times {10^7}\,

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In the laminar flow of air $$(Pr=0.7)$$ over a heated plate, if $$\delta $$ and $${\delta _T}$$ denote, respectively the

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The total emissive power of a surface is $$500$$ $$W/{m^2}$$ at a temperature $${T_1}$$ and $$1200$$ $$W/{m^2}$$ at a
te

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A balanced counter-flow heat exchanger has a surface area of $$20\,\,{m^2}$$ and overall heat transfer coefficient of $$

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Annual demand of a product is $$50,000$$ units and the ordering cost is Rs. $$7,000$$ per order. Considering the basic e

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A project consists of $$7$$ activities. The network along with the time durations (in days) for various activities is sh

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Sales data of a product is given in the following table:
Regarding forecast for the month of June, which one of the f

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A manufacturer has the following data regarding a product:
Fixed cost per month $$=$$ Rs. $$50,000$$
Variable cost per u

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The uniaxial yield stress of a material is $$300$$ $$MPa.$$ According to Von mises criterion, the shear yield stress $$(

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A cube and a sphere made of cast iron (each of volume $$1000\,\,c{m^3}$$) were cast under identical conditions. The time

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The flowing stress (in $$MPa$$) of a material is given by $$\sigma = 500{\varepsilon ^{0.1}},$$
When $$\varepsilon $$

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In a two stage wire drawing operation, the fractional reduction (ratio of change in cross sectional area to initial cros

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During a $$TIG$$ welding process, the arc current and arc voltage were $$50$$ $$A$$ and $$60$$ $$V,$$ respectively, when

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A single point cutting tool with $${0^0}$$ rake angle is used in an orthogonal machining process. At a cutting speed of

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Which one of the following statements is TRUE?

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During the development of a product, an entirely new process plan is made based on design logic, examination of geometry

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A drill is positioned at point $$P$$ and it has to proceed to point $$Q.$$ The coordinates of point $$Q$$ in the increme

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A rod is subjected to an uniaxial load within linear elastic limit. When the change in the stress is $$200$$ MPa, the ch

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In a plane stress condition, the components of stress at a point are $${\sigma _x} = 20$$ MPa, $${\sigma _y} = 80$$ MPa

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A cantilever beam OP is connected to another beam PQ with a pin joint as shown in figure. A load of $$10$$ kN is applied

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A hollow shaft (d0 = $$2$$di, where d0 and di are the outer and inner diameters respectively) needs to transmit $$20$$ k

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The deflection of a spring with 20 active turns under a load of 1000 N is 10 mm. The spring is made into two pieces each

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A rope brake dynamometer attached to the crank shaft of an $$I.C.$$ engine measures a brake power of $$10$$ kW when the

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A hollow shaft of $$1$$ m length is designed to transmit a power of $$30$$ kW at $$700$$ rpm. The maximum permissible an

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A cantilever beam with square cross-section of 6 mm side is subjected to a load of 2kN normal to the top surface as show

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A gas is stored in a cylindrical tank of inner radius $$7$$ m and wall thickness $$50$$ mm. The gage pressure of the gas

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The number of degrees of freedom of the planetary gear train shown in the figure is

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In a certain slider-crank mechanism, lengths of crank and connecting rod are equal. If the crank rotates with a uniform

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In a spring-mass system the mass is m and the spring constant is $$k$$. The critical damping coefficient of the system i

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A single-degree-freedom spring mass system is subjected to a sinusoidal force of $$10$$ N amplitude and frequency $$\ome

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The Vander-waals equation of state is $$\left( {p + {a \over {{v^2}}}} \right)\left( {v - b} \right) = RT,$$ where $$p$$

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Work is done on an adiabatic system due to which its velocity changes from $$10$$ $$m/s$$ to $$20$$ $$m/s,$$ elevation i

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The $$COP$$ of a Carnot heat pump operating between $${6^ \circ }C$$ and $${37^ \circ }C$$ is ____________

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One kg of air ($${R = 287\,\,J/kg}$$-$$K$$) under goes irreversible process between equilibrium state $$1\,\,\left( {{{2

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Which of the following statements regarding a Rankine cycle with reheating are TRUE?
(i) increase in average temperature

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In a Rankine cycle, the enthalpies at turbine entry and outlet are $$3159$$ $$kJ/kg$$ and $$2187$$ $$kJ/kg$$ respectivel

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